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 that the underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

Materials engage students in both problems and exercises through the grade level. Problems where students learn new mathematics are typically found in the Lesson and Word Problem of the Daily Teacher-Led Instruction. Examples include:

• Mission 2, Topic B, Lesson 6, Word Problem states, “Have students work with a partner. Give each set of students a small ball and a cube. We are going to do a test. Take turns with your partner. Roll the ball back and forth between you a few times. Watch the ball carefully as it rolls. Now, try to roll the block between you. Talk to your partner about what happens. Why do you think the objects behave so differently? What would be the best way to get the block to your partner? Why don’t cups that have a circle on the bottom roll off the table? Note: This Word Problem requires students to start thinking about the differences between balls and cubes in preparation for today’s lesson.”
• Mission 3, Topic D, Lesson 14, Lesson, students explore conservation of volume by pouring. The materials state, “In the last lesson, we talked about the capacities of our containers. I wonder what the capacity of this bowl is. How could I find out? Tell me when to stop! (Use a spoon to fill the bowl.) There. Let me draw how the rice looks in this bowl on my recording sheet. (Demonstrate.) look at this bottle. I wonder if the capacity of the bottle is more or less than the capacity of the bowl. How could we find out? Good idea! I will use this funnel so I don’t lose any. (Pour the rice into the bottle.) What do you notice? Hmmm. I didn’t spill any. What do you think happened? Yes. The capacity of the bottle is more than the capacity of the bowl. Let me draw how the rice looks in the bottle. (Draw.) What will happen if I pour the rice back into the bowl?”
• Mission 4, Topic C, Lesson 15, Lesson, students represent decomposition and compositions addition stories to 8. The materials state, “We are going to play the gravity game today! Let’s pretend my cubes are space rocks. Help me count how many rocks I am putting into my cup. I have 8 space rocks in my cup. This side of the tapes is the land (point). I will use gravity and my magic tape line to help me find some number sentences about 8. How many space rocks fell on land, and how many fell into the ocean? Let me shake it 8 times, and then, I will pour it out to see what happens! (Demonstrate and pour the cubes onto the surface.) What happened? Can we make a number sentence about our picture? Write the number sentence on your personal board. Did anyone think of a different number sentence that tells how our cubes look right now? (Allow time for sharing and discussion.)”

Exercises where students apply learning to build mastery are typically found in the Fluency portion of the daily, Teacher-Led Instruction and the Digital Activities and Problem Set during Two Stations. Examples include:

• In Mission 4, Topic G, Lesson 33, Fluency Practice, Core Fluency Differentiated Practice Sets states, “This activity assesses students’ progress toward mastery of the required fluency goal for kindergarten: Add and subtract within 5. Distribute Practice Sets A, B, or C based on student performance in Lesson 30. Students who correctly answered all questions on a Practice Set in the previous attempt should move to the next practice Set. All other students should try to improve their scores on Practice Set A. Students complete as many problems as they can in 96 seconds or the time allotted. Assign a counting pattern and start number for students who finish early, or have them play an independent game like the Make 10 Memory Game (Lesson 28). Collect and correct any Practice Sets completed within the allotted time.”
• In Mission 5, Topic A, Lesson 5, Problem Set, “Direct students to circle 10 objects and check the extra ones. Have them count the total using the Say Ten way. Watch to see that they count the 10 ones within the circle first from left to right, row by row. They then match the drawing to its numerical representation.”
• In Digital Activities, Numbers to 15, Sum Snacks 10-15, students see an animal with a basket of fruit. The materials state, “Frog has 10 apples. Give him 1 more.” Students continue adding fruit to the animal’s baskets as directed.

The instructional materials reviewed for Zearn Math Kindergarten meet expectations that the design of assignments is not haphazard: exercises are given in intentional sequences.

Lesson activities within each Mission are intentionally sequenced developing student understanding and leading towards mastery of the content. In each lesson students explore concepts, create concrete and pictorial representations, and participate in math discussions. Following the lesson, students participate in Stations. Digital Activities are designed to build number sense, and Problem Sets are designed to provide practice of lesson concepts and fluency.

The instructional materials reviewed for Zearn Math Kindergarten meet expectations that there is variety in what students are asked to produce. For example, students are asked to produce answers and solutions; but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

While engaged in lessons and Problem Sets during Two Stations, students are prompted to produce both oral and written answers. Students work in whole groups, small groups, and with partners during lesson instruction and are prompted to produce arguments and explanations. Example include:

• In Mission 2, Topic B, Lesson 6, Lesson, students find and describe solid shapes using informal language without naming. The materials state, “I have something new for you to explore today! You will be working with your partner. Please take everything out of your bag. I will give you a few minutes to look and talk with your partner about what you notice. Place your things on your desk. Stand up and look down at them as though you were a bird. What do you notice? Now pretend you are an ant. Bend down and look from eye level across the top of your desk. When we did this with your flat shapes, you said you couldn’t see them anymore. What happens this time? You’re right. They are not flat. We call these solids. Find the solid that looks like this. (Hold up the sphere.) Tell me about this solid. (Hold up the cube.) Look at this solid. Find the one that looks like it on your desk. How is it different? (Continue examining the solids until students have had a chance to describe them all. Encourage the students to use language such as edges, corners, sides, points, and curves in their discussion.) Put your shapes back in the bag. Take out your detective materials. You and your partner are going to hunt for these shapes around our classroom. When you find one, draw it on your paper. (Allow students five minutes to identify some of the solids in the environment.) Please return to your seats. Would anyone like to show and share about what they found?”
• In Mission 4, Topic E, Lesson 28, Word Problem states, “Use your clay to make 10 tiny grapes. With your marker, draw a pretty plate on your personal white board. Now, put some of the grapes on the plate. How many grapes do you have in all? How many grapes are on the plate? How many are not on the plate? Draw a number bond about your work.”
• In Mission 6, Topic B, Lesson 5, Fluency, Finish Line states, “(Distribute linking cubes as 10-sticks.) How many cubes do you have? (Give students time to count if necessary). Pretend that your 10-stick of cubes is a little train. (Have students orient their trains the same way by giving them a point of reference in the classroom.) Put your finger on the first cube. Let’s use our number order words as we touch each cube. Ready? Good. Now, break apart your cubes so none are connected. (Give students a moment to do this.) This time, I want you to pretend that they are little people running in a race! The start line is the edge of your personal white board. The finish line is the opposite side of your board. Watch me make my people run. (Demonstrate how to make cubes run.) On your mark, get set, go! (Allow about 10-30 seconds for students to participate.) Stop! The race is over. (Do not allow students to change the position of the cubes at this point.) Get out your marker. Listen carefully to what I want you to do. Circle the first runner. Mark an X next to the tenth runner. Underline the fifth runner. Now, point and show your partner who is first, second, and so on.”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations that manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods. 

Digital Activities provide online tools and virtual manipulatives to enhance learning. Each Mission’s Lesson provides a detailed list of which materials are needed for the Fluency activity, Word Problem, and Lesson. Examples include:

• In Mission 1, Topic C, Lesson 8, Word Problem, Materials Needed states, “Counters in a bag.” Manipulatives are used to help students learn “that the total count is not changed when objects are arranged in different orientations.”
• In Mission 3, Topic E, Lesson 16, Lesson, Materials Needed states, “My square recording sheet (Template), 1 four-inch square of construction paper, 1 four-inch diameter paper circle, 20 one-inch paper or plastic square tiles, 1 small bag of large flat beans, my square recording sheet (Template).” Students use manipulatives to make informal comparisons of area. The materials state, “I wonder how many beans you would need to cover your square? (Various responses.) Work with your partner to put as many beans as you can on your square without piling them. (Allow time for experimentation and discussion.)”
• In Mission 5, Topic B, Lesson 9, Fluency, Grouping Teen Numbers into 10 Ones, Materials Needed states, “Bag with about 20 small objects and work mat. Note: The bags should have a variety of objects between 11 and 20.” Students use manipulatives to “Practice separating and counting objects as ten ones and some ones” to solidify understanding of teen numbers.

The instructional materials reviewed for Zearn Math Kindergarten meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Each Mission Organizer contains Notes on Pacing for Differentiation. Some lessons include a Multiple Means of Representation side box in the Teacher’s Full Mission PDF that provides scaffolding strategies. Examples include:

• In Mission 2, Overview, Notes on Pacing for Differentiation states, “If pacing is a challenge, consider omitting lessons 5 and 8. Instead, embed experiences with position words in other content areas and throughout the students’ day. It is not essential that students be introduced to position words through the context of shapes.”
• In Mission 3, Topic A, Lesson 3, Note: Multiple Means of Representation states, “Students who are struggling to make comparisons may benefit from extra practice. Determining what objects are longer than or shorter than helps to prepare students for comparing two different lengths with a third object in this lesson.”
• In Mission 5, Overview, Notes on Pacing for Differentiation states, “If writing numbers 21-100 overwhelms students, omit the Problem Sets in Lesson 15, 16, and 17. Instead, complete the verbal counting activities in the lessons that prepare them for numeral writing to 100 as required in Grade 1. This allows for completion of these three lessons in just one or two days. Lesson 19 is exploratory in nature and addresses some standards beyond the level of Kindergarten. It works well as an extension lesson if students are advancing quickly, but if pacing is a challenge, it could be omitted.”
• In Mission 6, Topic A, Lesson 1, Note: Multiple Means of Engagement states, “Scaffold understanding of ordinal numbers by modeling them for students who may need additional support. Ask students to get up one at a time to demonstrate first in line, second in line, and third in line. While pointing to each corresponding student, have students practice saying who is first, second, and third in line.”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for providing teachers with strategies for meeting the needs of a range of learners. Both the Multiple Means of Representation side boxes in the Teacher’s Full Mission PDF and Using Digital Activities to Support Each Student’s Developing Math Understanding provide strategies for meeting the needs of a range of learners. Examples of strategies for meeting the needs of a range of learners include:

• In Mission 2, Topic A, Lesson 1, Note: Multiple Means of Engagement states, “For enrichment, ask questions that engage thinking at higher levels. ‘What would that shape look like if it was not flat? Can you make a picture of that shape but make it so that it is sticking up?’”
• In Mission 5, Topic A, Lesson 1, Note: Multiple Means of Action and Expression states, “For enrichment, challenge students by providing extensions to the Word Problem such as: 1. If Marta had 15 peanuts to start with, how many does she have left? 2. How many more peanuts does Marta need to have 10 in her hand? 3. Draw a picture to show Marta’s peanuts.”
• In Mission 6, Topic A, Lesson 6, Note: Multiple Means of Engagement states, “Students who need additional support may benefit from extra practice creating a variety of three- and four-sided shapes. Give them extended time with a geoboard.”
• Kindergarten Guide to Using Digital Activities, Using Digital Activities to Support Each Student’s Developing Math Understanding, Mission 1, Hop Skip Splash! 10 Activities, Multiple Means of Engagement, “This intentional limited use of language allows students to focus on the mathematics without having to overcome any language barriers. Offer sentence frames such as “I knew to count forward because…” or “When the first number in the sequence was not 1, I had to…”
• Kindergarten Guide to Using Digital Activities, Using Digital Activities to Support Each Student’s Developing Math Understanding, Mission 3, Sum Snacks, 6 Activities, Multiple Means of Engagement, “The prompts used in Sum Snacks are deliberately short, and the combination of on-screen text and on-screen pictures of the animals and fruit will help ELLs with language development, both mathematical language and everyday language. Offer sentence frames such as “I know to stop adding fruit when…” or “I found the total by…” or “I need more to make ten.”
• Kindergarten Guide to Using Digital Activities, Using Digital Activities to Support Each Student’s Developing Math Understanding, Mission 5, The Counting Train, 6 Activities, Multiple Means of Engagement, “In order to further support language development, consider using the guiding questions above to encourage students to make connections between representations and language. Offer sentence frames such as “I found the total by…” or “The train helped me see that…”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Within the lesson, Word Problems and Problem Sets provide opportunities for students to solve using multiple entry-points. Examples include:

• In Mission 2, Topic A, Lesson 2, Word Problem states, “It’s pizza time! On a piece of paper, draw a large, round pizza pie. Don’t forget your favorite toppings! With your crayons, show how you would cut the pizza into enough slices for your family. Compare your slices to those of a partner. Are they alike? Carefully describe the shape of a slice to your partner. Note: The purpose of this problem is two-fold; first, to have the students create three-sided figures, and second, to set up a potential non-example for use later in the lesson. The curved edge of the crust in their drawing means that the slices are not actually triangles.”
• In Mission 4, Topic C, Lesson 15, Word Problem states, “You are having a party! You get 8 presents. 2 presents have stripes, and 6 presents have polka dots. Draw the presents, and write the number sentences two different ways on your personal white board. Note: Decomposition and composition of the number 8 serves as an anticipatory story context for this lesson.”
• In Mission 6, Topic B, Lesson 5, Lesson states, “Find two squares in your pattern block box. How do you know they are squares? (S: They each have four sides.The sides are all the same length. They have corners like an L. They look like the face of a cube!) Place the squares on your personal white board. See if you can make a different rectangle from your squares. (Pause.) Tell me about your work.”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

Many lessons include a Multiple Means of Representation side box in the Teacher’s Full Mission PDF that provides strategies for meeting the needs of English Language Learners. Examples of strategies provided for English Language Learners include:

• In Mission 2, Topic A, Lesson 2, Note: Multiple Means of Engagement states, “Support English Language Learners’ capacity to discuss how the shapes they made on their geoboards are examples of triangles by providing them with sentence frames such as, ‘My shape is a triangle because it has . . .’ to use as discussion starters with their partners.”
• In Mission 3, Topic D, Lesson 15, Note: Multiple Means of Action and Expression states, “Scaffold the lesson for English Language Learners by using motions. For example, hold up the scoop when directing students to count the scoops it takes to fill their containers, and hold up the funnel when directing students to use the funnel if they need it.”
• In Mission 5, Topic A, Lesson 5, Note: Multiple Means of Action and Expression states, “Support English Language Learners by using gestures during the lesson. Flash 10, and gesture with your hands for the word. Flash 1. Gesture again for the word. This engages students to figure out the intent and bypasses potential confusion in oral directions.”
• Kindergarten Guide to Using Digital Activities, Using Digital Activities to Support Each Student’s Developing Math Understanding, Mission 2, The Counting Train, 4 Activities, Multiple Means of Engagement, “The Counting Train was specifically designed to limit the use of language, allowing all students, including English Language Learners, greater access. There are no on-screen directions for students to read, and the activity remains constant: select the number that represents the total number of objects. This intentional limited use of language allows students to focus on the mathematics without having to overcome any language barriers.”
• Kindergarten Guide to Using Digital Activities, Using Digital Activities to Support Each Student’s Developing Math Understanding, Mission 4, Sum Snacks, 10 Activities, Multiple Means of Engagement, “It is common for ELLs to struggle with numbers 11 to 19 as their names do not make their meanings clear nor is there a clear language pattern from 11 to 19. Hearing these numbers read aloud while also having a visual representation on screen will help students master the numbers 11 to 19. Offer sentence frames such as “I know to stop adding fruit when…” or “I found the total by…”
• Kindergarten Guide to Using Digital Activities, Mission 6, Make and Break, 5 Activities, Multiple Means of Engagement, “To help support K students still learning to read, including English Language Learners (ELLs) and other students of special populations who would benefit from extra audio support, Make and Break uses audio prompts to direct students. Make sure your students know that they can replay the directions by pressing the read aloud button on each screen. The prompts used in Make and Break are deliberately short, and the combination of on-screen text, color, and the on-screen five frame will help ELLs with language development, both mathematical language and everyday language.”

The instructional materials reviewed for Zearn Math Kindergarten meet expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

The materials have very few graphics of adults and children. When seen, a variety of demographics and personal characteristics are presented. A variety of names are used in word problems. Examples include:

• 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 4, Topic B, Lesson 12, a picture of a female student with brown skin is shown to represent the relationship between 5 and 10. The materials state, “A student demonstrates 7 as 5 on the top and 2 on the bottom.”
• In Mission 6, Topic B, Lesson 7, Fluency Template, a picture of a clipart, female, coach with brown skin is shown at the top of the My Sprint Progress Log.