Kindergarten - Gateway 1

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for assessing grade-level content.

Assessments are located in the Assessment Guide book. Assessments consist of a Prerequisite Skills Inventory, Middle-of-Year Test, End-of-Year Test, 20 Module Tests, and 5 Unit Performance Tasks. Each Module Assessment consists of a printable and interactive Form A and Form B.

The Interactive Middle of Year Test assesses the standards taught in approximately the first half of the year, and the Interactive End of Year Test assesses the full year of standards. Examples include:

• End of Year Test, Item, 18 "Mica builds this shape. Which shapes could Mica have used to build his shape?" (K.G.6)
• End-of-Year Test, Item 6, "Cal uses trucks to show one way to make 6. Which equation shows another way to make 6?" The item shows a group of 3 trucks and a group of three more trucks. (K.OA.3)

Module Tests are available digitally and in the Assessment Guide. Examples include:

• Module 4 Test, Forms A and B, Items 4-6, students classify objects into given categories. Form A, Item 4, instructs students to, “draw lines from the cats to the words to show if they are big or small. You will draw lines to all the cats.” (K.MD.3) 
• Module 8 Test, Forms A Items 5, students are instructed to count, “How many turtles? Fill in the blank with the correct number.” (K.CC.3)
• Module 12 Test, Forms A and B, Items 1-3, students are read a word problem and given a picture. Then students select the equation that matches the word Item and the picture. In Form A, Item 3, “Carl has five plants. He has one plant that is big. Carl has four plants that are small. Which equation tells about Carl's big and small plants?" Form B, Item 2, “There are seven sports balls. Four of them are soccer balls and the rest are tennis balls. Which equation shows how many are tennis balls?” (K.OA.1) 
• Module 12 Test, Forms A and B, Items 5 and 7, students represent subtraction with objects, drawings, or equations by writing a subtraction equation to match a picture representation. In Form B, Item 7, “ Lisa has ten shapes. Two shapes are gray and the rest are white. How can an equation be used to model how the groups are put together? Fill in the blanks with the correct numbers.” (K.OA.1)
• Module 16 Test, Forms A and B, Items 1 and 3, students identify shapes by selecting the matching shape. In Form A, Item 1, “Tom sees this shape (triangle). Which is the same shape as Tom’s?” (K.G.4)
• Module 16 Test, Forms A and B, Items 2, 5, and 7 students analyze shapes to identify the correct number of sides or vertices and whether the shapes are 2 dimensional or 3 dimensional. In Form B, Item 5, “Which shows a two-dimensional shape?” (K.G.4)
• Module 20 Test, Form A, Items 1-2, students identify objects that are heavier or lighter. Form A, Item 2, “Stacy has this tennis ball. Which object has less weight than Stacy’s tennis ball?” (K.MD.2)
• Performance Assessments with multiple tasks for each unit are provided in the Assessment Guide. Module 4 Task 3, “Yoshi and Neela are picking flowers. They pick more than 10 flowers but no more than 19 flowers. Write a number that could be the number of flowers they pick.” (K.CC.3)

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of Modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 20, which is approximately 75%. 
• The approximate number of Lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 77 out of 96, which is approximately 80%.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 128 out of 162, which is approximately 79%.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each module. As a result, approximately 80% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for HMH Into Math Kindergarten meets the expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Throughout the instructional materials, supporting work of the grade is connected to major work. Examples of how the materials connect supporting work to the major work of the grade include:

• In Module 4, Lesson 1, Step It Out, the supporting work of K.MD.3 is connected to the major work of K.CC.5 as students classify objects into given categories and count to answer "how many?" questions. In Problem 2, “Pat has seven cubes. She classifies the cubes by color. How many cubes does Pat have of each color?”
• Module 4, Lesson 4, On Your Own, Problem 4, the supporting work of K.MD.3 (Classify objects into given categories; count and sort the objects) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students solve “Amelia has 8 buttons in 3 colors to classify. She wants to know how many buttons are in each category. Then she wants to sort each category by count.” 
• In Module 14, Lesson 5, the supporting work of K.G.4 (Analyze and compare two- and three-dimensional shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students answer “Does the shape have any flat surfaces? If so, how many?”  "Does the shape have flat or curved surfaces? What do you notice about the surfaces?" 
• Module 15, Lesson 1, Step It Out, the supporting work of K.G.1 (Describe objects in the environment using names of shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students solve "How many objects shaped like a sphere are in the picture? How many objects shaped like a cube are in the picture?”
• Module 16, Lesson 2, Spark Your Learning, Persevere, the supporting work of K.G.2 (Correctly name shapes) and K.G.4 (Analyze and compare two- and three-dimensional shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students count the number of sides of shapes to answer: "Which plate has four sides? Which plate has four corners? Which plate has four equal sides?; Build Understanding, sample guided discussion "How many sides are there?"
• Module 16, Lesson 3, Build Understanding,  the supporting work of K.G.4 (Analyze and compare two- and three-dimensional shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) in the Sample Guided Discussion: "How many vertices does it have? How many triangles do you see in Task 4? Are the triangles similar or different?"

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 162 days. The suggested amount of time and expectations for teachers and students in the materials are viable for one school year as written and would not require significant modifications.

• The provided scope and sequence found in the Planning and Pacing Guide includes materials for 114 instructional days.
• There are 3 days per year for the Growth Measure Assessments.
• There are 5 Units. There is 1 day per Unit for the Performance Task, for a total of 5 days. 
• There are 20 Modules, with 1 day for each Module Opener, Are You Ready?, and 1 day for each Module Review and Module Test, for a total of 40 days.

The suggested pacing from the publisher is 1 day per lesson for most lessons. However, some lessons are listed for 2 days. There are no lessons that require more than 2 instructional days to complete. 

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for being consistent with the progressions in the Standards, providing all students with extensive work of the grade, and explicitly identifying prior knowledge needed for grade level work.

In the Planning and Pacing Guide, there is a Correlations Chart where all grade-level standards are represented. Tasks are aligned to grade-level work and are connected to prior knowledge..

The instructional materials clearly identify for each module Teaching for Success that shows the progressions of the standards from “Prior Learning”, to “Current Development,” and to “Future Connections,” respectively. In the beginning of each lesson, Mathematical Progressions include the same progressions with “Future Connections” explicit to the lesson. Examples of “Future Connections” include:

• Module 5, Lesson 1, Mathematical Progressions, Future Connections, “Children will make connections among a variety of representations to explain addition situations (Grade 1, Lessons 1.1 - 1.7). Children will relate counting to addition (Grade 1, Lesson 1.2).”
• Module 11, Lesson, 3, Mathematical Progressions, Future Learning, “Children will use addition within 20 to solve word problems involving situations of adding to and putting together with unknowns in all positions (Grade 1, Lessons 5.1-5.4).”
• Module 19, Teaching for Success, Mathematical Progressions Across the Grades, Future Connections, “Children will order three objects by length (Grade 1, Lesson 17.1); and, compare the lengths of two objects using a third object (Grade 1, Lesson 17.2).”

 A typical lesson includes multiple opportunities for students to engage with extensive work of the grade. Build Understanding, Step It Out, and Connect Concepts and Skills are intended to engage students with new grade-level content. During On Your Own (independent practice), and More Practice/Homework, students work with grade-level problems. For example:

• Unit 1 introduces the counting sequence and numbers to 5. In Modules 1 through 4, students identify, compare, classify, sort, add, and subtract within 5. Modules 5-6 introduce word problems involving addition and subtraction. 
• Module 4, Lesson 3, On Your Own, Problem 3, “Classify the peppers by size and draw the peppers in each category. Mosi has six peppers in her garden. Some peppers are big and the rest are small. __ peppers (big). __ peppers (small).”
• Module 5, Lesson 7, Step It Out, “Draw to show the total number of children riding their bikes on the trail. Write an equation to model the problem. ‘Three children are riding their bikes on a trail. Two more children join them. How many total children are riding?”
• Module 6, Lesson 7, On Your Own, Problem 8, “Three brown butterflies and two orange butterflies are flying. How many total butterflies are flying?” 
• Unit 4, Number and Operation in Base Ten consists of Module 17, Place Value Foundations: Represent Numbers to 20, and Module 18, Place Value Foundations: Represent Numbers to 20 with a written numeral. In Module 17, students compose ten and some more ones to make 14, 15, 19, and 20. In Module 18, students count and write from 11 to 20. 
• Module 17, Lesson 3, Build Understanding, Problem 1, “The ten cubes at the top of the page represent ten ones. How can you use those cubes and draw some more ones to show the number? Write the numbers to show ten ones and some more ones. 16, __ones and __ones.”

In addition to including Mathematical Progressions identifying prior learning for each lesson, the beginning of each module explicitly identifies and engages prior learning during the "Are You Ready?" activities designed to diagnose mastery, inform grouping and differentiation. Warm-Up Options in all lessons, and Spark Your Learning activities in Build Understanding and Connect Concepts and Skills lessons are intended to assist with activating prior knowledge. Examples include: 

• In Module 1, Lesson 4, Mathematical Progressions, Prior Learning is identified as “Children used counting and numbers to determine quantities up to 5.” 
• In Module 3, Teaching for Success, Mathematical Progressions, prior Grade K skills address K.CC.4 and K.CC.5, when children counted and ordered numbers to represent numbers zero to five. 
• Module 5, Lesson 3, Mathematical Progressions, Prior Learning: "Children represented addition by acting out situations, Grade K Lesson 5.1," 
• In Module 11, Lesson 5, Prior Learning: “Children wrote addition equations within 10." This addressed standard K.OA.1 in Grade K, Lesson 5.5.
• Module 13, Lesson 4 , Mathematical Progressions, identify prior learning as "Children learned about ways to make numbers to 9. (Grade K, Lessons 1.5, 13.1–13.3) Children used objects and drawings to represent addition problems within 10. (Grade K, Lesson 12.1) Children wrote addition equations within 10. (Grade K, Lesson 11.5) Children solved word problems within 10 (Grade K, 12.5)." This learning connects to the current development lessons which target K.OA.3 and K.CC.4b. In these lessons, children decompose the number 10 and use objects, drawing, and equations to find and represent different ways to make 10. From these lessons, future connections will be made with 1.OA.1, found in lessons 5.1-5.4, 6.1-6.3, 6.6-6.7, 7.1-7.3, and 7.7, where students represent and solve addition and subtraction problems.
• Module 15, Lesson 2, Mathematical Progressions, identify prior learning from Grade K Lessons 14.1 - 14.4 (K.G.3 and K.G.1- describing three-dimensional shapes and using positional words like above or below). This learning connects to the current development lessons which target K.G.1. In these lessons, students begin to use the positional words next and beside. From these lessons, future connections will be made with 1.G.1, found in Grade 1 Lessons 14.1 - 14.2, where students distinguish between defining attributes and build and draw shapes to possess defining attributes.
• Module 6, Lesson 1, Are You Ready?, includes writing numbers to make 5 (K.OA.5 ) that builds to students representing addition with objects, fingers, images, or equations (K.OA.1). 
• Module 12, Lesson 4, Activate Prior Knowledge, reviews prior learning of subtraction problems within 10 (K.OA.2 ). Based on this Math Routine , students participate in Interactive Reteach, Grade K, Lesson 2.2, or complete a prerequisite skills activity.
• Module 20, Lesson 3, Spiral Review,, includes review questions that will help determine if students have retained information taught in the past. This Spiral Review assesses whether children will identify a hexagon from a group of shapes (K.G.A.2 ). These Spiral Reviews are located in the More Practice/Homework section of the student materials.

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, including:

• In Module 12, Lesson 4, the Learning Objective, “Use objects, drawings, and equations to solve take apart problems within 10,” is shaped by K.OA.A, (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from).
• In Module 17, Lesson 3, the Learning Objective, “Understand the numbers 16 to 19 by decomposing the numbers into ten ones and some more ones using objects,” is shaped by K.NBT.A, (Work with numbers 11–19 to gain foundations for place value).
• In Module 19, Lesson 2, the Learning Objective, “Understand how to compare the lengths of two objects,” is shaped by K.MD.A, (Describe and compare measurable attributes).

The materials include problems and activities connecting two or more clusters in a domain or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

• In Module 2, Lesson 5, connects K.CC.B and K.CC.C as students count how many counters are in each group. Students point to the counter as they count, trace, and write the corresponding numbers. “How many counters will you need to show for the number that comes after 2?” Students then place 3 counters, counting aloud as they place each one, and then write the number.  
• In Module 11, Lesson 6, Step It Out, connects K.CC.A  and K.OA.A as students count groups of objects or animals and represent each number counted to create and solve subtraction equations. Problem 2, “Listen to the subtraction word problem. Mark an X on the campers that are leaving. Write an equation to model the problem. Explain what each number represents. Eight campers are in a campground. Two campers are driven away. How many campers are there now?”
• In Module 17, Lesson 2, connects K.NBT.A  and K.CC.C as students build the numbers 14 and 15. On Your Own, Problem 4, “Circle ten pears. Circle some more pairs to show the number 15. Write the numbers to represent the number of pears.”