## Achievement First Mathematics

##### v1.5
###### Usability
Our Review Process

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## Report for Kindergarten

### Overall Summary

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

### Focus & Coherence

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Above-grade-level assessment questions are present but could be modified or omitted without a significant impact on the underlying structure of the materials.

The series is divided into nine units, and each unit contains a Unit Assessment available online in the Unit Overview document and can also be printed for students. The Unit Assessments contain written and interview questions. Some units contain suggestions for use of Post-Unit Assessment questions as Pre-Unit Assessment questions. Teachers are directed to adjust instruction according to the Pre-Assessment results.

Examples of assessment questions aligned to grade-level standards include:

• Unit 2, Geometry Interview Questions, Task 1, “Put a triangle above a square and ask, ‘Where is the triangle in relation to the square?’” (K.G.1)

• Unit 5, Counting & Comparing Unit 5 Assessment, Question 2, “Look at the slices of pizza, (picture of five slices of pizza). Circle the group of ice cream cones that has more than the slices of pizza, (picture of one group of eight ice cream cones and another picture of six ice cream cones).” (K.CC.6)

• Unit 6, Counting Unit 6 Assessment, Question 9, “There were 10 cupcakes on the table. Jamaine ate 4 cupcakes. How many cupcakes are on the table now?” (K.OA.2)

• Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 3, “Draw a picture and write a number sentence to show 17 as tens and ones.” (K.NBT.1)

There are examples of above-grade-level assessment questions. In Unit 8, four of the seven questions assess above-grade-level content. The Guide to Implementing AF Math: Grade K, “Teachers should remove these items or use them for extension purposes only.” For example:

• Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 4, “How many tens are in the number 37? A. 3 B. 37 C. 7 D. 73.” The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value.

• Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 5, “Keisha drew sticks and dots to show how many blocks she had. How many blocks does Keisha have? A. 34 B. 7 C. 43 D. 44.” A picture representing 43 is between the question and answers. The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value.

• Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 6, “Gloria wants to draw a picture to represent the number 26 as tens and ones. What could she draw to show the number 26 as tens and ones?” The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value.

• Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 7, “Use sticks and dots to show 42.” The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value.

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each unit consists of lessons that are broken into four components: Introduction, Workshop/ Discussion, Independent Practice, and Exit Ticket. In addition to lessons, there are Math Stories “to enable students to make connections, identify and practice representation and calculation strategies, and develop deep conceptual understanding through the introduction of a specific story problem type in a clear and focused fashion with deliberate questioning and independent work time,” and Math Practice (Practice Workbook) for students “to build procedural skill and fluency.” Examples include:

• Unit 2, Lesson 4, Introduction and Workshop Resources, students describe objects in the environment using names of shapes and describe the relative positions of these objects using terms (K.G.1). Students play a game called “Where is my Shape?” where they pick a card that tells them to draw a shape above, below, beside, in front of, behind, and next to a picture of a Ninja Turtle. The full intent of the standard is met as all relevant positional words are included in this lesson. Practice Workbook B includes five problems that address K.G.1.

• Unit 2, Lesson 6, Exit Ticket, students engage with K.G.6 as they compose 2D shapes out of other 2D shapes by noticing their attributes. Students are provided with eleven exit tickets to independently practice the standard. “Jordan filled his hexagon using all triangles yesterday. Today he started using triangles but then ran out. How can he finish his puzzle? Circle the shape that would fit.” Students are given a picture of a hexagon with three triangles inside forming a trapezoid. They are then provided with three multiple choice items with shape pictures: A. trapezoid B. square C. oval.

• Unit 3, Lesson 1, Introduction and Workshop, students engage with K.CC.3 as they count objects and represent them with the written numerals 0-20. This is one of fifty lessons addressing this standard. As a result, the full intent of the standard is met for all students as this lesson focuses on students counting objects up to 15 and writing the corresponding numeral, prior lessons focused on up to five objects, then up to ten objects, and future lessons go up to 20 objects. Students are provided with extensive work on K.CC.3 through introduction activities, games, workshop time, and independent practice time. Lesson 1, Introduce the Math, “We are now experts at counting and writing numbers up to 10! Over the next few days we are going to be working with bigger numbers, up to 15. Let’s count to 15 together. Today, we are going to keep practicing counting by playing Counting Bags/Jars.” In the game Counting Jar, students are directed to count objects and write the corresponding numeral. The directions for the game are to “1. Take 1 bag; 2. How many? (move and count/organize and count); 3. Record.”

• Unit 6, students engage with K.OA.2 in 22 lessons. Lesson 6, Exit Slip, students solve addition and subtraction word problems. “Freddy had 6 books on his bookshelf at home. He went to the library and got 4 more books. How many books does he have now?”

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

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When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of units devoted to major work of the grade, including assessments and supporting work connected to the major work, is 6 out of 9, which is approximately 67%.

• The number of lessons devoted to major work of the grade, including assessments and supporting work connected to the major work, is approximately 124 out of 163, which is approximately 76%.

• The instructional block includes a math lesson, math stories, and math practice components. The non-major component minutes were deducted from the total instructional minutes resulting in 9,420 major work minutes out of 13,855 total instructional minutes. As a result of dividing the major work minutes by the total minutes, approximately 68% of the materials focus on major work of the grade.

A minute-level analysis is most representative of the materials because the minutes consider all components included during math instructional time. As a result, approximately 68% of the materials focus on major work of the grade.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work within the lesson plan in the “Standards in Lesson” section, as well as in the Guide to Implementing AF Math: Grade K. Additional connections exist within the materials, although not always stated by the publisher. In addition, the publisher identifies the CCSSM clusters at the top of each lesson plan. However, in some cases, supporting clusters are misidentified as major clusters. For example, in Unit 2, Lesson 3, the publisher incorrectly identifies the Geometry Clusters as the major work of the grade. Examples of the connections between supporting work and major work include:

• Unit 1, Lesson 5, Introduction, students engage with the supporting work of K.MD.3, classify objects into categories, and the major work of K.CC.5, count to answer “how many” questions. In Step 4, students sort pattern blocks by shape, then answer, “How Many? We need to figure out how many are in each group.”

• Unit 2, Lesson 3, Exit Ticket, students engage with the supporting work of K.G.2, correctly name shapes, K.G.5, model shapes in the world by building shapes from components, and the major work of K.CC.5, count to answer “how many” questions. Students count sides and vertices and build them using geoboards. Problem 3 states, “Circle the shape that has 4 corners.” Students are shown pictures of a hexagon, a circle, a triangle, and a square.

• Unit 2, Lesson 12, Understand: Introduce the Problem, students engage with the supporting work of K.G.4, analyze and compare two-dimensional shapes, and the major work of K.OA.2, solve addition word problems. Students are asked to visualize the shapes being mentioned. The teacher says, “Get ready to make a mind movie! Close your eyes and turn on your ears!” The teacher poses the problem by reading it 2-3 times, “Noah has three shapes. Noah has one square. Noah has one rectangle. Noah has one triangle. Noah counts all the corners of each shape. How many corners does Noah count all together? Show and tell how you know.” After the problem is read, students create a drawing of the three shapes based on their knowledge of their attributes. They then count the corners to add them, and represent the addition with an equation. In this lesson K.G.4 is the only standard identified, not K.OA.2.

• Unit 4, Lesson 5, Introduction, students engage with supporting work of K.MD.2, compare two objects to see which holds “more of”/”less of” the attribute, and the major work of K.CC.6, count to determine which group holds more. Students play a game called “Which holds more?” where they compare two objects and determine which holds more scoops of rice. The teacher asks, “How can we figure out which object has a larger capacity or holds more?” Students might say, “We can put in scoops of rice and count each to compare.”

• Unit 9, Lesson 5, Workshop engages with the supporting work of K.MD.3, classify objects into categories, count the number of objects in each category, and sort the categories by count; and the major work of K.OA.3, compose and decompose numbers less than or equal to 10 in more than one way while finding multiple combinations of 10 pink and blue beads to make groups of 10. Workshop worksheet, “Introduction: Linda has pink beads and blue beads. Linda has some bags. Linda wants to put 10 beads in each bag. Some must be pink and some must be blue. How many different ways can Linda put pink beads and blue beads in bags? Show all of your mathematical thinking.”

• Kindergarten Practice Workbook A, students engage with the supporting work of K.MD.3, classify objects into given categories, and the major work of K.CC.5, count the number of objects to answer “How many?” Problem 1, “Color each group of 3.” The directions are followed by a picture of three rectangles, five triangles, three circles, and four squares.

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Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The publisher identifies the CCSSM Clusters at the top of each lesson plan. However, in some cases, supporting clusters are misidentified as major clusters. For example, in Unit 2, Lesson 8, the publisher incorrectly identifies the Geometry clusters as the major work of the grade. Examples of connections include:

• Unit 3, Lesson 24, Exit Ticket, students engage with K.CC.B, count to tell the number of objects, and K.NBT.A, work with numbers 11-19 to gain foundations for place value, as they count a number represented in two ten frames. Problem 1 shows two tens frames with ten and six ones, “How many are there?”

• Unit 2, Lesson 8, Workshop, Student Workshop Worksheet students engage with K.G.A, identify and describe shapes, and K.G.B, analyze, compare, create, and compose shapes, as they match the faces of 3D solids to 2D shapes. “Makkelle had a can of soup. She wanted to put a label on it that would cover the whole top face. What shape would the label be? A. (insert a picture of a rectangle) B. (insert a picture of a circle) C. (insert a picture of a triangle).” Students are provided with a cylinder to represent the can of soup.

• Unit 8, Lesson 7, Workshop, Exit Ticket, students engage with K.NBT.A, work with numbers 11-19 to gain foundations for place value, and K.OA.A, understand addition as putting together and adding to, and understand subtraction as taking apart and taking from, as they make drawings to decompose teen numbers into ten ones, and some more ones. Problem 1, “Write a number sentence to show the number 13 as a group of ten ones and some more ones.”

• Practice Workbook B, students engage with K.G.A, identify and describe shapes, and, although not stated, K.G.B, analyze, compare, create, and compose shapes, as they draw shapes in relation to one another. Problem 2, “Look at the star. Draw a circle below the star. Draw a triangle above the star. Draw a rectangle next to the star.”

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Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The Unit Overview supports the progression of Kindergarten standards by explicitly stating connections between prior grades and current grade level work. Each Unit Overview contains an Identify the Narrative component that identifies connections to what students learned before entering school and concepts previously learned in Kindergarten.

Each Unit Overview also contains an Identify Desired Results: Identify the Standards section that makes connections to supporting standards learned prior to the unit. In addition, some lessons make connections to previous grade-level learning in the Narrative section. Examples include:

• Unit 2, Geometry Unit Overview, Identify the Narrative, “Coming into this unit, students use the informal language of their everyday world to name and describe flat shapes (rectangle, triangle, square, circle, hexagon) without yet using mathematical concepts and the vocabulary of geometry. At this stage, a figure is a square because it looks like a book; another figure is a circle because it is round like the wheel of a car. Students make these observations without explicitly thinking about the attributes or properties of squares and circles.”

• Unit 3, Counting Unit Overview, Identify the Narrative, “Up to this point in K, students have worked intensively within 10. They have counted sets of objects and pictures and written numerals up to 10. This unit will help students build on their knowledge of numbers within 10 and extend it to larger quantities.”

• Unit 4, Measurement Unit Overview, Identify the Narrative, “After two units of counting (students can now count groups and record numbers to 20), and one unit of Geometry where students observed, analyzed, composed, decomposed and classified objects by shape, students now compare and analyze length, weight, capacity. This unit supports students’ understanding of amounts and their developing number sense.”

• Unit 5, Counting and Comparing Unit Overview, Identify The Narrative, “Lessons 10-12 ask students to write out hundreds charts to 100. This relates back to the pattern between and within the decades that students discovered in Unit 3. The kindergarten standard is to orally count to 100, while writing numbers to 100 is a first grade standard. In Kindergarten students must be able to orally count to 100 and write numerals up to 20. When doing the hundreds chart activities, point students toward appropriate resources in order to master the writing of numbers to 100 while allowing ample time for students to practice counting their strips and hundreds charts aloud.”

• Unit 6, Addition and Subtraction Unit Overview, Identify Desired Results: Identify the Standards, K.OA.1, K.OA.2, and K.OA.3 (all are addition and subtraction standards) are identified as the standards to be learned in Unit 6. The previous kindergarten standards identified as foundational are counting standards, K.CC.1, K.CC.2, K.CC.4, K.CC.5, K.CC.6, and K.CC.7.

• Unit 8, Two-Digit Numbers Unit Overview, Identify Desired Results: Identify the Standards, K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones) is identified as one of the standards to be learned in Unit 8. The previous kindergarten standards identified as foundational are the counting standards (K.CC.1, K.CC.2, K.CC.3, K.CC.4) and K.OA.1 (Represent addition and subtraction).

The Unit Overview documents contain an Identify the Narrative component that looks ahead to content taught in future grades. In addition, the Linking section includes connections taught in future grades, units, or lessons. Evidence of future grade-level work supporting the progressions in the Standards is identified. Examples include:

• Unit 1, Sorting and Counting Unit Overview, Identify The Narrative, Linking, ”Looking ahead to the remainder of kindergarten, students will continue the counting sequence beyond 10 and up to 100. They will use the counting skills developed in this unit to develop strategies for addition and subtraction and to compose and decompose numbers within ten (K.OA.3) and into tens and ones, beginning with teen numbers (K.NBT.1) and then with all two-digit numbers (1.NBT.2). They will use their understanding of counting to compare sets (K.CC.6) and their place value understanding to compare two digit numbers. (1.NBT.3)”

• Unit 2, Geometry Unit Overview, Identify The Narrative, Linking, “Most importantly, it will help them access more complex geometrical standards in first grade in regard to distinguishing between defining attributes versus non-defining attributes, composing two-dimensional shapes to create a composite shape, creating new shapes from the composite shapes, and partitioning circles and rectangles. In second grade, students will need to draw shapes based on a given set of attributes; in third grade, students will focus on quadrilaterals and understand that a quadrilateral can also be categorized in a number of different ways; in fourth grade, students focus on points, line, ray, and parallel versus perpendicular lines.”

• Unit 5, Counting and Comparing Unit Overview, Identify the Narrative, Linking, “Students expand the counting sequence beyond 100 in first grade and begin to relate the way we say and write numbers to place value understanding.”

• Unit 8, Two-Digit Numbers Unit Overview, Identify The Narrative, Linking, “In first grade, students will use their understanding of place value to represent two-digit numbers in expanded notation and begin to add and subtract two-digit numbers.”

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In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The instructional materials reviewed for Achievement First Mathematics Kindergarten foster coherence between grades and can be completed within a regular school year with little to no modification.

The Guide to Implementing AF, Kindergarten includes a scope and sequence which states, “Not every lesson is entirely focused on grade level standards, and, therefore, some lessons can be used for either remediation or enrichment.” As designed, the instructional materials can be completed in 141 days. One day is provided for each lesson and one day is allotted for each unit assessment.

• Nine units with 155 lessons in total.

• The Guide to Implementing identifies lessons as either R (remediation), O (on grade level), or E (enrichment). There are 22 lessons identified as E (enrichment), 1 identified as R (remediation) and 132 identified as O (on grade level).

• Eight days for unit assessments. Unit 9 does not have a unit assessment.

The publisher recommends 85 minutes of mathematics instruction daily.

• There are two lesson types, Game Introduction Lesson or Task Based Lesson. Each lesson is designed for 45 minutes.

• Math stories are designed for 25 minutes.

• Calendar/practice is designed for 15 minutes.

### Rigor & the Mathematical Practices

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. The materials make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor and Balance

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately.

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Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Achievement First Mathematics Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials include problems and questions that develop conceptual understanding throughout the grade-level. Examples include:

• Unit 2, Lesson 5, Introduction, students engage with K.G.6, compose simple shapes to form larger shapes, as they complete puzzles using geometric shapes. “Step 1 says I’m going to pick a puzzle. Step 2 says I need to Decide what shape might fit. T & T: How can I make sure that happens? Strategy 1: Keep trying shapes until one fits the space. Strategy 2: Look at the space you are trying to fill. What shape might fit because of its attributes? Then find the shape that has the same attributes. Remember! You can flip and turn the pattern blocks. What shape do you think would fit? Why did you pick that shape?”

• Unit 3, Lesson 2, Introduction and Workshop, students engage with K.CC.4, demonstrate understanding of the relationship between numbers and quantities, as they play “Counting Bags/Jars.” Students count the number of pattern blocks in the bag and then show the same amount using cubes. During the Workshop the teacher asks students, “How do you know this is the same amount / how are you showing the same amount?”

• Unit 5, Lesson 6, Introduction, students engage with K.CC.6, identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, as they play a game called Compare. During the Introduction, two cards are drawn (example, 7 and 9) and students are asked to pictorially show which is more or less by drawing circles on their whiteboards. The teacher asks, “How do you know from the picture?” A sample student response might be, “I know because in the picture you can see that there are extra circles in the row of 9 and the row of 7 is missing some.”

• Unit 6, Lesson 3, Introduction, students engage with K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sound, acting out situations, verbal or equations, as the students complete a dice game while the teacher checks for understanding with questions leading the students to describe their thinking. Workshop, “Step 1: Roll 2 cubes; record their amounts. (“roll” a 4 and a 2) Show first cube: How many? 4 (record) Show second cube: How many? 4 (reccord) Show second cube: How many? (give time to count as needed) 2 (record) Lap 2: Conceptual: Which strategies are kids using? What misconceptions are arising? Check for Understanding: How did you solve? Why does that work? How does your equation match what you did?”

• Unit 8, Lesson 2, Workshop, students engage in K.NBT.1, compose and decompose numbers 11 to 19 into ten ones and some further ones, as students bundle objects into a group of ten and count on to determine the number of objects in a bag. The teacher is given suggestions for guiding the students to develop the concept of teen numbers. “What did you notice about the group of ten ones, loose ones and the way we write the numbers?”

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

• Unit 6, Lesson 10, Exit Slip, students engage with K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situation, verbal explanations, expression, or equations, as they find the difference between two numbers using manipulatives and represent with an equation. “Use your counters and tens frames to find the difference. Fill in the equation to show what you did.” Students are provided with the digits, 8 and 5, and given a blank equation to fill in.

• Unit 7, Lesson 6, Exit Slip, students engage with K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way, as they look at a picture of a rekenrek and find another equation that is equal/the same. Problem 1, “Look at the picture and equation in box 1. Use your teddies to write another equation that is equal/the same.” In box 1, there is a picture of a rekenrek with 4 on the top and 1 on the bottom and the matching equation, 4 + 1 = 5

• In Unit 8, Practice Workbook G, students engage with K.NBT.1, compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, as they independently draw pictures to show the decomposition of the number 18 into ten ones and 8 more ones. Problem 6, “Draw a picture to show 18 as ten ones and some more ones. Write a number sentence to match.”

• In Unit 9, Practice Workbook F, students engage with K.OA.4, by finding the number that makes 10 for any number 1 to 9 by using objects or drawings and recording the answer. Problem 3, “Draw circles and write a number to show how many more are needed to make 10.” Students are given 2, 4, 7, 6, 3, 1, 8, 9, and 5.

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Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials for Achievement First Mathematics Kindergarten meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. These skills are delivered throughout the materials in the use of games, workshop, practice workbook pages and independent practice, such as exit tickets.

The materials develop procedural skill and fluency throughout the grade-level. Examples include but are not limited to:

• Unit 3, Lesson 12, Workshop Worksheet, students engage with K.CC.5, count to answer “How many?” questions about 20 things arranged in a line, a rectangular array, or a circle, as they count 18 pieces of silverware arranged in a rectangular array. “Mr. Lohela was having a dinner party. He set out the silverware. How many pieces of silverware did he set out?”

• Unit 6, Lesson 19, Introduction, students engage with K.OA.5, fluently add and subtract within 5, as they represent a story problem. “Step 1: Visualize. Make a mind movie while I read. There were 7 carrot sticks on Hubina’s plate. She ate 3 of them. How many carrot sticks are on her plate? Step 2: Represent and Retell. Now you need to show the story. You can use your cubes or your whiteboard and marker; it’s up to you. Remember to include what we know and what we need to figure out. When you are done, put your whiteboard and cubes flat and be ready to explain how you represented and how it matches the story.”

• Unit 7, Practice Workbook E, Making 3, 4, and 5 finger Combinations, students engage with K.OA.5, fluently add and subtract within 5, as they play a game to develop fluency within 5. “The teacher uses different finger flashes and students determine how many fingers are needed to make a target sum.” Once students understand the game, they play with a partner.

• Unit 8, Practice Workbook E, students engage with K.OA.5, fluently adding and subtracting within 5, as they use fingers to calculate the missing addend. “Activity: Making 3, 4, and 5 Finger Combinations. T: I’ll show you some fingers. I want to make 3. Show me what is needed to make 3. (Show 2 fingers.) S: (Show 1 finger.)”

The materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level. Examples include but are not limited to:

• Unit 3, Practice Workbook C, students engage with K.CC.3, write numbers from 2 to 20, as they independently complete a number sequence filling in missing numbers from 10 -15. Problem 5, “Fill in the missing numbers, “10, 11, ____, ____, ____, ____.”

• Unit 6, Lesson 22, Assessment, students engage with K.OA.5, fluently adding and subtracting within 5, as they complete equations. Problem 5, “Solve. 2 + 3 = ___.”

• Unit 7, Lesson 8, Exit Slip, students engage with K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way, as they independently create equations with a sum of 10. “Show all of the ways you could make 10. (You may not need to fill in every equation.)” Blank equations equalling 10 follow the directions.

• Unit 8, Practice Workbook E, students engage with K.OA.5, fluently add and subtract within 5, as they independently solve a series of addition problems with a sum of 2-5. Problem 1, “$$3 + 2 =$$____”

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Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Students are given multiple opportunities to engage in real-world applications, especially during Math Stories, which include both guided questioning and independent work time, and Exit Tickets to independently show their understanding.

Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Examples include:

• Unit 2, Guide to Implementing AF Math, Math Stories, November, students engage with K.OA.2, solve addition and subtraction word problems, as they solve routine put-together/take apart-total unknown word problems. Sample Problem 1, “5 red crayons and 5 green crayons were in the basket. How many crayons were in the basket?”

• Unit 3, Guide to Implementing AF Math, Math Stories, January, students engage with K.G.5, drawing shapes, in a non-routine problem. Sample Problem 13, “Ms. Chen draws a square and a triangle on the board. How many sides did she draw?”

• Unit 3, Lesson 25, Understand: Introduce the Problem, students engage with K.CC.5, count to tell how many, in a non-routine word problem, “4 friends line up in a row. Every friend is wearing sneakers. How many sneakers are there lined up in a row? Show and tell how you know.”

• Unit 7, Lesson 9, Understand: Introduce the Problem, students engage with K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way, by following the story problem protocol and using an efficient strategy to find all of the solutions to a routine word problem. “The grocer got another size box! He now has a box that holds exactly 9 apples. He has red and green apples that he needs to put into the box. What are all of the ways he could put red and green apples into his box?”

Materials provide opportunities for students to independently demonstrate routine and non-routine applications of the mathematics throughout the grade level. Examples include:

• Unit 3, Lesson 6, Exit Ticket, students engage with K.CC.2, count forward beginning from a given number within the known sequence, as they use a routine counting on strategy to add numbers on two dice. Problem 1, “Use a strategy to find the total. Write the total on the line.” Students are shown dice with six and three dots, respectively.

• Unit 7, Lesson 5, Exit Ticket, students engage with K.OA.2, solve non-routine addition and subtraction word problems within 10, as students calculate take apart problems with both addends unknown. “There are 8 kids on the bunk bed. Show as many ways they can be arranged on the top and bottom as you can.” Nine blank equations are provided for students, “___ + ___ = 8.”

• Unit 8, Lesson 6, Exit Ticket, students engage with K.NBT.1, compose and decompose numbers 11-19, in a routine story problem. “Marco picked a card that looks like this (image of two ten frames-1 with 10 dots and 1 with 6 dots). How many? Write the number on the line.”

##### Indicator {{'2d' | indicatorName}}

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the program materials. Examples include:

Conceptual understanding

• Unit 3, Lesson 16, Exit Slip, students engage with K.CC.5, count to answer “how many” questions about as many as 20 things, as they represent a quantity 10 -20 pictorially by using a strategy to keep track of the count. The Exit Slip shows the number 16 with two blank ten frames. Students are expected to draw circles on the ten frame to represent 16.

• Unit 6, Lesson 11, Exit Ticket, students engage with K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sound, acting out situations, verbal or equations, as they represent and solve subtraction problems while using counters and tens frames. “Use your counters and tens frames to solve. 7 - 3 =____ and 9 - 5 = _____”

• Unit 9, Practice Workbook F, students engage with K.OA.3, decomposing numbers less than or equal to 10 into pairs in more than one way, as they draw pictures to show more than one way to make each number. Problem 4, “Draw a picture to show 2 ways to make each number. 6; 4; 7; 6; 3; 1; 8; 9; 5.”

Procedural skills (K-8) and fluency (K-6)

• Unit 6, Lesson 5, Exit Slip, students engage with K.OA.5, fluently add and subtract within 5, as they are given an image with two numbers to add them together, and a spot for an equation. “Cube 1 (6) Cube 2 (3) Equation _____ + _____= _____.”

• Unit 7, Practice Workbook E, Shake and Spill, students engage with K.OA.5, fluently add and subtract within 5, as they spill five two-sided counters in a cup to find combinations of 5. “The students determine how many of each color is showing and record the sum using drawings or equations. The students should ‘shake and spill’ several times to show different pairs of numbers that sum to 5.”

Unit 8, Practice Workbook E, students engage with K.OA.5, fluently adding and subtracting within 5, as they solve put together and take apart problems with the result unknown within 5. Problem 8, “$$2 + 2 =$$ ___.”

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Indicator {{'2e' | indicatorName}}

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The Standards for Mathematical Practice are identified and incorporated within mathematics content throughout the grade level. The Mathematical Practices are listed in the Unit Overviews as well at the beginning of each lesson.

There is intentional development of MP1 to meet its full intent in connection to grade-level content. Examples include:

• Unit 3, Lesson 25, Pose the Problem, students make sense of a real world situation. “4 friends line up in a row. Every friend is wearing sneakers. How many sneakers are there lined up in a row? Show and tell how you know.”

• Unit 5, Lesson 9, Understand: Introduce the Problem, students make sense of a comparison in quantity. “I’m going to read you a problem. As I read, I want you to make a mind movie just like we do in Math Stories to visualize what is happening and what we need to figure out. Toy Trucks: Hector has 6 toy trucks. Eric has 5 toy trucks. Hector says he has a greater amount of toy trucks than Eric. Is Hector correct? Show and tell how you know.”

• Unit 8, Lesson 8, Assessment and Criteria for Success delineates expectations that students make sense of a problem. “Students should represent the story by either drawing a picture or writing numbers to represent the beads. They can compare the quantities of beads using concrete/pictorial methods (one-to-one matching) or more abstract methods (number line, counting sequence) or they should be able to explain their representation and solution and connect it back to the problem. For example, ‘I wrote 10+5 because Tanya has ten beads and 5 beads. Then I wrote 10+3 because Marie has 10 beads and 3 beads. I know that 10+5 is 15 and 10 + 3 is 13. I just know that 15 is bigger than 13. So YES, Tanya is correct.’”

• Unit 9, Lesson 1, Narrative, “Students engage with MP1 as they work to interpret the problem, plan solution pathways, and monitor progress. Teachers give students ample time to initiate and execute a plan before intervening; when/ if they do intervene, they ask probing questions that support students in problem solving broadly.”

There is intentional development of MP2 to meet its full intent in connection to grade-level content. Examples include:

• Unit 6, Lesson 1, Narrative, “Teachers help students engage with MP2 when they ask students to reason about the relationships between the quantities as they add two parts to make a whole. Students recognize that the addition symbol means put together and use that to model that when they put two quantities that are parts together they make a quantity that is the sum of those parts, the whole.”

• Unit 7, Lesson 6, Narrative, “Students reason abstractly and quantitatively (MP 2) when they describe the relationship between ways to decompose the same total as equivalent: ‘I can decompose 8 into 5 + 3 and 4 + 4, so 5 + 3 is the same as 4 + 4 because both are ways to make 8.’”

• Unit 8, Lesson 3, Narrative, “By having students draw a picture to show the value of quantity along with writing an equation, teachers help them transition from quantitative to more abstract reasoning.”

• Unit 8, Lesson 13, Narrative, “Students engage with MP2 today as they reason about the value of the digits of two-digit numbers; by requiring students to represent the tens and ones with concrete objects and/or pictures, teachers help students to understand the meaning of quantities and to shift from quantitative to abstract reasoning about numbers and their values.”

##### Indicator {{'2f' | indicatorName}}

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP3 to meet its full intent in connection to grade-level content. Examples include:

• Unit 3, Lesson 18, Introduction, teachers are provided guidance in helping students to construct viable arguments demonstrating how to find the total of three numbers rolled on dot cubes. “Step 2 is for us to find out the total. When we did this before, we only had to figure out the total for two dot cubes. How would we do it for three dot cubes? SMS (student might say): It’s the same! It’s just more dots, so I can count them all. If a student says this, have a student come up and demonstrate touching each dot and counting and a student showing the amounts on fingers and counting all. SMS (student might say): I can just see (subitize) and say the number on one dot and count on from there. Have a student demonstrate.”

• Unit 4, Lesson 4, Share/Discussion, during Workshop, students are picking two objects and determining which is heavier or lighter using either a balance or hefting. “Facilitate a discussion around a major misconception (i.e. an object that is longer/taller doesn’t always have to be heavier). Show non-example and related example: Which is correct? Why doesn’t ___’s work? OR, 2-3 students share their work/strategies: How did ___ compare their objects? How did ___ compare their objects? What is the same about these strategies? What is different? Why do both work?”

• Unit 5, Lesson 3, Mid-Workshop Interruption, students determine which number is more and which is less by building towers or matching one to one. “If >$$\frac{2}{3}$$ of students are successful, ask students to describe the relationship between 2 towers (green 8 and blue 3) in a turn and talk. Hunt for a student who says one tower is more and another who says the other tower is less. Share their answers and ask who is right; students should see that both students are right- the green tower is more and the blue tower is less. Discuss how this is true; students should articulate that they are opposites and that if one tower is more the other will always be less and vice versa. Challenge students to circle the amount that is more as well one the recording sheets moving forward. If >\frac{2}{3} of students are successful, call students back together to clarify expectations through a misconception protocol or role play.”

• Unit 7, Lesson 1, Introduction, students name and record (with equations) various ways to decompose the totals four and five. During a demonstration, the teacher tosses three red chips and one yellow chip. “Step 2: What do you see? The purpose of this question is to get students to generate the numbers they will use in their number sentences; feel free to use the questions below to help: If students say, ‘I see 4 counters/chips,’ ask, ‘What colors do you see?’ If students say, ‘I see red and yellow,’ ask, ‘How many red do you see? How many yellow?’ If students say, ‘I see red and yellow,’ but don’t notice the total, ask, ‘How many do you see altogether/How many does that make altogether?’”

• Unit 7, Lesson 11, Introduction, Play Again and Check for Understanding, teachers are instructed to pose a fictional problem for the students to analyze. “Rather than playing a full game, pose this problem: Mr. Lynch was playing the game, and he drew a 3, so he recorded like this: 3 + ____ = 10 (show). Then when he went to show that many on his tens frame, he realized that he didn’t have any! They had all been cut in half for an art project. So he used just the top half, like this (Show the top row of the tens frame with 3 counters on it.). Then, he said, ‘How many to ten?’ and he counted the empty squares. 2! He wrote 3 + 2 = 10. Does this work? Why not? SMS (student might say) That is how many to 5, not ten. The tens frame works because it has 10 squares in all, so if we show how many we have we can count the empty squares to figure out how many to ten. There are not 10 squares in all.”

##### Indicator {{'2g' | indicatorName}}

Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP4 to meet its full intent in connection to grade-level content. Examples include:

• Math Stories Guide, Promoting Reasoning through the Standards for Mathematical Practice, MP4, “Math Stories help elementary students develop the tools that will be essential to modeling with mathematics. In early elementary, students become familiar with how representations like equations, manipulatives, and drawings can represent real-life situations.” Within the K-4 Math Stories Representations and Solutions Agenda, students are given time to represent, retell, and solve the problem on their own.

• Unit 6, Lesson 7, Introduction, Step 1, “There were 3 horses in the field. 4 more horses came out of the barn and into the field. How many horses are in the field now?” Step 2, “Now you need to show the story. You can use your cubes or your whiteboard and marker; it’s up to you. Remember to include what we know and what we need to figure out. When you are done, put your whiteboard and cubes flat and be ready to explain how you represented and how it matches the story.”

• Unit 9, Lesson 4, Task, “Beads in a Bowl: There are some beads in a bowl. The first friend takes 3 beads out of the bowl. The next friend takes 3 beads out of the bowl. The last friend takes 4 beads out of the bowl. There are no more beads in the bowl. How many beads were in the bowl? Show and tell how you know?” Narrative, “Students engage with MP4 as they use mathematical models to decontextualize the story. Students may represent pictorially or with equations, number bonds, or tape diagrams. Teachers also support the development of MP4 when they help students connect the models in the debrief and ask students which model is most useful for solving and why.”

There is intentional development of MP5 to meet its full intent in connection to grade-level content. Examples include:

• Unit 1, Lesson 15, Narrative, “Students engage with MP5 today as they are strategic about when they subitize and when they count to find the total. Teachers encourage students to be strategic and to consider the limitations of a strategy when he/she asks students why they are able to subitize a small amount but not a larger amount. In the workshop, teachers circulate and ask students which strategy they are using and why/why they are not using another strategy.”

• Unit 6, Lesson 12, Narrative, “Students engage with MP5 today when they choose from several strategies to represent and solve subtraction problems. Students can choose from any of the many strategies listed in the key points and have access to manipulatives, ten frames, whiteboards, and markers to use as tools. While there are target strategies for teachers to highlight, the class discusses multiple strategies and no strategy is preferred. The class relates different strategies to one another, noting that they ALL work for subtraction. By ensuring that students are choosing strategies themselves without teachers encouraging the use of a ‘preferred’ strategy, teachers help students to choose their own strategies and tools and explore their benefits and limitations.”

• Unit 7, Lesson 11, Narrative, “Teachers help students to develop MP5 today by making a variety of tools available to students. They can use counters or other manipulatives, a tens frame, or fingers as tools. They can also draw pictures or use known facts or counting strategies to solve.” Exit Ticket, “How Many to Ten? Use your counters/cubes and tens frames to help you. (1. 7 + __ = 10; 2. 4 + __ = 10).”

At times, the materials are inconsistent. The Unit and Lesson Overview narratives describe explicit connections between the MPs and content, but lessons do not always align to the stated purpose.

The materials do not provide students with opportunities or guidance to identify and use relevant external mathematical tools and resources, such as digital content located on a website.

##### Indicator {{'2h' | indicatorName}}

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP6 to meet its full intent in connection to grade-level content. Many problems present students with the opportunity to attend to precision within the mathematics and the reasoning of the answer. Examples include:

• Unit 4, Lesson 7, Introduction, students are prompted to use sentence frames for precision to compare the capacity of two containers. “Which one held more rice? The _______ held more rice than the _______. I know because it held _____ scoops of rice and the _____ held ______ scoops of rice. Be sure to prompt for accurate comparative language.”

• Unit 1, Lesson 12, Introduction, Narrative, students play a game with a partner where they have to count cubes that have been placed on an image of a donut. “Students engage with MP6 as they use a strategy that ensure that they count each object exactly once, which is particularly challenging today as the objects are arranged in a circle. By helping students keep track of the count and by emphasizing the importance of doing so, teachers help students to attend to precision and to value that practice.”

• Unit 5, Lesson 12, Assessment and Criteria for Success, students use precision to count to 100. “Students should put the Fruit Loops down on their hundreds chart and count orally to 100. Students should put each Fruit Loop onto a string (that is taped to the desk) and count orally as they put each Fruit Loop on the string. Once students finish their necklace, they should double check and count each Fruit Loop to make sure they have exactly 100 Fruit Loops on their necklace.”

The instructional materials attend to the specialized language of mathematics. The materials use precise and accurate mathematical terminology. Examples include:

• Unit 2, Lesson 9, Narrative, “Students engage with MP6 throughout the lesson as they use precise vocabulary to describe 2d and 3d shapes and their attributes. During the Introduction, students hunt around the room for 2D and 3D shapes. 'T&T: How could I know when I’ve found a shape?’ Students might say, ‘Look for the shapes that have the square/circle faces that you are looking for! You can also look for pointy vertices and/or the rounded or straight edges.’”

• Unit 4, Lesson 1, Introduction, Introduce the Math, “Today we’ll figure out how long (kinesthetic: make arms wide horizontally) or tall (kinesthetic: make arms wide vertically) things are by comparing two objects. That’s called length...When we are talking about how long or how tall things are, they can be LONGER (longer-choral response and motion: start with hands together and move apart) or SHORTER (shorter-choral response and motion: start with hands apart and move together).”

• Unit 5, Lesson 1, Assessment and Criteria for Success, students use the terms more, greater, the same, and equal to describe sets of objects. Questions are provided for teachers to support students in the use of these terms. “Teachers should circulate during workshop to gather data on student mastery. All students should be able to use the words, ‘more,’ ’greater,’ ‘the same,’ and ‘equal’ to describe their sets. Teachers should ask: 1. Which is more/has a greater amount of cubes? How do you know? 2. How can you describe this tower? (pointing to a tower that is more). 3. How can you describe these towers? (showing two towers that are the same).”

##### Indicator {{'2i' | indicatorName}}

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP7 to meet its full intent in connection to grade-level content. Examples Include:

• Unit 2, Lesson 5, Narrative, “Students engage with MP 7 when they look at a composite shape and decompose it into smaller shapes using the structure of the shapes to help them.”

• Unit 5, Lesson 10, Introduction, students engage with MP7 as they fill in a hundreds chart. “Fill in your hundreds chart. You will each get a blank chart like this one. You will count to yourself in a whisper voice and fill in the numbers. Today, we are starting with zero so I will write zero here (model writing zero off to the side before the first box). What comes next? I notice on your hundreds chart the numbers go across like this, so I will write 1 here. Now I’ll keep counting and writing the numbers (model up to 10).”

• Unit 8, Lesson 2, Introduction, Step 4, “What do you notice about the group of ten ones and loose ones and how we write the number? SMS (student might say): I notice that there is 1 group of ten ones and so there’s a one right there. Then there’s 4 loose ones so there’s a 4 right here.” The teacher replies, “Yes, this is called the tens place. There is the digit 1 here to show 1 group of ten ones. This is called the ones place. There’s the digit 4 here to show 4 loose ones.”

There is intentional development of MP8 to meet its full intent in connection to grade-level content. Examples Include:

• Unit 3, Lesson 23, Narrative, “Students look for and express regularity in repeated reasoning (MP 8) when they articulate that each number we say is one more than the one before and when they generalize that understanding in order to find one more than numbers beyond 20. Extension, “Play one more within a greater magnitude with cards from 20-50 (We know how to count to 50 now, so let’s try playing this game with some really big numbers!!!) Why does this work with all numbers?”

• Unit 5, Lesson 1, Narrative, “Teachers help students to use repeated reasoning (MP 8) to generalize how they can compare a set by prompting them to build towers and compare their lengths.”

• Unit 7, Lesson 8, Introduction, “(Show representation on recording sheet) How does this representation match the story? It shows that there are 10 apples in each box and that some are red and some are green. It shows that we need to figure out all of the ways we could fill the boxes with some red and some green. (Make sure students understand that each ‘Row’ or ‘rectangle’ represents a box.)” Mid-Workshop Interruption, “Which starting combination helped us find more solutions? 1 + 9. Why does that help us find all of the solutions? It is the smallest possible amount of [red or green] apples and the largest possible amount of [opposite color] apples. Then we add one [red or green] apple at a time and take away one [opposite color] apple at a time until we have the largest possible amount of [red or green apples] and the smallest possible amount of [opposite color] apples, so we know we have found all of the solutions.”

### Usability

The materials reviewed for Achievement First Mathematics Kindergaten do not meet expectations for Usability. The materials partially meet expectations for Criterion 1, Teacher Supports, partially meet expectations for Criterion 2, Assessment, and do not meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Does Not Meet Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials, include standards correlation information that explains the role of the standards in the context of the overall series, and provide a comprehensive list of supplies needed to support instructional activities. The materials contain adult-level explanations and examples of the more complex grade-level concepts, but do not contain adult-level explanations and examples and concepts beyond the current grade so that teachers can improve their own knowledge of the subject. The materials provide explanations of the instructional approaches of the program but do not contain identification of the research-based strategies.

##### Indicator {{'3a' | indicatorName}}

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. Teacher guidance is found throughout the materials in the Implementations Guides, Unit Overviews, and individual lessons.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• The Guide to Implementing AF Math provides a Program Overview for the teacher with information on the program components and scope and sequence. This includes descriptions of the types of lessons, Math Stories, Math Practice, and Cumulative Review.

• The Math Stories Guide (K-4) provides a framework for problem solving.

• Each Unit Overview includes a section called “Key Strategies” that describes strategies that will be utilized during the unit.

• The Teacher’s Guide supports whole group/partner discussion, ask/listen fors, common misconceptions and errors.

• In the narrative information for each lesson, there is information such as “What do students have to get better at today? Where will time be focused/funneled?”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Each lesson includes anticipated challenges, misconceptions, key points, sample dialogue, and exemplar student responses. Examples from Unit 3, Counting, Lesson 13 include:

• “What is new and/or hard about the lesson? This is the first lesson in which students create equivalent sets of greater than 15. Students who used matching one-to-one to create equivalent sets within 10 or 15 will find that this strategy is inefficient and prone to error with larger numbers. They will discover that counting out a set is a more reliable strategy. Today’s lesson requires students to keep track of information and the count – they must keep track as they count the first set, remember that total as they determine how to record it with a numeral, and then keep track of the count as they count out another set of that many, all the while applying the 1:1 and cardinal principles to ensure accuracy.”

• “Exemplar Student Response: “I used [move and count/ touch and count/ organize and count]. I [moved/ touched/ lined up and touched] each object as I counted it, and the last number I said was [x], so there are x objects. I created the same amount by [getting one cube to match every one of these cubes/ counting out cubes until I had x in all]. I know they are the same amount because they both are x objects.”

• “Note: Students may not suggest matching one-to-one, as they have been counting out sets in previous lessons. There is no need to push for matching as a strategy, as long as students are able to articulate that both sets are the same. (Counting out is the preferred strategy, as it is required by the standard.) If students want to do matching one to one, a student should be called up to the front to demonstrate as it will not be possible from rug.”

• “Potential Misconception: Students lose track of what has already been counted and end up double-counting or leaving some out (when counting to tell how many and/or when counting out an equivalent set).”

• “Mid-Workshop Interruption: What is the next level for the skill in the aim? What do you want most of your students to start doing? What is a major misconception that needs to be clarified? If > \frac{2}{3} of students are successfully counting, recording and creating equivalent sets, push students to all use counting out to build the equivalent set (as opposed to matching one-to-one). Students may count out as they match one-to-one to build understanding of equivalency.”

• “Continue to circulate and check for students to apply the learning. Make note of student success in applying in your Rapid Feedback tracker to inform the path for the Discussion.”

• “Share/Discussion: Lead a discussion around a major misconception OR students share work OR ask students to apply their learning in a new way. Use workshop data to determine the appropriate discussion path.”

Each lesson includes both “What” and “How” Key Point sections that describe what students should know and be able to do and how they will do it. Examples from Unit 3, Counting, Lesson 13 include:

• “What Key Points: We use a strategy to keep track when counting so that we only say one number for each object; the number we say last tells how many.”

• “How Key Points: Strategies for counting to answer how many: Move and Count: I can move each object as I count to keep track of which I have counted and which I still need to count. Touch and Count: I can touch each object as I count to keep track of which I have counted and which I still need to count. (Works best with small quantities or in conjunction with organize and count.) Organize and Count: I can arrange the objects into a line or array (or into strategic groups which unlikely at this point) and move or touch and count from left to right/ top to bottom to keep track of which I have counted and which I still need to count.”

##### Indicator {{'3b' | indicatorName}}

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for  containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. There is very little reference or support for content in future courses.

Materials contain adult-level explanations and examples of the more complex grade/course-level concepts so that teachers can improve their own knowledge of the subject. Examples include:

• Unit Overviews provide thorough information about the content of the unit which often includes definitions of terminology, explanations of strategies, and the rationale about incorporating a process. Unit 3 Overview, First Steps, “In everyday use, ‘to count’ has two meanings. It can mean to recite the whole number names in their right order, beginning at 1 (I can count to 20. One, two, three, four, …) It can also mean to check a collection one by one in order to say how many are in it (I counted and found there were 14 left). Key understanding 1 focuses on the latter meaning. The former is an aspect of Key Understanding 4.”

• The Unit Overview includes an Appendix titled “Teacher Background Knowledge” which includes a copy of the relevant pages from the Common Core Math Progression documents which includes on grade-level information.

Materials do not contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject. Examples include:

• The Common Core Math Progression documents in the Appendix are truncated to the current grade level and do not go beyond the current course.

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series. Examples include:

• Guide to Implementing AF Kindergarten, Program Overview, “Scope and Sequence Detail is designed to help teachers identify the standards on which each lesson within a unit is focused, whether on grade level or not. You will find the daily lesson aims within each unit and the content standards addressed within that lesson. A list of the focus MPs for each lesson and unit and details about how they connect to the content standards can be found in the Unit Overviews and daily lesson plans.”

• The Program Overview informs teachers “about how to ensure scholars have sufficient practice with all of the Common Core State Standards. Standards or parts thereof that are bolded are addressed within a lesson but with limited exposure. It is recommended that teachers supplement the lessons addressing these standards by using the AF Practice Workbooks to ensure mastery for all students. Recommendations for when to revisit these standards during Math Practice and Friday Cumulative Review are noted in the Practice section of each unit.”

• The Unit Overview includes a section called Identify Desired Results: Identify the Standards which lists the standards addressed within the unit and previously addressed standards that relate to the content of the unit.

• In the Unit Overview, the Identify The Narrative provides rationale about the unit connections to previous standards for each of the lessons. Future grade-level content is also identified.

• The Unit Overview provides a table listing Mathematical Practices connected to the lessons and identifies whether the MP is a major focus of the unit.

• At the beginning of each lesson, each standard is identified.

• In the lesson overview, prior knowledge is identified, so teachers know what standards are linked to prior work.

Explanations of the role of the specific grade-level/course-level mathematics are present in the context of the series. Examples include:

In the Unit Overview, the Identify the Narrative section provides the teacher with information to unpack the learning progressions and make connections between key concepts. Lesson Support includes information about connections to previous lessons and identifies the important concepts within those lessons. Examples include:

• Unit 9, Lesson 1 Narrative, “How does the learning connect to previous lessons? What do students have to get better at today? This is the first lesson in the final Kindergarten math unit. This unit will require scholars to use all of the knowledge and skills they’ve acquired throughout the year to make sense of various story problems and solve them. In this problem, students will need to understand that a square has four sides, then add two numbers to find the total number of chairs, and then compare the total to 10 to be able to say whether there are enough chairs for the students.”

• In the Unit Overview, the standards that the unit will address are listed along with the previous grade level standards/previously taught and related standards. Also included is a section named “Enduring Understandings: What do you want students to know in 10 years about this topic? What does it look like in the unit for students to understand this?” For example, in Grade K: Unit 9, the standards addressed are K.OA.2, K.OA, 1, K.OA.5. Previous Grade Level Standards/Previously Taught & Related Standards include K.CC.1, K.CC.2, K.CC.A.3, K.CC.4, K.CC.5, K.CC.6, K.CC.7, K.OA.3, and K.G.B.4. An example grade level enduring understanding is, “We can count a collection to find out how many are in it and use numbers to represent.” An example for what it looks like in this unit is, “Students will use counting to solve an assortment of story problems.”

##### Indicator {{'3d' | indicatorName}}

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for Achievement First Mathematics Kindergarten provides strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

• The Unit Overview includes a parent letter in both English and Spanish for each unit that includes information around what the students are working on and example strategies students will use. The letter includes information about common mistakes that parents can watch for as well as links to websites that can provide assistance.

• There is also a suggestion related to the Unit Overview, “This guide can be printed and sent home to families so that parents/guardians can better support their scholars with homework.”

##### Indicator {{'3e' | indicatorName}}

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Materials explain the instructional approaches of the program.

• The Implementation Guide states, "Our program aims to see the mathematical practices come to life through the shifts (focus, coherence, rigor) called for by the standards. For students to engage at equal intensities weekly with all 3 tenets, we structured our program into three main daily components Monday-Thursday: Math Lesson, Math Stories and Math Practice. Additionally, students engage in Math Cumulative Review each Friday in order for scholars to achieve the fluencies and procedural skills required."

• The Implementation Guide includes descriptions of “Math Lesson Types.” Descriptions are included for Game Introduction Lesson, Task Based Lesson, Math Stories, and Math Practice. Each description includes a purpose and a table that includes the lesson components, purpose, and timing.

Materials do not include and reference research-based strategies.

• The materials do not explicitly name any strategies as research-based strategies.

##### Indicator {{'3f' | indicatorName}}

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

Each lesson includes a list of materials specific to the lesson. Examples include:

• Unit 2, Lesson 5, the Lesson Overview includes: “Materials: pattern block puzzles, pattern blocks, puzzles! VA, math workshop rules VA, Attribute Blocks.”

• Unit 6, Lesson 9, the Lesson Overview includes: “Materials: story problem steps poster, blown up intro problem, whiteboards/markers, and cubes/other manipulatives.”

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for Assessment. The materials identify the standards, but do not identify the practices assessed for the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. There are connections identified for standards, but not the mathematical practices.

Materials identify the standards assessed for the formal assessments. Examples include:

• Each Unit Overview provides a chart that identifies CCSS Math Content standards for each item on the Unit Assessment. Occasionally, an individual item on the assessment identifies the standard, but in general, student-facing assessments do not include the standards.

• Each lesson includes an Exit Ticket that aligns with the standard of the lesson.

Materials do not identify the practices assessed for the formal assessments.

##### Indicator {{'3j' | indicatorName}}

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The assessment system provides multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but does not provide suggestions for following-up with students. Examples include:

• Assessments include an informal Exit Ticket in each lesson and a formal Unit Assessment for every unit.

• There is guidance, or “look-fors,” for teachers about what the student should be able to do on the assessments.

• All Unit Assessments include an answer key with exemplar student responses.

• Some units include a section titled “Evaluating Student Learning Outcomes” which provides a detailed description of what the student is expected to do.

• There are no strategies or suggestions if students do not demonstrate understanding of the concept, and no next steps based on the results of the assessment.

##### Indicator {{'3k' | indicatorName}}

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series. There are a variety of question types including multiple choice, short answer, and constructed response and mathematical practices are embedded within the problems.

Assessments include opportunities for students to demonstrate the full intent of grade-level/ course- level standards across the series. Examples include:

• In the Unit 4 assessment, the full-intent of standard K.MD.2 (directly compare two objects with a measurable attribute in common) is met. Item 1, “(Give the student the book and the pencil) Ask the students which item is shorter. Use the words longer/shorter. How did you figure that out? How did you know that?”

• In the Unit 5 assessment, the full-intent of standard K.CC.6 (tell whether the number of objects in one group is greater/less than/or equal to the number of objects in another group) is met. Item 1 compares numbers and groups within 10. Students are provided six colored tiles, 10 colored tiles, the number 4, and the number 7 and must tell which group has more. In item 2, students are given an image of six pizza slices in a row and two groups of ice cream cones in an array configuration (eight in one group and six in another group) and they must tell which group of ice cream cones that has more than the pizza slices.

• In the Unit 8 assessment, the full-intent of standard K.NBT.1 (compose and decompose numbers from 11-19 into ten ones and some further ones) is met. Item 1, “Which number sentence shows 14 as tens and ones? (MC-A. 7 + 7, B. 8 + 6, C. 10 + 4, D. 10 + 1)).” Item 2, “How many (image of a filled ten-frame and 2 dots outside of the ten-frame; MC-A. 10, B. 12, C. 11, D. 22).” Item 3, “Draw a picture and write a number sentence to show 17 as tens and ones.”

Assessments include opportunities for students to demonstrate the full intent of the mathematical  practices across the series. Examples include:

• In the Unit 1 Assessment, Task 5, students engage with MP1: Make sense of problems and persevere in solving them. “Can you sort these blocks? How did you sort them?”

• In the Unt 6 Assessment, Item 9, students engage with MP2: Reason abstractly and quantitatively. “There were 10 cupcakes on the table. Jamaine ate 4 cupcakes. How many cupcakes are on the table now?”

• In the Unit 8 Assessment, Item 1, students engage with MP7: Look for and make use of structure. “Which number sentence shows 14 as tens and ones? (a. 7 + 7; b. 8 + 6, c. 10 + 4 ; d. 10 + 1).”

##### Indicator {{'3l' | indicatorName}}

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Achievement First Mathematics Kindergarten do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. This is true for both formal unit assessments and informal exit tickets.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Achievement First Mathematics Kindergarten do not meet expectations for Student Supports. The materials do not provide strategies and supports for students in special populations or for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level/series mathematics. The materials provide some extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials do provide manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for Achievement First Mathematics Kindergarten do not meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials do not provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations.

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for Achievement First Mathematics Kindergarten partially meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Some lessons include an Extension/Application Problem that allows teachers to extend the thinking of the lesson during discussion. However, extension problems are intended for all students as there is no identified differentiation for advanced students. Examples Include:

• Unit 2, Lesson 4, Extension/Application problem extends students’ understanding of describing relative positions of objects.“Students in Syracuse were lined up at the door to go to lunch. Nariya was first in line, Kelton was behind her, Samuel was in front of Kelton. Who will walk out the door first -- Kelton or Samuel?”

• Unit 5, Lesson 8, Extension/Application problem extends students’ understanding of comparing two numbers.“Shanaya is collecting cards that show numbers that are less than 6. Which card should she collect?”

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for Achievement First Mathematics Kindergarten provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning; however, there are no opportunities for students to monitor their learning.

The program uses a variety of formats and methods over time to deepen student understanding and ability to explain and apply mathematics ideas. These include: Exercise Based Lessons, Task Based Lessons, Math Stories, Math Practice, and Cumulative Review.

In the lesson introduction, the teacher states the aim and connects it to prior knowledge. In Pose the Problem, the students work with a partner to represent and solve the problem. Then the class discusses student work. The teacher highlights correct work and common misconceptions. Then students work on the Workshop problems, Independent Practice, and the Exit Ticket. Students have opportunities to share their thinking as they work with their partner and as the teacher prompts student responses during Pose the Problem and Workshop discussions. Math Stories provide opportunities for students to question, investigate, sense-make, and problem-solve using a variety of formats and methods.

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Achievement First Mathematics Kindergarten provide some opportunities for teachers to use a variety of grouping strategies. Grouping strategies within lessons are not consistently present or specific to the needs of particular students. There is no specific guidance to teachers on grouping students.

The majority of lessons are whole group and independent practice; however, the structure of some lessons include grouping strategies, such as working in a pair for games, turn-and-talk, and partner practice. Examples include:

• Unit 4, Lesson 3, Introduce the Math, students work in pairs to play the game “Heavier or Lighter” to determine which object weighs more. Consolidate the learning suggests, “transition as necessary into groups.”

• Unit 9, Lesson 2, Exploration, “After 8-10 minutes, have students engage in a turn and talk to share their answers and explain their reasoning. The partner who is not sharing first should agree/disagree and explain why. Encourage students to use their work to support their argument).”

##### Indicator {{'3q' | indicatorName}}

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for Achievement First Mathematics Kindergarten do not meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Materials do not provide any resources for students who read, write, and/or speak in a language other than English to meet or exceed grade-level standards through regular and active participation in grade-level mathematics.

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Achievement First Mathematics Kindergarten provide a balance of images or information about people, representing various demographic and physical characteristics. Examples include:

• Lessons portray people from many ethnicities in a positive, respectful manner.

• There is no demographic bias seen in various problems.

• Names in the problems include multi-cultural references such as Mario, Tanya, Kemoni, Jiang, Paige, and Tomi.

• The materials are text based and do not contain images of people. Therefore, there are no visual depiction of demographics or physical characteristics.

• The materials avoid language that might be offensive to particular groups.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Achievement First Mathematics Kindergarten do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials do not provide suggestions or strategies to use the home language to support students in learning mathematics. There are no suggestions for teachers to facilitate daily learning that builds on a student’s multilingualism as an asset nor are students explicitly encouraged to develop home language literacy. Teacher materials do not provide guidance on how to garner information that will aid in learning, including the family’s preferred language of communication, schooling experiences in other languages, literacy abilities in other languages, and previous exposure to academic everyday English.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Achievement First Mathematics Kindergarten do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials do not make connections to linguistic and cultural diversity to facilitate learning. There is no teacher guidance on equity or how to engage culturally diverse students in the learning of mathematics.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Achievement First Mathematics Kindergarten provide supports for different reading levels to ensure accessibility for students.

The materials include strategies to engage students in reading and accessing grade-level

Mathematics such as teacher reading the problem, visualizing, and creating “mind-movies.” Examples include:

• In Unit 5 Lesson 9, Introduction, Pose the Problem, “I’m going to read you a problem. As I read, I want you to make a mind movie just like we do in Math Stories to visualize what is happening and what we need to figure out. Toy trucks: Hector has 6 toy trucks. Erick has 5 toy trucks. Hector says he has a greater amount of toy trucks than Eric. Is Hector correct? Show how you know.”

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Achievement First Mathematics Kindergarten meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Manipulatives are accurate representations of mathematical objects and are connected to written methods. Examples include:

• Unit 3, Lesson 2, Workshop, students count to tell how many by using bags of 5 to 15 manipulatives (cubes or counters). Students play “Counting Bags/Jars,” where they “move and count, touch and count, or organize and count” the manipulatives and then “record with a number.”

• Unit 5, Lesson 5, Workshop, students use number cards to identify whether the objects in one group are greater than, less than, or equal to the number of objects in another group (K.CC.6). Students draw two cards from a deck, record the numbers, and then circle which number is the greatest. They can use a variety of strategies to determine the larger number including matching “non-linking manipulatives (teddy bears, pennies, counters, anything that doesn’t connect)” to each number.

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Achievement First Mathematics Kindergarten do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, or provide teacher guidance for the use of embedded technology to support and enhance student learning. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Achievement First Mathematics Kindergarten do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials do not contain digital technology or interactive tools such as data collection tools, simulations, virtual manipulatives, and/or modeling tools. There is no technology utilized in this program.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Achievement First Mathematics Kindergarten do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials do not provide any online or digital opportunities for students to collaborate with the teacher and/or with other students. There is no technology utilized in this program.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Achievement First Mathematics Kindergarten have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The student-facing printable materials follow a consistent format. The lesson materials are printed in black and white without any distracting visuals or an overabundance of graphic features. In fact, images, graphics, and models are limited within the materials, but they do support student learning when present. The materials are primarily text with white space for students to answer by hand to demonstrate their learning. Student materials are clearly labeled and provide consistent numbering for problem sets. There are several spelling and/or grammatical errors within the materials.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Achievement First Mathematics Kindergarten do not provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

There is no technology utilized in this program.

## Report Overview

### Summary of Alignment & Usability for Achievement First Mathematics | Math

#### Math K-2

The materials reviewed for Achievement First Mathematics Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades K-2 do not meet expectations for Usability, Gateway 3.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

#### Math 3-5

The materials reviewed for Achievement First Mathematics Grades 3-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades 3-5 do not meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

#### Math 6-8

The materials reviewed for Achievement First Mathematics Grades 6-8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades 6-8 do not meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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