Kindergarten - Gateway 2

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meets expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop conceptual understanding. For example: 

• Lesson 5, Session 3, Develop, Try It supports students in developing conceptual understanding of K.OA.3 by decomposing numbers less than or equal to 10 into pairs in more than one way by using objects. The materials state, “Have children use cubes to make a 2-color train of 3, 4, or 5.”
• In Lesson 18, Session 2, Develop states, “Say: There are 4 markers and 2 of them are taken to be used. Write 4-2 on the board, saying 4 markers minus 2 markers as you write. *Have children model the expression using their own markers. Have them count a group of 4 and then show what the minus sign means by taking 2 of the markers away. *Ask: How many markers are left? 4 minus 2 is how many: 2 * Repeat with other number pairs and familiar classroom objects. Have children tell how many are left, but do not write the complete equation using the equal sign at this time.” (K.OA.1)
• In Lesson 28, Session 5, Refine, in the student Worktext, students use counters to model teen numbers in different ways by placing counters on the 10 frames and then completing a number bond and equation. (K.NBT.1)  Students also complete 10 frames, a number bond and an equation to model teen numbers with counters. On the last problem, they draw the counters to match the equation and then write a total.

Examples of students independently demonstrating conceptual understanding include:

• In Lesson 8, Session 1 Explore, Additional Practice states, “Have children show the meaning of the word less. Have children fill in each of the boxes to show the meaning of the word less. Tell children that they can use words, numbers, and pictures. Encourage them to show as many ideas as they can.”  (K.CC.6)
• In Lesson 19, Session 5, Refine, Apply It states, “There are 4 apples, Max eats 1. How many apples are left?” Students use a five frame and counters to conceptually understand and solve the problem. 
• In Lesson 24, Session 3, Develop provides opportunities for students to independently demonstrate conceptual understanding of K.OA.2. The materials state, “Have children use drawings to solve word problems. Say: Ellen uses 6 star beads and 3 heart beads to make her necklace. How many beads does she use in all? Have children use drawings and write an equation to match. Repeat with two more addition word problems.”
• In Interactive Practice, Make 10, students make ten by using ten frames, finding the missing addend, and matching ten frames which together make ten. (K.OA.3)
• In Interactive Practice, Make Teen Numbers, students make teen numbers by using ten frames, finding the missing addend, and matching sums and equations. (K.NBT.1)

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. 

The materials include problems and questions, interactive games, and math center activities that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. 

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop procedural skill and fluency throughout the grade level. For example:

• In Lesson 11, Session 2, Develop, Connect It, students match groups of objects to number statements. Students are shown pictures of objects to add such as three green apples and four red apples. Students then match the pictures with the matching number statement. 
• In Lesson 11, Session 5, students are asked to make numbers by drawing counters in two colors on a 10 frame. Then, they are asked to write the number of counters for each color. For instance, the first problem asks students to “Make 6.” Students then draw some red and some yellow counters and write the number of each color they used to make six.
• Games provide practice with fluency. In Hungry Fish, students combine the numbers in the bubble together until they equal the amount shown on the fish. Levels Addition to 3-5 and 6-10 and Subtraction 3-5 and 6-10 are appropriate for Kindergarten. In Hungry Guppy, students combine the dots to equal the picture of the dots shown on the guppy with numbers up to 6.

K.OA.5 (Fluently add and subtract within 5) requires students to develop grade level fluency. This standard is addressed in several lessons, including:

• In Lesson 16, Fluency and Skills Practice states, “Have children match pictures to the addition equations.” Students are given six problems with pictures of linking cubes trains using two colors on the left and addition sentences on the right (ex. 4+1=5 to match with a picture of 4 black cubes and 1 white cube). 
• In Lesson 17, Session 1 Explore, Develop Fluency states, “Materials: None, children use their fingers. Why: A quantity (4) may be seen as 4, or as composed of two parts, preparing children for work with addition. How: Ask children to first show with their fingers how many red counters there are, then say the number aloud together. Repeat for the yellow counters and for the total.” 
• In Lesson 20, Student Worktext, Session 3, Develop, Practice Facts to 5, students see 3 red dots and 1 blue dot and are presented with the problem 3+1=___. In another problem, they see 4 green dots with an X over one and the problem, 4-1=___.

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. Within each lesson, there are Fluency and Skills Practice pages that students complete on their own.  In addition, there are Learning Games and Math Center Activities that engage students with fluency practice. Examples of when students get opportunities to independently demonstrate procedural skill and fluency include:

• In Lesson 19, Session 3, Develop, Practice Subtracting within 5, students see a group of 5 balloons where 2 are floating away. They are given 5 -___=___  and are expected to fill in the blanks with the correct numbers. (K.OA.5 Fluently add and subtract within 5.)
• Learning Games which provide independent practice include:
• In Match, students match the card that has two numbers or a number and dots that are being added/subtracted to the other card that shows the correct answer. Levels Intro to Add, Addition to 3-5 and 6-10 and Subtraction 3-5 and 6-10 are appropriate for Kindergarten.
• In Hungry Fish, students combine the numbers in the bubble together until they equal the amount shown on the fish. Levels Intro to Add, Addition to 3-5 and 6-10 and Subtraction 3-5 and 6-10 are appropriate for Kindergarten.
• In Hungry Guppy, students combine the dots to equal the picture of the dots shown on the guppy with numbers up to 6.
• In the Math Center Activities, there are games provided to work on facts to 5, including: 
• In the Lesson 16 activity Addition Vocabulary, students read an equation, draw it, and then a partner checks their work. 
• In the Lesson 17 game Add and Move, students use addition equations and counters for partners to move around a game board based on the number in the total of their equation. 
• In the Lesson 18 activity Subtraction Vocabulary, students read an equation, draw it, and then a partner checks their work. 
• In the Lesson 20 game 5 Beans, students use equations and counters to check their partner.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. 

Opportunities for students to independently demonstrate the use of mathematics flexibly are present in a variety of contexts. The instructional materials include multiple opportunities for students to engage in routine application of mathematical skills and knowledge of the grade level, including:

• In Lesson 17, Session 1, Explore, students solve “1 girl and 2 boys get on the bus. How many children are on the bus?”
• In Lesson 23, Session 3, Develop, Try It provides opportunities for students to engage in routine applications of grade level mathematics. The materials state, “Directions- Explain to students that they are going to use cubes to act out a subtraction story. Say: There were 10 balloons. 2 balloons popped. How many balloons are left? Have children use their cubes to solve the subtraction problem and then write the equation.” 
• In Lesson 24, Session 3, Develop, Connect It provides opportunities for students to engage in routine applications of grade level mathematics. The materials state, “Directions: For each problem, tell an addition story and have children use drawings to model it and solve it and then write the equation to match. When all three problems have been completed, have several children share their answers and thinking. Say: Mercer eats 4 crackers. She eats 6 more. How many crackers has she eaten in all. Have children draw the crackers to solve the problem and then write an equation to match. Repeat with each other word problem.” 
• In Lesson 24, Session 5, Extend, students solve the routine change unknown problem using counters to represent the story: “I had 10 crackers. I ate some, and now I have 8. How many crackers did I eat?”
• In Lesson 25, Session 1, Explore, students solve a routine problem: “Mateo has 6 apples. He has two plates. How many apples can he put on each plate?” (K.OA.3)

The instructional materials include multiple opportunities for students to engage in non- routine application of mathematical skills and knowledge of the grade level. 

For example, in i-Ready, Assess & Teach, Classroom Resources:

• In Lesson 4, Session 2, Develop shows a picture of a table set up for a party with presents, plates, spoons, cups, cake, etc. Students solve “Do you think there are more than 3 people coming to this party? Why or why not?” 
• In Lesson 17, Student Worktext, Session 4, Refine, students are given pictures to create story problems that represent the picture, and then they solve the problems. For example: 2 red apples, 1 yellow apple (2+1=?), 3 blue butterflies, 1 yellow butterfly (3+1=?). Twelve total problems are provided in this session. 
• In Lesson 19, Student Worktext, Session 4, Refine, students are given nine pictures for subtraction problems within 5 and create a story problem that goes along with each picture. 
• In Lesson 25, Session 4 Refine, Additional Practice, the directions state, “For the second problem, have children choose a total, tell another story, and find two ways to solve.” (K.OA.3)

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.  

 All three aspects of rigor are present independently throughout the program materials. The instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently throughout the grade level.

Students engage in instruction to develop conceptual understanding:

• In Lesson 28, Student Worktext, Session 1, Explore, Student Worktext, students demonstrate their understanding of teen numbers by providing four examples of the number 17 in four different boxes. The directions state, “Have children show the meaning of 17. Have children fill in each of the boxes to show the meaning of 17. Tell children that they can use words, numbers, and pictures. Encourage them to show as many ideas as they can.”

Students engage in instruction to develop procedural skills and fluency:

• In Lesson 20, Student Worktext, Session 1, Explore, students solve addition and subtraction problems. The directions state, “Have children solve addition and subtraction problems. Review the plus, minus, and equal signs. Ask children to model addition and subtraction facts within 5 with fingers and write the total or difference.”

Students engage in application of mathematical knowledge and skill:

• Lesson 19, Student Worktext, Session 4, Refine, students apply their skills by completing the subtraction problem using counters and an equation. The directions state, “Have children act out a subtraction story problem using counters. Give each child 5 counters. Say: 5 cups are to be filled with juice. You pour juice in 3 cups. How many are left to fill? Have children act out the story and write an equation to solve.”

Students have opportunities to engage in multiple aspects of rigor simultaneously:

• Lesson 8, Student Worktext, Session 1, Explore, students show their understanding of the word less by creating examples using a variety of methods. They can use application techniques in their examples. The materials state, “Have children show the meaning of the word less. Have children fill in each of the boxes to show the meaning of the word less. Tell children that they can use words, numbers, and pictures. Encourage them to show as many ideas as they can.” Students are demonstrating understanding with visual and numerical representations as well as words and engaging in application of the mathematics through the creation of examples using words and pictures.
• In Lesson 16, Session 2, Develop, Connect It states, “For each picture, have children count and tell the number of red apples and the number of yellow apples. Then have them find the box with the addition expression that matches those numbers. Have them draw a line to connect the picture to the matching expression. Ask children to show the addition with their fingers and tell how many apples in all.” This connects the conceptual understanding that adding is joining together and the procedural fluency of using expressions to denote the symbolic representation.
• In Lesson 26, Session 3, Develop, students develop conceptual understanding of teen numbers by using linking cubes and making a train of ten cubes with single cubes and connecting their understanding of physical representations of teen numbers to the procedural skill of counting.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for carefully attending to the full meaning of each practice standard. 

The instructional materials attend to the full meaning of each mathematical practice in i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources. 

Math Practice 1: Make sense of problems and persevere in solving them.

• In Lesson 2, Session 2, Deepen Understanding states, “As children work on the Connect It problem, allow them sufficient time to make sense of the problem. This time encourages them to try different approaches. Children build confidence by using what they have learned to persevere in finding different approaches. Finding different approaches also allows children to revise their thinking on subsequent problems. Ask: How can you match groups? Listen for: I counted. I drew lines between pairs of objects. I used counters and rearranged them.”
• In Lesson 5, Session 3, Develop, Deepen Understanding states, “MP1 Make sense of problems. When children have finished the problems, challenge them to think more broadly about their process. As children decide how many of each color to use to make each total, they are making sense of the problem.” Students break numbers apart using two cube colors to show the number pairs.
• In Lesson 29, Session 2, Develop, Deepen Understanding states, “MP1 Make sense of problems. As children figure out how many more vases of flowers are needed to have 100 flowers, listen to and look for different strategies.” MP1 is about making sense of problems but it also has a second part to persevere in solving them.

Math Practice 2: Reason mathematically and quantitatively.

• In Lesson 23, Session 2, Deepen Understanding states,”After all of the pictures and equations have been matched, have children describe each of the quantities and situations in each picture. Through telling about the subtraction situations in the pictures, children are making sense of quantities and their relationships.”
• In Lesson 25, Session 2, Develop, Deepen Understanding states, “MP2 Reason abstractly and quantitatively. After the problems have been completed, have children describe how each number relates to the parts of the story. This lets children practice reasoning abstractly and quantitatively.” 
• In Lesson 32, Session 3, Develop, Deepen Understanding states, “MP2 Reason quantitatively. Generalize: Ask: Will more than 1 item always be heavier than 1 of the same item? Listen for children to reason quantitatively and explain that if all the items were the same, then each one will weigh the same, so if the items are put together, then there will always be more weight than just 1.”

Math Practice 4: Model with mathematics.

• In Lesson 7, Session 1, Connect It, Prepare to find 1 more states, “Have children fill in each of the boxes to show the meaning of 1. Tell children that they can use words, numbers, and pictures. Encourage them to show as many ideas as they can.”
• In Lesson 19, Session 1, Explore, Student Worktext pages, the directions for these problems state, “Have children act out subtraction word problems. Pose the problem: In a parking lot, there are 5 cars parked in a row. 1 car leaves. How many cars are still in the row? Act out the subtraction. Model the subtraction. Solve another problem. There are 4 cars in a row. 2 cars leave the row. How many cars are still in the row?”
• In Lesson 24, Session 2, Develop states, “Kai buys 3 pink flowers and 4 yellow flowers. How many flowers does Kai buy in all?  Have children circle the flowers Kai buts to solve.”
• In Lesson 32, Session 3, Develop, Discuss It states, “Is a bigger object always heavier than a smaller object? Why or why not? Show children a basketball and larger beach ball. Which is bigger? Have children draw an object that is similar in size to a basketball and another that is similar in weight to a basketball.” 

Math Practice 5: Use appropriate tools strategically. 

• In Lesson 10, Student Worktext, Refine, the student toolkit gives students the options of using two-color counters, cups, and crayons to help solve finding pairs to make ten. 
• In Lesson 24, Student Worktext, Explore, the student toolkit gives students the options of using connecting cubes or counters to create an equation with a sum of 9.

Math Practice 6: Attend to Precision

• In Lesson 7, Session 1, Explore, Try It, students attend to precision when they are counting out counters and saying the number as they place each counter on a balloon.  Teachers are instructed to ask, “How many counters did you put down each time as you counted? Why?” and to listen for “1 counter. Each time I counted another number. Each number is 1 bigger (or greater), so it needs another counter each time.”
• In Lesson 28, Session 3, Develop, Try It, students attend to precision when filling their ten frames by filling the first ten frame before moving onto the second ten frame.

Math Practice 7: Look for and make use of structure.

• In Lesson 5, Session 2, Develop, students make use of structure as they work on problems where single objects are comprised of smaller units. The materials state: “After discussing all problems, ask children to make observations about how the cars are the same. These observations help them see single objects as being composed of smaller units. Encourage children to make similar observations about different number pairs throughout this lesson to focus on the structure of composed numbers. Ask: How many yellow cars and how many blue cars are in the second and third trains? How many cars in all for each train? What can you tell me about these numbers?”
• In Lesson 15, Session 2, Develop states, “When discussing the shapes in Connect It, prompt children to think about the shapes that can be made by putting two smaller shapes together. This helps children make use of structure.” Ask: “Where in the classroom can you see where shapes have been put together to make a larger shape? Can all shapes be used to make the same shape?”
• In Lesson 27, Session 2, Develop states, “When discussing number pairs that make teen numbers, prompt children to think about all the teen numbers as 10 and some extras. These discussions lay the groundwork for children to recognize patterns in writing teen numbers. Later, they will apply the patterns to all two-digit numbers.” Ask: “How are teen numbers the same? How are they different? Say: There are 18 balls. Sarah counts 10 balls and puts them in a bag. She knows she has 8 balls left. How does Sarah know how many balls are left to put in the bag?” 

Math Practice 8: Look for and express regularity in repeated reasoning.

• In Lesson 30, Session 2, Develop, Deepen Understanding states, “MP8 Use repeated reasoning. Generalize: Listen for the mistake 31, 32, 33, 34, 45, 36, 37, 38 39. When children identify 45 as the mistake, ask them how they know. Listen for children who talk about the number that is 1 more, or following the ones or tens pattern.” 
• In Lesson 31, Session 2, Develop, Deepen Understanding states, “MP8 Use repeated reasoning. Generalize: Can I use the same steps to compare the length of two sticks and to compare the height of two towers?  Listen for children who are able to apply the same steps to compare in both situations. First, they must align the two objects, and then they can see which goes farther.” 

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.  

Student materials consistently prompt students to construct viable arguments and to analyze the arguments of others. Features of the instructional materials that engage students in constructing viable arguments and/or analyzing the mathematical reasoning of others are Discuss It-Support Partner Discussion and Support Whole Class Discussion-Compare and Connect. In the Program Implementation tab, Implementation Support, Try-Discuss-Connect Routine Resources, teachers find different ways to encourage Math Practice 3 in their math classrooms. Try It provides Three Reads routine, Co-Craft Questions and Problems, and Turn and Talk routine. Discuss It provides the Turn and Talk, Collect and Display, Say It Another Way, and Compare and Connect routines. Connect It provides Collect and Display, Turn and Talk, and Say It Another Way routines. 

These routines provide students with opportunities to construct viable arguments. Examples include:

• In Lesson 5, Session 3, Develop, Try It, students make cube trains of two different colors. Students explain to their partner how they made their train. Students look to see if they made the same trains or different colored trains. In Discuss It, students realize that it does not matter the arrangement of the colors, they had the same total. 
• In Lesson 17, Student Worktext, Session 1, Explore, students justify that they understand the meaning of addition with three different examples. The directions state, “Have children show what it means to add. Have children fill in each of the boxes to show the meaning of addition (joining). Encourage them to use pictures, words, and numbers. Tell children to think of as many different ways as they can.”
• In Lesson 14, Session 1, Explore states, “Support Whole Class Discussion: Have children share how they decided which shape to hold up. Why did you hold up your shape? Why can more than one different shape be held up? Repeat several times, each time saying a different attribute. Give attributes that fit multiple shapes that fit only one shape.”

Students also have opportunities to analyze the mathematical arguments of others. Examples include:

• In Lesson 3, Session 2, Develop, students talk in pairs about the groups they see. The materials state, “Did your partner notice something that you did not see?”
• In Lesson 12, Sections 1-5 allow students to identify shapes by circling and placing an X on them. This is an opportunity to see claims of other students and where they place their circles or Xs, and if they are correct and why. In Session 3, Develop, students tell a partner how they will identify each of the shapes. The materials state, “What do you know? What did you notice about your partner’s approach?”
• In Lesson 32, Session 2, Develop, students talk in pairs about how they know which objects to mark with an X. The materials state, “Did your partner choose the same object as you? If not, is your partner still correct? Do you agree with your partner’s explanation?”

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Teacher materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others, frequently throughout the program. In the i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Teaching and Learning Resources, there are Discourse Cards. The cards assist teachers with talking points such as: “Do you agree with the strategy, answer, or explanation? Do you disagree with the strategy, answer, or explanation? What do you think about what another student said?” In the Program Implementation tab, Implementation Support, the Student Handbook lists the eight Mathematical Practices in student-friendly language. Listed for MP3 is a strategy for teachers to scaffold students with the practice: “Show and explain. Share your math ideas to help others understand you.” Also, Discuss It supports teachers with another student routine: “Ask your partner: Do you agree with me? Why or why not? Tell your partner: The strategy I used to find the answer was ...” The instructional materials support teachers to engage students in constructing viable arguments. Examples include:

• In Lesson 4, Session 3, Develop, Deepen Understanding, MP3 Construct Arguments states, “After they complete Connect It, have children work in pairs and listen to each other explain how they found whether a number is greater or less. Explaining how they decided which groups have a number that is greater helps children construct viable arguments about quantities. Generalize: Prompt children to identify that there are different ways to compare numbers and quantities.”
• In Lesson 12, Session 3, Develop, Deepen Understanding, MP3 Construct Arguments states, “When children are completing the page, they should be able to communicate their reasoning for coloring shapes a certain color, ringing some and not others, and crossing shapes out as well as leaving some shapes untouched. Generalize: Prompt children to recognize that there are many ways to describe and sort shapes.” 
• In Lesson 23, Session 3, Develop, guides partnerships in how to lead partner discussions. The materials state, “Have children tell a partner how they solved the subtraction problem and wrote the equation. Support as needed with questions such as: How did you start? Why did you solve the problem that way?” 

Ready Classroom Mathematics materials support teachers to engage students in analyzing the arguments of others. Examples include:

• In Lesson 17, Session 1, Explore,  guides partnerships in how to lead partner discussions. The materials state, “Have children tell a partner a story for each equation. Then have them use counters to show their own story in the space above each equation. Support as needed with questions such as: How did you decide which numbers to use in your addition story? How were your stories alike? How were they different?”
• In Lesson 23, Session 3, Develop, Deepen Understanding, MP3 Construct Arguments and Critique Reasoning states, “When children have completed the page, say: A class is given a subtraction story to solve: ‘There are 10 balloons and 3 float away. How many are left?’ Ellen, Mack and Jess have solved the problem. Ellen used pictures of balloons and crossed out the ones that floated away, Mack used her fingers. and Jess used a cube train. Ask: How can the girls get the correct solution when they are not solving the problem in the same way? Generalize: Encourage children to think of different ways they could solve the same problem, and then discuss whether they feel that one way is better for them to use than another.”
• In Lesson 31, Student Worktext, Session 2, Develop, students compare length and height of objects in a picture. The materials state, “Support Partner Discussion: Have children talk in pairs about the comparisons they made. Have them compare the boats, flowers, bats, benches and trees. Make sure they understand that taller refers to height and longer refers to length. Have children circle the longer or taller object for comparison. Support as needed with questions such as: Did you and your partner say the same comparison statement for the same set of objects, or did you say different statements? Did your partner find any objects to compare that you did not? Do you agree with all your partners statements?”

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations that materials explicitly attend to the specialized language of mathematics. 

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. In the Program Implementation tab, an Academic Vocabulary Glossary is provided. This is set up with the vocabulary explicit to each unit. There is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit. There is also a “Connect Language Development to Mathematics” that helps to develop language routines with students. 

The Ready Classroom Mathematics materials provide explicit instruction on the use of mathematical language. Examples include:

• In Unit 1, Beginning of Unit Tab, there is a Build Your Vocabulary page and a Connect Language Development to Mathematics page. The Build Your Vocabulary page is a student work page designed to introduce the vocabulary for the unit. The Connect Language Development to Mathematics page provides information on how to use the student vocabulary page. This page has a vocabulary routine that extends to other units. The routine calls for the following to be done with each vocabulary word: Assess prior knowledge, Say (pronounce) the word, Define the word, and Use the word. This routine is defined only in the Connect Language Development in Unit 1 but is referenced in later units.
• On the Build Your Vocabulary page, students are given two different sets of words, “My Math Words” and “My Academic Words.” The guidance provided to the teacher under the Connect Language Development to Mathematics page states, “My Math Words in all units, My Math Words provides access to prior knowledge and understanding of critical math words and phrases through teacher-guided activities. My Academic Words in Units 4-6, My Academic Words provides an early entry point to those all-purpose academic words students will engage with throughout their study of mathematics. Use the Academic Vocabulary Routine to provide explicit instruction and active engagement.” The Academic Vocabulary Routine directions are then provided and broken up into four parts. The four parts listed are, “Assess Prior Knowledge, Pronounce the Words, Define the Words, Use the Words.” 
• In Lesson 12, Session 3, Develop, the materials provide explicit instruction on the use of mathematical language. Teachers support students with the Latin roots tri- and hex-. “Draw a triangle and a hexagon. Ask children to count the sides of each shape. Tell children that tri- means three and hex- means six. Guide children to complete these sentences: A triangle has ___ sides. A hexagon has ___ sides.” 
• In Lesson 21, Session 2, Develop, Develop Language states, “Why: Introduce children to the term categories. How: Explain that it helps to group related objects together when thinking of ideas for math stories. For example, in the pet store scene there are 8 dogs. The dogs can be divided into two groups, or categories, based on their patterns. One category is spotted and the other is solid. Ask: How many dogs are in the spotted category? How many are in the solid category? How can we combine these two groups into a larger category for a number story?” 
• In Lesson 32 Compare Weight, Session 1, Explore, Describe Measurable Attributes of Objects states, “Hold up the jug of water. Ask: How can you describe the size of this object? Listen for: How tall. How long. How heavy. How much it holds. Explain that weight is the word for how heavy or light something is. If it is hard to lift, it has a lot of weight and we say it is heavy. If it is very easy to lift, it does not have much weight and we say it is light.”

Ready Classroom Mathematics materials use precise and accurate terminology and definitions when describing mathematics.

Lesson Vocabulary is listed on every Lesson Overview page for each section. For example, Lesson 6, Lesson Overview, the following Lesson Vocabulary is listed:

• five: the counting number after 4
• six: the counting number after 5
• seven: the counting number after 6 
• eight: the counting number after 7
• nine: the counting number after 8
• ten: the counting number after 9