Kindergarten - Gateway 2

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

Materials include problems and questions that develop conceptual understanding throughout the grade-level. The Daily Teacher-Led Instruction portion of the lesson provides opportunities for students to explore, engage in, and discuss conceptual understanding of mathematical content. Examples include:

• In Mission 1, Topic E, Lesson 18, Lesson, students count beans in a bag. The materials state, “You have beans in your bag! I wonder how many? Does anyone want to wonder with me? Could you count them without taking them out of your bag? I’d like each of you to take out 4 beans. (Pause.) Now, put them back in the bag. What happened to the 4 beans? We might not be able to see them, but are they still part of the group? This time, take out 4 beans and put them in your cup. Put your hand on top of your cup, and shake them up. Shake harder! Pour them into the circle on your work mat like this. (Demonstrate.) Let’s count how many are inside your circle.” This activity supports conceptual understanding of K.CC.4, understand the relationship between numbers and quantities. 
• In Mission 2, Topic A, Lesson 2, Lesson, students identify triangles and learn their attributes and classifications. The materials state, “We are going to look at some more shapes today to see what else you notice. (Put a triangle on the classroom board.) Tell me about this shape. We call this shape a triangle.” This activity supports conceptual understanding of K.G.2, correctly name shapes regardless of their orientations or overall size. 
• In Mission 4, Topic A, Lesson 4, Lesson, students represent decomposition story situations with drawings using numeric number bonds. The materials state, “Let’s pretend today! Pretend that you have 5 apples. Show me with your cubes how the group of 5 apples would look on your mat. I’m going to draw the linking cubes into this number bond on the board, just like you put them in your whole. Now, pretend that 3 of your apples are red and 2 are green. Show me with your other set of cubes how that would look on your mat. Good! I’ll draw those cubes in the number bond, too. Look carefully at your groups of cubes. Let’s show how they would look in the number bond if we used numbers instead. Take your cubes off, and write the number with your marker as we have done before. Who would like to tell me how to fill in our numbers?” This activity supports conceptual understanding of K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way.
• In Mission 5, Topic A, Lesson 4, Lesson, students count straws the Say Ten way to 19 making a pile for each ten. The materials state, “(Place a linking cube on each of your fingers.) How many cubes do you see? (Ask your helper to place a cube on her right pinky finger.) Now, how many cubes do you see? You’re all correct! Eleven is 10 and 1. I’m going to teach you to count the Say Ten way! (With a linking cube on each finger, raise your hands again.) How many linking cubes is this? Every time Lucy adds another cube to her fingers, we’ll say, ‘Ten’ (show your hands) and the number of ones you see on her fingers. Ready? Excellent! Now, go back to your seats, and we’ll practice counting the Say Ten way using straws.” This activity supports conceptual understanding of K.NBT.1, compose and decompose numbers from 11 to 19 into ten ones and some further ones.
• In Mission 6, Topic A, Lesson 3 Lesson, students build solid shapes using flat shapes. The materials state, “Look at the cube we already have. (Hold it up.) How many squares will I need to use? Let’s count together. What if I trace one of the squares on my paper and cut it out? (Demonstrate.) I will attach it to one of the squares. (Cover one side of the skeleton (cube) with the paper to create a face, and hold the shape up for observation.) What do you notice?” The teacher continues to trace squares, cut them out, and attach them to the skeleton of a cube. This activity supports conceptual understanding of K.G.5, model shapes in the world by building shapes from components.

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. The online Daily Activities provide opportunities for students to practice conceptual understanding independently. Examples Include:

• In Digital Activities, Number to 10, Next Stop Top 8-9, students see ten frames with random configurations of eight or nine, students hit the “Freeze!” button and one of the configurations is displayed along with a number bond. Students use the ten frame to finish filling out the number bond. For example, after hitting “Freeze!” the student may see 5 purple discs and 3 red discs to help fill out the number bond 5 + ___ = 8. Students demonstrate conceptual understanding of K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way.
• In Digital Activities, Numbers to 15, Make and Break 11-15, students use a ten frame, a five frame, and a stack of counters to build teen numbers. For example, students are provided with a filled ten frame and are told to “Make 11.” Students must drag the appropriate number of counters to the five frame. Then students fill out a number bond and an equation after building out the ten frame and five frame, “One part is 10, the other part is 1, what is the whole?” Students demonstrate conceptual understanding of K.NBT.1, compose and decompose numbers from 11 to 19.
• In Digital Activities, Numbers to 10, Make and Break 10, students are shown a ten frame that is partially filled and then asked to “Make 10.” Students drag the needed counters into the ten frame to make 10. Next students are given a number sentence, “5 and 5 make ___,” and fill in the total. Students demonstrate conceptual understanding of K.OA.4, For any number from 1 to 9, find the number that makes 10 when added to the given number.
• In Digital Activities, Numbers to 10, The Counting Train 1-10, students are shown several hot air balloons, pick one, and several animals fall out. Students must count the number of animals and place them in the correct number car of the train. Students demonstrate conceptual understanding of K.CC.4, understand the relationship between numbers and quantities; connect counting to cardinality.
• In Digital Activities, Numbers to 10, Make and Break 6-7, students are shown a partially completed ten frame and asked to “Make 6.” Students drag counters to correctly fill the ten frame. Then students are given a number sentence, “5 and 1 make ___,” and fill in the total. Students demonstrate conceptual understanding of K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way.

The instructional materials for Zearn Math Kindergarten meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade-level. Each lesson begins with three Fluency Practice Activities and development of procedural skill occurs during the Lesson. Examples include:

• In Mission 1, Topic A, Lesson 4, Fluency Practice, Finger Flashes, students are shown a number of fingers by the teacher and students state how many fingers are shown. The materials state, “Concentrate heavily on 5. Use a similar sequence, but interject 5 frequently and repetitiously. Students will be delighted at their ability to instantly recognize the group of 5.” This activity provides an opportunity for students to develop fluency of K.CC.5, count to answer “how many?” questions about as many as 20 things.
• In Mission 2, Topic B, Lesson 7, Fluency Practice, Show Me Shapes, students analyze solid shapes and objects scattered on the rug to gain fluency with recognizing attributes and using geometric vocabulary. The materials state, “Look at the shapes that are on the rug. I will ask you to find a certain kind of shape. When you find it, hold it up. Ready? Show me shapes that have points. Yes. Put them back on the rug, and listen to what I want you to find next. Show me shapes that have no points. Yes. Now, show me shapes that have a curve.” This activity provides an opportunity for students to develop fluency of K.G.2, correctly name shapes regardless of their orientations or overall size.
• In Mission 3, Topic C, Lesson 10, Lesson, students practice the procedural skill of using a balance to determine which item is heavier. The materials state, “I have nothing on my balance, what do you notice? (Place a pencil on one side and a marker on the other side of the balance.) Which is heavier, this pencil or this marker? How do you know?” This activity provides an opportunity for students to develop the procedural skill of using a balance to compare items, K.MD.1, describe measurable attributes of objects such as length or weight.
• In Mission 4, Topic A, Lesson 1, Fluency Practice, Make 5 Matching Game, students practice seeing if two numbers make 5. Directions state, “Shuffle and place the cards face down in two equal rows. Partner A turns over two cards. If the total of the numbers on both cards is 5, then she collects both cards. If not, then Partner A turns them back over in their original place face down. Repeat for Partner B.” This activity provides an opportunity for students to develop fluency of K.OA.5, fluently add and subtract within 5. 
• In Mission 5, Topic B, Lesson 7, Lesson, students practice the procedural skill of using number bonds. The materials state, “Our number bond is not complete! We haven’t shown the parts! What number parts are made by the two colors.” The sample response provided is “10 ones and 5 ones.” This activity provides an opportunity for students to develop the procedural skill using number bonds to decompose numbers, K.NBT.1, compose and decompose numbers from 11 to 19 into ten ones and some further ones.

Following the Daily Teacher-Led Instruction, students split into two groups for practice. The Digital Activities portion of the stations provides games for students to independently practice fluency. Examples include:

• In Digital Activities, Numbers to 5, Sum Snacks Increasing to 5, students count apples to feed animals. The materials state, “Give tiger 2 apples, give lion 4 strawberries, and give fox one apple.” This digital activity provides an opportunity for students to develop fluency of K.CC.1, count to 100 by ones and by tens.
• In Digital Activities, Numbers to 10, Next Stop Top 3-5, students hit freeze and a number appears with two connecting bubbles. One bubble states a number such as 3 and students have to select the number that when added to 1 makes 3. Students are also given the two connecting number bubbles and must determine the total. This digital activity provides an opportunity for students to develop fluency of K.OA.5, fluently add and subtract within 5.
• In Digital Activities, Numbers to 15, Hop, Skip, Splash! 10-12, students see lily pads with consecutive numbers on them and one of the lily pads is missing a number. For example, “8, 9, 10, __, 12, 13.” Students type in the missing number. This digital activity provides an opportunity for students to develop fluency of K.CC.2, count forward beginning from a given number within the known sequence.
• In Digital Activities, Numbers to 5, The Counting Train 1-5, students select a balloon, animals drop from the balloon and students count to determine how many animals dropped from the balloon. Then students select the train car with the correct number to match the written number with the number of animals from the balloon. This digital activity provides an opportunity for students to develop fluency of K.CC.4, understand the relationship between numbers and quantities; connect counting to cardinality.
• In Digital Activities, Numbers to 5, Make and Break 2-5, students are given a five frame and a stack of counters. They are asked to make a number and use the counters to fill the five frame. For example, students are instructed to “Make 2.” Then students are given a number sentence and must fill in the total, “1 and 1 make ____”. This digital activity provides an opportunity for students to develop fluency of K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way.

The instructional materials for Zearn Math Kindergarten meet expectations for being 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. 

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

• In Mission 3, Topic H, Lesson 29, Word Problem, students directly compare two objects with a measurable attribute in common. The materials state, “Demoss had a very small carton of orange juice. His mom poured it into a very tall glass without spilling any juice. Close your eyes, and think about what that might look like. Draw the little carton of juice. Now, draw the juice after she poured it into the big glass. Does Demoss have more or less juice, or does it look different?” This problem allows students to apply mathematics of K.MD.2, directly compare two objects with a measurable attribute in common, to see which object has “more of” or “less of” the attribute, and describe the difference. 
• In Mission 4, Topic D, Lesson 24, Word Problem, students use their personal white board to solve, “Robin had 8 cats in her house. 3 of the cats went outside to play in the sunshine. Draw her cats. Use your picture to help you draw a number bond about the cats. How many cats were still in the house? Can you make a number sentence to tell how many cats were still inside? Share your work with your partner. Did he do it the same way?” This problem allows students to apply mathematics of K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
• In Mission 5, Topic A, Lesson 5, Word Problem, students draw pictures of flutes with holes covered to solve, “Pat covered 16 holes when playing the flute. She covered 10 holes with her fingers on the first note she played. She covered 6 holes on the next note she played. Draw the 10 holes. Draw the 6 holes. Use your drawing to count all the holes the Say Ten way.” This problem allows students to apply mathematics of K.CC.5, count to answer “how many” questions about as many as 20 things.
• In Mission 6, Topic B, Lesson 7, Word Problem, students draw a cake and use a ruler to divide the cake into shareable pieces. The materials state, “Pretend you are having a party. Draw a big rectangle on your personal white board to show a delicious pretend chocolate cake. Now, use your ruler, and draw lines to show how you would slice it to share the cake with the party guests. Where would you draw the lines? How many pieces did you make? Compare your cake to your partner’s. Did you both do it the same way? Who has more pieces?” This problem allows students to apply mathematics of K.MD.2, directly compare two objects with a measurable attribute in common, to see which object has “more of” or “less of” the attribute, and describe the difference. 

The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. Examples include:

• Mission 1, Topic F, Lesson 28, Problem Set, students count and add to solve word problems, "Bobby picked 4 red flowers, Then he picked 2 purple flowers. How many flowers did Bobby pick?" This problem set allows students to apply mathematics of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10.
• Mission 4, Topic A, Lesson 3, Problem Set, students independently engage in solving a non-routine application problem, "Look at the picture. Tell a story about the birds going home to your neighbor. Draw a number bond, and write the numbers that match your story. This problem set allows students to apply mathematics of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10.
• Mission 4, Topic C, Lesson 16, Problem Set, students independently solve addition word problems, "There are 4 snakes sitting on the rocks. 2 more snakes slither over. How many snakes are on the rocks now? Put a box around all the snakes, trace the mystery box, and write the answer inside it." This problem set allows students to apply mathematics of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10.
• Mission 4, Topic C, Lesson 17, Problem Set, students independently solve addition word problems, “Listen and draw. Charlotte is playing with pattern blocks. She has 3 squares and 3 triangles. How many shapes does Charlotte have?” This problem set allows students to apply mathematics of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10.

The instructional materials for Zearn Math 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.

Instructional materials attend to conceptual understanding independently throughout the grade-level. Examples include:

• In Mission 3, Topic F, Lesson 20, Lesson, students compare different length linking cubes. The materials state, “Yes! (Demonstrate.) The 7-stick is longer than the 3-stick, and the 3-stick is shorter than the 7-stick. How did you know? (Discuss comparison strategies. Did they line them up in their minds? Did they mentally match one-to-one? Did they estimate?) Let’s count the cubes on each side. (Count chorally, and write the numbers on the board.) What do you notice about the numbers 7 and 3? Which is more?” This activity provides the opportunity for students to develop conceptual understanding of 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.
• In Mission 4, Topic B, Lesson 8, Lesson, students model decompositions of 7 using shapes from a bucket and write number bonds. The materials state, “Find 4 shapes with three straight sides and three corners, and put them in front of you. You have a set of 4 . . .? Now, find 3 shapes with no corners, and put them in front of you. You have a set of 3. . .? push both of your sets together. How many shapes are in front of you?” This activity provides the opportunity for students to develop conceptual understanding of K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way.

Instructional materials attend to procedural skill and fluency independently throughout the grade-level. Examples include:

• In Mission 5, Topic C, Lesson 10, Fluency Practice, Counting, students count forward from a given number. The materials state, “Count by ones from 11-20, changing the directions both the Say Ten way and the regular way.” This activity provides the opportunity for fluency practice of K.CC.2, count forward beginning from a given number within the known sequence.
• In Mission 6, Topic B, Lesson 6, Fluency Practice, Sprint: Make 10, students practice making 10, “Take out your pencil and one crayon of any color. For this Sprint, you are going to write the missing number needed to make 10. (Demonstrate one example if needed.)” This activity provides the opportunity for fluency practice of K.OA.4, for any number from 1 to 9, find the number that makes 10 when added to the given number.

Instructional materials attend to application independently throughout the grade-level. Examples include:

• In Mission 4, Topic B, Lesson 8, Word Problem, students represent raisins using balls of clay. The materials state, “Ming has 5 raisins. Represent her raisins with the clay. Dan has 2 raisins. Represent his raisins, too. How many raisins are there in all?” This problem provides the opportunity for students to apply the mathematics of K.CC.5, count to answer “how many?” questions about as many as 20 things.
• In Mission 5, Topic C, Lesson 10, Word Problem, students solve, “Ms. Garcia is painting her fingernails. She has painted all the nails on her left hand except her thumb. How many more nails does she need to paint? How many does she have left to paint after she paints her left thumb? Draw a picture to help you.” This problem provides the opportunity for students to apply the mathematics of K.OA.4, for any number from 1 to 9, find the number that makes 10 when added to the given number.

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

• In Mission 2, Topic A, Lesson 3, Lesson, students determine the attributes of a rectangle. The materials state, “We are going to talk about another type of shape today. Look at the shape on the board. Use your math words to tell about it. (Place an exemplar rectangle on the board.) This shape is called a rectangle. (Write Rectangle on board, and affix the shape beneath it.) (Place another rectangle on the board.) Tell about this shape. Hmmm. I wonder if we will have another pattern today. Let’s put this over by the other rectangle. How about this shape? (Place a square on the board.) So, this is a rectangle, too? (Yes.) This special rectangle, in which all the sides are the same length, is called a… How about this one? (Affix to board.) Is this a rectangle? It has straight sides and four corners.” The teacher puts a rhombus and several other shapes on the board asking the students if the shape is a rectangle. This activity develops conceptual understanding and procedural skill of K.G.2, correctly name shapes regardless of their orientations or overall size.
• In Mission 4, Topic C, Lesson 18, Lesson, students solve both addends unknown word problems to 8 to find addition patterns in number pairs. The materials state, “Listen to my silly story: The students were playing with 7 balls on the playground. They accidentally kicked some of the balls into a big puddle, and now, some are muddy! What is one way the balls might look now? Turn and talk to your partner about your ideas. (Allow time for discussion.) Let’s make a math problem about my silly story. Draw 7 balls on your personal white board. (Demonstrate drawing empty circles.) Make some muddy. (Do not draw mud on any of the circles. Let students develop partners on their own.) Student A, show us your drawing. How many of your balls got muddy? Could we make a number sentence for Student A’s picture?” Students continue showing combinations of 7 and writing number sentences. This activity provides the opportunity to apply the mathematics and practice the procedural skill of K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way.
• In Mission 5, Topic B, Lesson 6, Word Problem and Lesson, students solve the Word Problem using pictures and linking cubes. The materials state, “There are 18 students: 10 girls and 8 boys. Show the 18 students as 10 girls and 8 boys. Have one color of your cubes represent the boys and another one the girls from the story in the Word Problem. Show me the boys and girls that were in school. When you are done, check your partner’s work to be sure you agree. Everyone hold up the stick that represents the girls. Hold up the stick that represents the boys. How many girls are there? How many boys are there? Put the boys together with the girls. Count with your partner the Say Ten way to see how many students you have.” This activity provides the opportunity to apply the mathematics and conceptual understanding of K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Materials consistently prompt students to construct viable arguments. Examples include: 

• In Mission 3, Topic B, Lesson 6, Lesson, students compare the length of a linking cube stick to various objects. The materials state, “Find your 10-stick. Look at the items from your mystery bag. Point to something that you think might be shorter than your 10-stick. Now compare the length of your 10-stick with the length of your object. Test your guess. Were you correct? (Allow time for discussion and comparison of the lengths.) This time, point to something that you think will be longer than your 4-stick. Test your guess. Were you correct?”
• In Mission 4, Topic A, Lesson 1, Word Problem states, “Julia went to the beach and found 3 seashells. Her sister Megan found 2 seashells. Draw the seashells the girls found. How many did they find in all? Talk to your partner about how you know.”
• In Mission 5, Topic B, Lesson 8, Word Problem states, “Peter drew a number bond of 13 as 10 and 3. Bill drew a number bond, too, but he switched the 10 and 3. Show both Bill’s and Peter’s number bonds. Draw a picture of thirteen things as 10 ones and 3 ones. Explain your thinking to your partner about what you notice about the two number bonds” 

Materials consistently prompt students to analyze the arguments of others. Examples include:

• In Mission 3, Topic B, Lesson 4, Word Problem states, “Write the following sentence frame on the board and then read it to the students. I am taller than _____. I am shorter than _____. Draw two things on your paper that would make your sentence true. Tell your sentence to your partner. Does he agree that it is true?”
• In Mission 3, Topic C, Lesson 9, Word Problem states, “Put the following sentence frame on the board, and then read it to the students. I am lighter than _______, but I am heavier than _______. Draw two things on your paper that would make this sentence true for you. Show your pictures to your partner. Does he or she agree with you? How much do you think you weigh?” 
• In Mission 5, Topic B, Lesson 9, Word Problem states, “A Pre-Kindergarten friend named Jenny drew 15 things with 1 chip and 5 more chips. Draw 15 things as 10 ones and 5 ones, and explain to your partner why you think Jenny Made her mistake.”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Materials assist teachers in engaging students to construct viable arguments. Examples include: 

• In Mission 3, Topic B, Lesson 4, Note: Multiple Means of Engagement states, “For enrichment, encourage students to explain and defend their placement of shorter than/longer than linking cube sticks to a partner.”
• In Mission 4, Topic C, Lesson 16, Note: Multiple Means of Representations states, “Help students, especially English Language Learners, to have meaningful conversations with each other by teaching them to ask questions, such as ‘Do you agree?’ and ‘Why did you do that?’ Teaching students to ask meaningful questions of each other extends their sharing and holds them accountable for sharing their thinking.”
• In Mission 5, Topic A, Lesson 2, Note: Multiple Means of Action and Expression states, “Deepen students’ understanding by asking them to explain strategies for identifying one more. Then, have them apply their strategies through practice with a partner. Ask students: Could you use the same strategy for solving two more and three more?” 

Materials assist teachers in engaging students to analyze the arguments of others. Examples include:

• In Mission 1, Topic B, Lesson 5, Note: Multiple Means of Engagement states, “For enrichment, students who would benefit from an extension of this lesson could play the role of teacher. The new teacher puts pictures in the appropriate column, but one is incorrect. The teacher asks how many are in the column, and then asks if the pictures are correct. ‘Do you agree with me?’ Have children explain their reasoning.”
• In Mission 3, Topic A, Lesson 1, Lesson, students watch a mock magic show analyzing the teacher’s mathematical thinking regarding measurement. The materials state, “I have two pencils. (Show students pencils of differing lengths.) This pencil is shorter than the other one. Now, close your eyes. (Place the pencils in your fist so that they appear to be equal.) Abracadabra! Look at the pencils now. They are the same length! It’s magic! (Varied responses.) Student C, come look at my pencils, and tell the class what you see. (Have Student C observe the pencils.) You are right. The endpoints of the pencils need to be in the same place for us to compare them fairly. Now, you will get a chance to be the magicians. You and your partner will have two strips of paper. Compare to see which one is longer.”
• In Mission 5, Topic C, Lesson 14, Student Debrief, students try different arrangements of objects to determine which method makes counting easier to track. The materials state, “(Show objects in a circle configuration, and have students count how many. Then, slide the objects to change the circle into a line.) How can you prove that the number is still the same? Tell your partner. Did he prove it to you? What are some ways you proved it? Which ways were the most convincing?”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for explicitly attending to the specialized language of mathematics.

Materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. Examples include:

• In Mission 2, Topic A, Lesson 2, Lesson, students identify shapes as triangles. The materials state, “Yesterday, when you were telling me about your shapes, you used a lot of math words to describe them. What were some of the things you noticed? We are going to look at some more shapes today to see what else you notice. (Put a triangle on the classroom board.) Tell me about his shape. We call a shape like this a triangle. (Write the word Triangle on the board, and affix the shape beneath it. Choose another triangle outline.) Tell me about this shape. (Affix the shape to the board under the first triangle.) I am beginning to see a pattern! How many corners does each shape have? (Three.) How many sides? (Three.) What do the sides look like? So, a triangle has three straight sides and three corners?”
• In Mission 4, Topic D, Lesson 20, Lesson, students use linking cubes to demonstrate 5 take away 3 leaves 2. The materials state, “Yes, 5 take away 3 is 2. There is a special Math Way to write what we just did. We had 5 cubes. I will write the number 5 to show all of the cubes together. (Demonstrate.) There is a special sign we can use when we want to show that we are removing some cubes. It looks like this. (Write the minus sign.) How many did we take away?” Later in the lesson students are instructed to read 5 - 2 = 3 as 5 minus 2 equals 3.
• In Mission 6, Topic A, Lesson 1, Student Debrief states, “Any combination of the questions below may be used to lead the discussion. What words did we use to help us complete our problems in order? Look at the triangles and squares you drew. Are all the sides equal in length? Find someone who drew a shape with equal length sides; find someone who drew a shape with unequal length sides. How did the words first, second, and third help us be good builders today? Can you think of a time when order is important? What would happen if we put our shoes on first and our socks on second? Can you think of other ways that we use words like first, second, and third?”

Materials use precise and accurate terminology and definitions when describing mathematics, and support students in using them. Examples include:

• In Mission 4, Topic C, Lesson 14, Lesson states, “Let’s write 5 + 2. Put your cars together on the track. What number equals 5 + 2? Let’s look at our number sentence. What does the 5 tell us? What does the 2 tell us? What does the 7 tell us?” The suggested student response states, “The 7 tells us about the total number of cars on the track.” 
• In Mission 4, Topic A, Lesson 3, Student Debrief states, “Guide students in a conversation to process the lesson and to debrief the Problem Set if you used it. Look for misconceptions and misunderstandings that can be addressed in the Debrief. Any combination of the questions below may be used to lead the discussion. What is a part? What is the whole? How do they work together?”
• In Mission 6, Topic A, Lesson 1, Lesson states, “Allow time for sharing and discussion. If students build shapes with five sides, or more than six sides, casually mention the name of the shape. Five sides is a pentagon. Seven sides is a heptagon. Eight sides is an octagon. Nine sides is a nonagon. Ten sides is a decagon.”