Kindergarten - Gateway 2

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Materials attend to the Kindergarten expected fluencies, add and subtract within 5. 

The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills.

The materials attend to the Kindergarten expected fluencies: K.OA.5 fluently add and subtract within 5. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency. Examples include:

• Module 6, Lesson 6, Addition: Developing fact fluency, Student Journal, “Addition: Developing fact fluency.” Students are given addition problems within 5 to practice and solve fluency. 

• Module 8, Lesson 6, Subtraction: Developing fact fluency, Student Journal, “Write the answers on the race track.” Students are given different subtraction problems within 5 to solve and practice fluency.

• Module 8, Lesson 6, Subtraction: Developing fact fluency, Small group 1, “Organize students into pairs and distribute the cards. They mix the cards and place them face up on a flat surface. They take turns to match the subtraction expression with the answer. Extend the activity by placing the cards face down to play a memory game.” Students are practicing subtraction fluency within 5 by playing this game. 

• Each module contains a summative assessment called Interviews. According to the program, “There are certain concepts and skills, such as the ability to route count fluently, that are best assessed by interviewing students.” For example, in Module 8’s Interview 1 has students counting from 21 to 50 and Interview 2 has students demonstrate fluency of adding within 5. 

• “Fundamentals Games” contain a variety of computer/online games that students can play to develop grade level fluency skills. For example Add ‘em up, students demonstrate fluency of adding within 5 (K.OA.5). 

• Some lessons provide opportunities for students to practice the procedural fluency of the concept being taught in the “Step Up” section of the student journal.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Teachers routinely engage students in engaging single and multi-step application problems during whole group and small group portions of lessons. Examples include:

• Module 3, Lesson 2, Number: Identifying groups that have more or fewer (up to 10), Small Group 1, students solve non-routine application problems by comparing quantities. (K.CC.6) “Organize students into small groups and distribute the resources. Ask each group to place a different number of blocks in each cup. Make sure the number is ten or fewer. Have them write the number of cubes in each cup on the cup itself. Then compare the number of cubes in their cups with those of other groups. Extend the activity by asking individual students to find another student who has a great number of cubes, the same number of cubes, or fewer cubes.”

• Module 6, Lesson 4,  Addition: Writing equations (add to), Small Group 2, students solve non-routine addition problems and write matching equations. (K.OA.1) “Organize students into pairs and distribute the resources. One student rolls the cube and places that number of counters on one side of the card. The other student repeats the action, placing the matching counters on the other side of the card. Together, the students count the total and say an addition equation to match. For example, “Three add two equals five.” The counters are removed from the card, and the activity is repeated several times.”

• Module 11, Lesson 2, Addition/subtraction: Solving word problems (acting out), Whole Class, Step 3 Teaching the Lesson, students use concrete tools to solve routine real-world problems involving addition and subtraction. (K.OA.1 and K.OA.2) “Slide 1: There are 9 leaves. 2 leaves blow away. How many leaves are left? Slide 2: 5 cars are in the parking lot. 4 cars drive away. How many cars are left? Slide 3: Kevin has 2 pennies? He finds 3 more pennies. How many pennies does he now have?” 

Materials provide opportunities throughout the grade level, within Thinking Tasks and Word Problems, for students to independently demonstrate multiple routine and non-routine applications of the mathematics. Example include:

• Module 6, More Math, Thinking Task, Question 3, students count and match a quantity with a picture in a non-routine problem. (K.CC.1 and K.OA.3) “Draw dots in each empty box to make the balance picture true. Write an equation to match.” An image shows a balance scale with seven dots on one side and two empty boxes on the other side of the balance. 

• Module 9, More Math, Word Problems, students use place value reasoning to identify and describe quantities in number puzzles in a routine problem. (K.CC.1, K.CC.2, and K.NBT.1) “Selena and Jamar have each written a number. Selena’s number is 2 less than Jamars’s number. Jamar’s number can be shown with a group of 10 counters and 2 more counters. What number did Selena write?” 

• Module 12, More Math, Thinking Task, Question 3, students use the commutative property to reason about and represent a non-routine problem. (K.OA.1 and K.OA.2) “Draw a picture to show 1 + 4 has the same total as 4 + 1.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices across the year and they are often explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, alongside the learning targets or embedded within lesson notes.

MP1 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 5, Lesson 3, Equality: Identifying two parts that balance a total, Step 3 Teaching the lesson, students think about different balancing problems and persevere to find the solution. “Afterward, invite groups to share their ideas and to explain the steps they followed to find the solutions. Ask questions such as, How does your picture show the same groups as your fingers? How do you know your answer is correct? Repeat the activity to identify two groups that balance seven. If students experience difficulty in starting the activity, encourage perseverance (MP1) by asking questions such as: What do you already know? What do you have to find out? Can you explain that another way? What tool have you tried? How did you do that? What different tools can you use?”

• Module 7, Lesson 6, 3D objects: Identifying objects, Maintaining Concepts and Skills, Word Problems, students make sense and persevere in solving an addition word problem with multiple possible answers. “Lisa has 10 blocks. Reece has fewer blocks than Lisa. If they put their blocks together, what number could they show?” The teacher asks, “What is happening in this problem? What do you know about this problem? What do you need to find out? What will we use to solve this problem? How could you show your thinking?”

• Module 8, Lesson 3, Subtraction: Representing situations (take from), Step 3 Teaching the lesson, students make sense and persevere in solving problems when they analyze subtraction situations to determine what they know and what they have to find out. “There are six eggs. Two eggs break. How many are left?” The teacher discusses “the points below (MP1): What is this problem about? What do you have to find out? Will you use addition or subtraction to find the answer? How did you decide? What subtraction sentence can we write to match?”

• Module 9, Lesson 3, Number: Working with position (up to 20), Mathematical practices and processes, students make sense of mystery teen numbers. “MP1 - when students analyze clues to solve mystery number situations, and persevere in their thoughts until they find a possible answer.” Student Journal, page 127, Question a, students are given a number track 1-20, “My number is between 11 and 15.” Teaching the lesson, “If necessary, clarify that a number between 11 and 15 will be greater than 11 and less than 15 (MP1).”

MP2 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 6, Lesson 2, Addition: Writing equations (put together), Step 3 Teaching the lesson, students reason abstractly and quantitatively about addition problems. “Project the first domino showing three and two dots (slide 1). Ask, What numbers are shown on this domino? (MP2) If necessary, remind students that one number is shown on each side of the domino. Confirm that the domino shows the numbers three and two. Ask, What is the total number of dots? What sentence can we write to show the adding? Have the students count all the dots to identify the total. Write 3 add 2 equals 5 on the board. (MP2)”

• Module 8, Lesson 4, Subtraction: Writing equations (take from), Mathematical practices and processes, “MP2 when students create an equation to match a word problem (decontextualize), and relate the equation to a model of the word problem (decontextualize).” Step 4 Reflecting on the work, “Say, Think of a take-away word problem you can create with felt characters. Allow time for the pairs to develop a problem. Then each pair acts out their take-away problem on the felt board for the other students to see, and says how many are left. Invite volunteers to write an equation that corresponds to each word problem on the board (MP2).”

• Module 9, Lesson 1, Number: Making groups that have one more or one fewer (up to 20), Step 3 Teaching the Lesson, students reason abstractly and quantitatively when they “make sense of quantities one more and one fewer than a given quantity, and say the number that each quantity represents.” Students are given a picture of 14 ladybugs, “Make a group of counters to show a quantity that is one more than 14. Allow time for the students to make the group. Ask, What number tells us the number that is one more than 14? (MP2)”

• Module 11, Lesson 3, Addition/Subtraction: Solving word problems (draw pictures), Mathematical practices and processes, “MP2 when students create a word problem to represent an operation”. Step 2 Starting the lesson, “Ask the students to think of and share a word problem that involves addition or subtraction (MP2).”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to meet the full intent of MP3 over the course of the year as it is explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, and alongside the learning targets or embedded within lesson notes.

Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments. In some lessons, teachers are provided questions and sentence stems to help students critique the reasoning of others and justify their thinking. Convince a friend, found in the Student Journal at the end of each module and Thinking Tasks in modules 3, 6, 9, and 12, provide additional opportunities for students to engage in MP3. 

Students engage with MP3 in connection to grade level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Module 1, Lesson 3, Number: Creating groups of pictures to match numerals (1 to 5), Step 2 Starting the lesson, students construct viable arguments as they explain why the total number of objects remains the same despite being rearranged and counted in a different order. “Invite three students to come to the front and stand in line. Say, Let’s all count the students: one, two, three. Point to each student as everyone counts. Repeat the counting, starting from a different student (order-irrelevance principle). Ask the three students to rearrange themselves, then ask the other students, Does the number change if the students move to a different space? Encourage students to explain their answer. Repeat the activity with a new group of students coming to the front. (MP3)”

• Module 3, Lesson 6, Capacity: Making comparisons, Step 2 Starting the Lesson, students construct viable arguments as the reason about the capacity of different containers. “Display containers A, B, and C. Say, Imagine that I wanted to fill each of these containers with rice. Which container would hold the most rice? How do you know? Invite students to share and justify their predictions. Encourage them to describe the attributes of the container that helped them form their prediction. For example, Container (B) is tallest, so it must hold more rice. (MP3)”

• Module 9, More Math, Thinking Tasks, Question 3, students construct a viable argument and critique the reasoning of others as they count and represent teen numbers. “Vincent has written that there are 71 bees in total. How do you know Vincent has made a mistake? You can draw a picture to help.” The correct answer is 17.

• Module 10, Lesson 5, 2D shapes: Identifying shapes, Student Journal, page 145, students construct viable arguments as they explain and justify their sorting decisions with 2D shapes. “Cut out the 2D shapes. Then sort and paste them where they belong on page 147.” There are labels for triangles, circles, squares, non-square rectangles, and other shapes. In Step 3 Teaching the lesson, the teacher encourages students “to sort their shapes in a method of their choice. Afterward, organize students into pairs to compare their sorting and describe their sorting rule. (MP3)”

• Module 11, Student Journal, pages 225- 227, Convince a friend, students construct viable arguments and critique the reasoning of others as they join simple 2D shapes to make larger 2D shapes. “Cut out the 5 shapes and join some of them to make the larger shape on page 227. Fatima thinks she can join 3 shapes to make the shape below. Corey thinks it can only be made with 2 shapes. Who do you agree with? Show how you know.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes. 

MP4 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 5, Lesson 1, Equality: Introducing the idea of balance, Whole Group Lesson Notes, Step 3 Teaching the lesson, students model with mathematics as they reason about equality. “Ask everyone to stand. Say, Let’s pretend to be a pan balance. Put your arms straight out to the sides. Hold a stapler in one hand, and the baseball bat in the other, and turn your back to the students so they can copy your movements. Say, The (bat) is heavier. Make your arm with the (bat) go down. Ask, How could you describe the stapler? Encourage several responses such as, “The stapler is lighter than the bat.” Select two different objects and repeat, with the arms moving to match lighter and heavier as you describe the comparison. (MP4 and MP6) Now select two identical items (for example, glue sticks) and hold one in each hand. Say, The (glue sticks) are the same. Extend your arms straight out to show balance. Repeat with different pairs of classroom objects. (MP4)”

• Module 6, Student Journal, page 127 and 129, Mathematical modeling task, students model with mathematics as they connect a picture representation with a matching equation. Students are given 9 ladybugs to cut out. “Cut out these pictures. Then paste them onto the leaves on page 129.” Students are given a picture of 2 leaves. “Paste ladybugs onto both leaves to complete the picture. Share your thinking.” Below the leaves is a blank equation for students to fill in, “___ + ___ = ___.”

• Module 8, Lesson 3, Subtraction: Representing situations (take from), Small group 1, students model with mathematics as they describe how the model relates to the problem situation and a matching equation. Students are given cards with pictures of subtraction situations and subtraction equation cards. “The subtraction equations cards are spread out faceup and the picture cards are placed facedown in a pile. Students take turns to select a picture card and find the matching subtraction equation card.”

• Module 11, Student Journal, page 223, Mathematical modeling task, students model with math as they compare representations for a given context. “Kylie uses 9 rings to make a paper chain. She uses 5 blue rings and some red rings. Blake wants to use 4 red rings and 5 blue rings to make his paper chain. Will their paper chains look the same? Show how you know.”

MP5 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to identify and use a variety of tools or strategies, working with the support of the teacher and independently, throughout the modules to support their understanding of grade level math. Examples include:

• Module 3, Lesson 3, Number: Comparing numbers (1 to 10), Step 3 Teaching the lesson, students use appropriate tools strategically to compare numbers within 10. “Bring the students together to share their results. Ask, Who used counters to identify the number that is greater? Who used a number track? What about counting? Encourage students to share their strategies. Establish that if using counters, the group that has more represents the greater number. If using a number track, the greater number is on the right because it represents a distance that is farther away from the start of the track. If counting, the greater number is said last (assuming the sequence is correct). (MP5)”

• Module 7, Lesson 4, Number: Analyzing teen numbers, lesson notes state, “MP5 when students choose a tool from the resource center to support their thinking about addition equations”. Step 4 Reflecting on the work, students are given, “10 + 1 = 11, 10 + 2 = 12, 10 + 3 = 13”, “Organize students into pairs and have them work together to prove that the equations are true. Suggest that they work with counters and ten-frames, or draw pictures to verify the equations. (MP5)”

• Module 9, Student Journal, page 185, Mathematical modeling task, students engage with MP5 as they choose appropriate tools and strategies to reason about 3D shapes. Students are given a picture of a basketball, a can of tuna fish, a box of tissues, and a dot cube (die), “Look at these 3D objects. Show other 3D objects that look similar.” Grade K Module 9 Activity notes for MMT and CAF, “Watch for how students determine which aspects of the objects they should attend to, and how the everyday objects relate to the idealized geometric objects. For example, some students may find objects within their room to compare features. Others may use the pictures to look for similarities and differences. Afterward, discuss the different tools, representations, and/or strategies the students used to help them solve the problem.”

• Module 11, Lesson 4, Addition/subtraction: Solving word problems (write equations), “MP5 - when students select and use tools to help them solve word problems”. Student Journal, page 157, Question a, students select and use tools to solve real world problems. “5 friends are playing in the pool. 2 friends get out of the water. How many friends are left in the pool?” Step 3 Teaching the lesson, the teacher asks, “What tool could we use to help figure out the answer? (MP5) Encourage responses such as cubes, counters, coins, and drawing a picture. Remind students that they can select a tool from the resource center to help solve the problem, if needed.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. MP6 is explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes. 

Students have many opportunities to attend to precision in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Lesson 1, Number: Creating groups of objects, Whole group lesson notes, Step 3 Teaching the lesson, students attend to the precision of mathematics by accurately counting a group of objects. “Ask each student to take five cubes, then sit in a large circle with the other students. Say, I will show and say a number, and you put that many cubes on your fingers. Hold your hand out in front of you. Ready? Show two cubes. Repeat with one, three, four, and five at random. After the students show several numbers of cubes, say, Put one cube on your finger. Now, put another one on. Count one, two. Now put another cube on. Count one, two, three. Continue for four and five. (MP6)”

• Module 2, Lesson 4, Number: Writing numerals 7 to 10, and 0, Student Journal, page 33, Question 1, students attend to the precision of mathematics by accurately writing numerals. “Follow the arrows. Trace then write the numerals.” Students practice writing the number 7, 8 and 9.

• Module 12, More math, Thinking tasks, Question 1, students see a picture of 1 hen in a pen and 4 hens coming into the pen, “Look at the picture. Write the total number of hens. ___”. According to the task rubric, “The precision of MP6 is visible and necessary for an accurate count and to write the matching number.” 

Students have frequent opportunities to attend to the specialized language of math in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 3, Module overview, Vocabulary development, students can attend to the specialized language of math as teachers are provided a list of vocabulary terms. “The vocabulary below will be introduced (bolded) and developed throughout this module. The words can be printed as cards from the resource list. The first file contains words that have been introduced in a previous module and the second contains words that are introduced in this module.” These words are also defined in the student glossary at the end of each Student Journal. The words are: Empty, fewer, full, greater, half full, heavier, least, length, lighter, longer, mass, more, number, numeral, shorter. Students are provided with a Building Vocabulary support page. The page includes: Vocabulary term (the bolded terms), Write it in your own words, and Show what it means.

• Module 6, Lesson 1, Addition: Adding two groups (put together), Whole group lesson notes, Step 3 Teaching the lesson, students attend to the specialized language of math by using terminology accurately. “Reinforce this by saying statements such as, Two put with four makes six. Two and four is six. Two and four equals six. Take this opportunity to introduce the mathematical language for addition, add and plus. Ask, Has anybody heard of the words add and plus before? What do you think these words mean? Lead a whole class discussion. Remind students to listen but not interrupt when others are sharing. Have the students give a thumbs-up if they agree with a suggestion or a thumbs-down if they disagree. Encourage students to explain why they agree or disagree. (MP3) At the end of the discussion, explain that each term involves putting two groups together to figure out a total. (MP6)”

• Module 7, Lesson 6, 3D objects: Identifying objects, Small group 1, Sorting 3D objects by name, students attend to the specialized language of math as they identify 3D shapes by the correct name and sort them. Students are given a box of real-world 3D objects and four large signs: cube, cone, cylinder, and sphere. “Organize students into pairs to sort the objects and name each object as they place it with the matching sign. They then count each sorted group.”

While there are examples of the intentional development of MP6, Attend to precision, throughout materials, there is also evidence of imprecise language. Example include:

• Module 10, Lesson 3, Addition: Exploring the commutative property, Step 3 Teaching the lesson, students “attach clothespins to the 8 hanger to represent 2 + 6. Rotate the hanger around to show 6 + 2 = 8.” The teacher says, “These two equations are addition facts. They are called turnaround facts because the two groups we are adding are the same but are turned around.”

• Module 10, Lesson 4, Addition: Introducing the think big, count small strategy, Step 3 Teaching the lesson, “MP6 - when students use correct language to describe the think big, count small strategy”. Directions include, “Invite a student to take a domino from the bag. Ask them to identify the greater number, then use the think big, count small strategy to figure out the total. Make sure they verbalize the strategy as they work. (MP6) For example, This domino shows four and two. The greater number is four. I do not need to count all the dots to find out the total. I just think big and count on two more: four, five, six. Four add two is six.” 

• Module 11, Lesson 1, Addition/subtraction: Interpreting word problems, Step 3 Teaching the lesson, students use key verbs for addition. “MP6 - when students identify and use precise addition and subtraction language.” Students are given a T-chart (slide 1) with the headers addition and subtraction, the teacher records and reads a student-created addition word problem aloud, “Ask, How do you know the problem is about addition? (MP6) Guide the students to discuss the language in the problem. Take note of any key verbs (for example, join, add, and put together) and record them below the addition heading.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices throughout the year and they are often explicitly identified for teachers in several places:  Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes.

MP7 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:

• Module 2, Lesson 5, Number: Introducing the number track, Step 4 Reflecting on the work, students look for and make use of structure while utilizing a number track to count on or back from a given number. “Have the students share their answers to Student Journal 2.5, and describe how they found the missing numbers. Look for students who were able to count on or back from a given number instead of counting from 1 for each example. (MP7)”

• Module 4, Lesson 4, Number: Working with benchmarks of five (Five-frame), Step 3 Teaching the lesson, students look for and make use of structure while answering questions about a five-frame. “Project the five-frame (slide 1) and say, This five-frame helps us see numbers greater than or less than five. Project the five-frame showing three counters (slide 2) and ask, How many counters are there? Are there more than or fewer than five? How many fewer? How do you know? Repeat to show two, four, six, and then eight counters (slides 3 to 6). (MP7)”

• Module 7, Lesson 4, Number: Analyzing teen numbers, Step 3 Teaching the lesson, Big Book, students look for and make use of structure “when they recognize the structure of a teen number (one group of ten and some more) in the scenes of the big book”. In The Bug Day Out, students see a picture of two water slide ride cars, each with ten seats. Ten bugs are in the first car, and 6 bugs are in the second car. The teacher asks, “how are the ladybugs arranged on the boats? Highlight that the ladybugs are seated in a group of ten and some more. Say, 16 is ten and six more. Repeat the discussion for the remaining pages. (MP7)”

• Module 11, Lesson 4, Addition/Subtraction: Solving word problems (write equations), Step 2 Starting the lesson, students look for and make use of structure as they “use the structure of domino arrangements to identify the number dot without counting one by one.” The teacher says, “I am going show a picture of dots. I want you to figure out the number of dots.” “Display one of the domino dot arrangement cards for about three seconds. Have the students share the number of dots they could see. Confirm the number of dots, then repeat the activity with other dot arrangement cards. (MP7)” 

MP8 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade level math concepts. Examples include:

• Module 3, Lesson 3, Number: Comparing numbers (1 to 10), Step 2 Starting the lesson, students look for and express regularity in repeated reasoning by counting orally from a given number. “Ask a student to say a number between five and ten. Count from that number to 15. Then have the class repeat the count with you. Repeat with different students choosing the starting number. Invite a student to start counting from eight and stopping at 15. Repeat with other students, starting from other numbers less than ten. Repeat at other times during the day. (MP8)”

• Module 4, Lesson 5, Number: Working with benchmarks of ten (ten-frame), Step 2 Starting the lesson, students look for and express regularity in repeated reasoning by counting orally from a given number. “Have the students count from 1 to 15. Ask, What number will we say after 15? Invite a student to count from 15 to 20. Then have the whole class count from 15 to 20. Count aloud from 1 to 20. Emphasize the n sound in the teen component of the teen numbers. Then have the students repeat the count with you several times. Repeat at other times during the day. (MP8)”

• Module 7, Lesson 2, Number: Matching representations for 19, 18, and 15, Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning when they “identify a quicker way of figuring out the total of finger representations of the numbers 18 and 19. For example, noticing that only one or two fingers are not raised, so they count back one or two from 20.” Students show 18 then 19 with their fingers and the teacher says, “We can start at ten and count the extra ones to figure out the total. Can you think of a quicker way we could figure out the total?” Students discuss and share their methods. “They may suggest counting back from 20 because there are only one or two fingers being held down. (MP8)”

• Module 10, Lesson 6, 2D shapes: Analyzing attributes of shapes, Student Journal, page 149, students look for and express regularity in repeated reasoning when they notice that the number of corners and the number of sides is the same in each 2D shape and then test and prove the generalization that every 2D shape will have the same number of corners as number of sides. Students see a picture of a square and five other polygons, “Write the number of sides and corners for each shape.” Reflecting on the work, “What do you notice about the number of sides and the number of corners for each shape? Do you think that would be true for all 2D shapes? Can you think of any shapes for which it might not be true? (MP8). Encourage students to share and test their ideas.”