2nd Grade - Gateway 2

The materials reviewed for STEMscopes Math Grade 2 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

STEMscopes materials develop conceptual understanding throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Conceptual Understanding and Number Sense, STEMscopes Math Elements, this is demonstrated.  “In order to reason mathematically, students must understand why different representations and processes work.” Examples include:

• Scope 2: Represent Numbers to 1,000, Explore, Explore 5 - Even and Odd, with teacher guidance, students develop conceptual understanding by determining whether a group of objects has an even or odd number of members. Preparation, “Plan to divide the class into 6 groups to complete this activity. Print a set of Station Story Mats. Prepare six stations with a story mat and linking cubes. Each Station Story Mat will need the corresponding number and color of linking cubes listed below: Station 1: 13 yellow linking cubes, Station 2: 20 blue linking cubes, Station 3: 19 red linking cubes, Station 4: 17 green linking cubes, Station 5: 18 brown linking cubes, Station 6: 12 orange linking cubes” Preparation and Facilitation Points, “4. Instruct students to begin by counting the total number of pieces of food (linking cubes). Have students share the pieces of food equally by lining up the linking cubes in pairs on the story mat. Tell students that if there is a piece of food left over, they will place it in the bottom square. 5. Instruct students to begin by counting the total number of pieces of food (linking cubes). Have students share the pieces of food equally by lining up the linking cubes in pairs on the story mat. Tell students that if there is a piece of food left over, they will place it in the bottom square.” (2.OA.3)

• Scope 6: Addition and Subtraction Strategies, Explore, Explore 2–Addition with More Than Two 2-Digit Numbers, with teacher guidance, students develop conceptual understanding of addition within 100. Procedure and Facilitation Points, “5. Instruct students to find the total value of each Gem Bag. Explain that they will use the Gem Evaluation Sheet to write a number sentence and show a strategy for how to find the gem bag’s total on the Student Journal. Strategies should use mental math. Encourage students to use the base ten blocks and Place Value Chart to check their mental math strategies and solutions. Have students draw pictorial models of their base ten blocks. 6. Monitor and talk with students as needed to check for understanding by using guiding questions.” (2.NBT.7)

• Scope 15: Data Analysis, Explore, Skill Basics–What Is the Difference Between a Picture Graph and a Pictograph?, Procedure and Facilitation Points, students develop conceptual understanding as they identify and note differences between types of graphs. “1. Give the Types of Graphs handout to each pair of students. Allow time for students to observe each graph and talk with their partners about what they notice. 2. Discuss the following questions: a. What do you notice that is the same about the two graphs? Both graphs have titles; both graphs have labels and data. b. What do you notice that is different about the two graphs? The picture graph uses pictures. The pictograph uses a key and symbols. 3. Guide students as they circle or point out the differences and similarities.  4. Pass out the Student Handout to each student. 5. Support students as they work in pairs to fill in the differences and similarities using the Venn diagram. 6. Bring students together as a whole group to share the similarities and differences each pair wrote on the Student Handout.” (2.MD.10)

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. Examples include:

• Scope 2: Represent Numbers to 1,000, Explore, Explore 1–Grouping Hundreds and Tens to Count Collections, students develop place value understanding within 1,000. Exit Ticket, given a picture of 7 rows with 30 cubes in each row, “Count the collection of cubes shown below. Circle groups of ten and groups of one hundred. Write how many hundreds and tens there are for the total number of cubes. Write how many groups of ten are in this number. Total Number of Cubes =  , ___ Hundreds, ___ Tens, ___ groups of ten in ___” (2.NBT.1)

• Scope 3: Numbers on a Number Line, Explore, Explore 3, Representing Addition and Subtraction on a Number Line, students represent whole-number sums within 100 on a number line diagram. Exit Ticket, “Read the problem and solve it using the open number line. Then write a number sentence that matches how you solved the problem on the number line.1. Two frogs were sitting on a lily pad when a duck flew overhead and scared them. One frog jumped across 65 lily pads before it stopped. The other jumped across 30 lily pads and then stopped. How many lily pads did the frogs jump across altogether? Number Sentence: ___” (2.MD.6)

• Scope 9: Arrays, Explain, Show What You Know–Part 1: Arrays with Concrete Objects, Student Handout, students use arrays and repeated addition to work towards multiplication. “Part 1: Arrays with Concrete Objects There are 3 rows of carrot plants in the garden. Each row has 5 carrots. What is the total number of carrots in the garden? Draw your model using circles. Write two equations to show your work.  ___ rows with ___ in each row equals ___. There are 5 rows of corn stalks. There are 4 corn stalks in each row. What is the total number of corn stalks in the garden?  Draw your model using circles. Write two equations to show your work. ___ rows with ___ in each row equals ___.” (2.OA.4)

The materials reviewed for STEMscopes Math Grade 2 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

STEMscopes materials develop procedural skills and fluency throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Computational Fluency, STEMscopes Math Elements, these are demonstrated. “In each practice opportunity, students have the flexibility to use different processes and strategies to reach a solution. Students will develop fluency as they become more efficient and accurate in solving problems.” Examples include:

• Fact Fluency: Addition and Subtraction, Related Facts Within 10, Fact Fluency–Station 2, Procedure and Facilitation Points, students develop procedural skill, with teacher support and guidance, to fluently add and subtract within 20 using mental strategies. “1. Divide the class into groups of 4. 2. Read the following directions: a. Mix all of the A and B cards together. b. Pass out one card at a time to each person until all cards are passed out. c. The person with the longest hair goes first. Continue going around the circle to the right. d. Each player chooses one card from his or her pile. i. If it is an A card, the player asks one of the following questions to find a match: i. I am looking for a card that has the related fact for ___ + ___. ii. Who has the related fact to the sum of ___ and ___? ii. If it is a B card, the player asks one of the following questions to find a match: i. I am looking for a card that has the related fact for ___ – ____.  ii. Who has the related fact to the difference of ___ and ___? e. When you have a match, place your cards down on the table. Write the related facts in the Student Journal. f. Continue playing until all cards have been matched. g. Mix up the cards, and play again.” (2.OA.2)

• Scope 6: Addition and Subtraction Strategies, Explore, Explore 1–Addition and Subtraction with 2-Digit Numbers, Procedure and Facilitation Points, students develop procedural skill with teacher support and guidance to add 2 digit numbers within 100. “1. Read the following scenario: “Carlos and Santos went to the grocery store with their grandma. As they were placing groceries into the cart, Grandma asked them to calculate how much they were spending by adding the price of each item. The boys asked Grandma if she had a calculator. Grandma’s eyes got wide, and she replied, ‘We didn’t have calculators when I was your age. We just used our brains.’ Can you use your mental math strategies to help Carlos and Santos keep track of how much they are spending on groceries?”... “6. Monitor and talk with students as needed to check for understanding by using guiding questions. a. DOK-1 What strategy did you use to estimate the solution to the problem? b. DOK-3 Why did you choose to use this estimation strategy? c. DOK-1 What strategy did you use to solve the problem? d. DOK-3 Why did you use this strategy?” (2.NBT.5)

• Scope 14: Time, Explore, Explore 3–Hour-and Minute-Hand Clocks, Procedure and Facilitation Points, students develop procedural skill, with teacher support and guidance, to read analog clocks. “3. Instruct students to read the clocks for each flight and find the time on their own geared clocks.Encourage students to discuss how to read the time with their partners. 4. Monitor and talk with students as needed to check for understanding by using guiding questions. a. DOK-3 What do you notice about the clock for this flight? b. DOK-1 Where is the hour hand? Minute hand? c. DOK-3 What do you notice about the hour hand when you are turning the clock hands to a certain time? d. DOK-1 How many minutes are in one hour? e. DOK-2 When we measure the distance the minute hand moves around the clock one time, how many intervals are there? f. DOK-2 If there are 60 minutes in an hour, how many minutes are in half an hour? g. DOK-3 What would be an example of a time to the half hour? h. DOK-2 If there are 60 minutes in an hour, how many minutes are in a quarter of an hour? i. DOK-3 What does “a quarter past” mean? What would be an example of time referred to as a quarter pastAnswers will vary. j. DOK-3 What does “a quarter ’til” mean? What would be an example of time referred to as a quarter ’til means a quarter of an hour (or 15 minutes) until the next hour. ” (2.MD.7)

The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:

• Fact Fluency: Addition and Subtraction, Doubles, Fact Fluency–Game 1, Station Instructions, students demonstrate fluency as they complete addition doubles facts. “2. Present the game instructions: a. Player 1 is the red side of the counter, and Player 2 is the yellow side of the counter. b. Player 1 spins the doubles spinner. c. Player 1 doubles or adds the same number to the number on the spinner. d. Player 1 verbalizes the strategy. ed. Player 1 covers the sum with a counter. f. Player 2 takes his or her turn, repeating the process. g. Play continues until one of the players has placed four adjacent counters horizontally, diagonally, vertically, or in a square. h. If the sum is already covered, the player loses his or her turn.” (2.OA.2)

• Scope 4: Compare Numbers to 1,000, Explain, Show What You Know–Part 2: Comparing Numbers, Student Handout, students demonstrate fluency comparing numbers using accurate symbols. “Compare the following numbers using the <, >, and = symbols. 190___109; 46___64; 816___618; 90___900; 283___238; 445___445” (2.NBT.4)

• Scope 6: Addition and Subtraction Strategies, Evaluate, Skills Quiz, Question 1, students independently demonstrate fluency while students add four two-digit numbers. “55 + 13 + 15 + 27 = ___.” (2.NBT.6)

The materials reviewed for STEMscopes Math Grade 2 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics.

STEMscopes materials include multiple routine and non-routine applications of mathematics throughout the grade level, both with teacher support and independently. Within the Teacher Toolbox, under STEMscopes Math Philosophy, Elementary, Computational Fluency, Research Summaries and Excerpt, it states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful.” 

This Math Story activity includes both routine and non-routine examples of engaging applications of mathematics. For example:

• Scope 6: Addition and Subtraction Strategies, Elaborate, Math Story - Beads, Beads, Beads, students solve both routine and non-routine problems with teacher support. “Read the passage and answer the questions that follow. 3. The first step was counting how many beads they had. Jen pulled out her craft box. Together, she and Sandy counted every color of bead. Then, they ran across the street to Sandy’s house and counted all of her beads. They made a chart to keep track of the bead supply. (The chart is given.) 4.The next step was to figure out how many beads it would take to make a necklace and a bracelet. The girls made several samples. They decided that necklaces needed 100 beads and bracelets needed 40 beads. Then, they set their prices—5 for a necklace and 3 for a bracelet. The next step was to show off their samples and take some orders. Use information from the story to answer each question below. 3. The girls were making a necklace with green and blue beads. If they used 33 blue beads, how many green beads did they use? Show your work in the box below. A 67 green beads, B 133 green beads, C 33 green beads, D 66 green beads” Students solve routine problems while solving word problems. “Use the Bead Color chart in the passage to answer questions 4 and 5. 4. How many purple beads did Jen and Sandy have together before they started making necklaces and bracelets? Choose a pictorial model to represent and solve the problem.” (2.OA.1)

Engaging routine applications of mathematics include:

• Scope 8: Money, Explore, Explore 4–Value of a Collection of Bills and Coins, To-Go Order Cards, students solve routine problems with teacher support as they solve problems involving money. “To-Go Order 1, The customer paid one twenty-dollar bill, two one-dollar bills, three quarters, two nickels, and six pennies. What was the total of this order?” (2.MD.8)

• Scope 15: Data Analysis, Explore, Explore 1–Representing Data Using Picture Graphs, Exit Ticket, students independently solve routine problems as they work with graphs. “You have just collected the following data to add to the class website. Use this data to create a picture graph using one symbol to represent all of the data. Answer the question.” Given a table labeled “Favorite Ice-Cream Flavors” showing  Chocolate with 5, Vanilla with 6, Strawberry with 3, Chocolate chip with 6. (2.MD.10)

Engaging non-routine applications of mathematics include:

• Scope 6: Addition and Subtraction Strategies, Explore, Explore 2–Addition with More Than Two 2-Digit Numbers, Procedure and Facilitation Points, students solve non-routine problems with teacher support as they solve word problems. “1. Read the following scenario: While the museum was closed over the holidays, someone came in and stole 6 bags of gems. Luckily, the person was caught just in time, and all the gems were found. The museum needs us to help find the value of the gems in each bag so that the museum can make sure that all the gems were returned. Can you help the museum find the value of each bag of gems? 2. Divide the class into groups of 3 or 4. Distribute a Place Value Chart, dry-erase marker, set of Gem Bags, base ten blocks, and a Gem Evaluation Sheet to each group. Give each student a copy of the Student Journal. 3. Direct students’ attention to the Gem Bags and Gem Evaluation Sheet. Encourage students to notice the gems in each bag and understand how to find each gem’s value using the Gem Evaluation Sheet. 4. Ask students to begin by looking at the value of each gem in the Gem Bag and estimating the sum of the values using compatible numbers. 5. Instruct students to find the total value of each Gem Bag. Explain that they will use the Gem Evaluation Sheet to write a number sentence and show a strategy for how to find the gem bag’s total on the Student Journal. Strategies should use mental math. Encourage students to use the base ten blocks and Place Value Chart to check their mental math strategies and solutions. Have students draw pictorial models of their base ten blocks.” (2.OA.1)

• Scope 12: Length, Explore, Explore 3–Solving Problems with Length, Exit Ticket, students independently solve non-routine problems with teacher support as they measure. “The teacher wants to put a border all around the edges of her classroom bulletin board. How much border is needed? Use a ruler to measure the total amount of border in centimeters the teacher will need to buy. The teacher will need to buy about ___ total centimeters of border to put around the edges of her bulletin board.” (2.MD.5)

The materials reviewed for STEMscopes Math Grade 2 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, and application include:

• Daily Numeracy: Second Grade, Daily Numeracy-Guess the Number, Procedure and Facilitation Points, students develop procedural fluency when comparing three digit numbers. “1. Gather students together with a sheet of chart paper and a marker. Students should not have anything with them for this activity. 2. According to the number range on the prompt, allow students to ask yes-or-no questions to help guess the number. 3. Respond to students with yes or no, according to the number given on the prompt. Record student questions and guesses on the chart paper so students can see what others have asked. 4. Possible student questions are listed below: a. Is the number odd? Is the number even? (Only for numbers up to 20), b. Is the number greater/less than ___? c. Is the number between ___ and ___? d. Does it have a (digit) in the (hundreds, tens, ones) place? e. Does it have ___ digits? 5. When students have guessed the number, project the answer to the prompt and discuss using relevant guiding questions: a. What questions were the most helpful when guessing the number? b. How did you eliminate other numbers? c. Is the number even or odd? (Only for numbers up to 20) How do you know it is even/odd? d. Can you mentally add 10 to this number? What would the new number be? e. Can you mentally subtract 10 from this number? What would the new number be? f. Can you mentally add 100 to this number? What would the new number be? g. Can you mentally subtract 100 from this number? What would the new number be?” 

• Scope 5: Addition and Subtraction Strategies, Explore, Explore 3–Addition and Subtraction with 3-Digit Numbers, students develop conceptual understanding, with teacher support and guidance, to add 3 digit numbers. Task Cards, “Mom starts with a balance of $262 at the beginning of the month. She knows a $459 paycheck is coming on the 15th. How much money will your family have then? 262+459” (2.NBT.7)

• Scope 15: Data Analysis, Engage, Hook–Animals at the Park, Procedure and Facilitation Points, students develop application of skills as they use data to create a bar graph with teacher guidance. “Part I: Pre-Explore, 1. Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. 2. Show the phenomena video. Ask the following questions: ‘What do you notice? Where can you see math in this situation?’ Allow students to share all ideas. 3. Explain the situation: Tamera and Yolanda were at the park collecting data for a science project. They counted the number of animals they saw in one hour at the park and wrote down the data on a tally chart. After they collected the data, they represented their data on a bar graph with intervals of one. When they got to school with their data, they shared their graph showing the number of animals they saw at the park. Create a bar graph showing what their data might have looked like. 4. Discuss the following questions: a. DOK-1 What information do we know? b. DOK-1 What information do we need to find out? What does their data look like on a bar graph? 5. Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. 6. Move on to complete the Explore activities. Part II: Post-Explore, 1. After students have completed the Explore activities for this topic, show the phenomena video again and repeat the situation. 2. Discuss the following questions: a. DOK-1 What information do we know? b. DOK-1 What information do we need to find out? What does their data look like on a bar graph? 3. Give each student a copy of the Student Handout. Instruct students to use the data in the tally chart on the first page of the Student Handout to help them complete the bar graph on the second page. Allow time for students to create their own bar graphs of Tamera and Yolanda’s data with intervals of one. 4. Discuss the following questions: a. DOK-1 What were the types of animals that were seen at the park by Tamera and Yolanda? b. DOK-2 How many of each type of animal did they see? c. DOK-2 Which type of animal did they see the most? d. DOK-2 Which type of animal did they see the least? e. DOK-2 How many more squirrels than ducks did they see? f. DOK-2 How many ducks and squirrels were seen at the park? g. DOK-4 If they sit at the park for 2 more hours, how many animals do you think they will see?” (2.MD.10)

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

• Scope 7: Addition and Subtraction Problem Solving, Explore, Skill Basics–Problem-Solving Model, Procedure and Facilitation Points, students apply understanding of addition and subtraction alongside conceptual understanding when using addition and subtraction to solve word problems. “1. Divide the class into pairs. 2. Give a Student Handout and dry-erase marker to each student. Give each pair of students one Problem-Solving Model Explanation Sheet. 3. Tell students they will practice solving addition and subtraction story problems using something called a Problem-Solving Model. 4. Direct students’ attention to the Problem-Solving Model Explanation Sheet. Explain each section of the model. 5. Project the first problem from the Story Problem Cards. As a whole-class group, practice solving the problem using the Problem-Solving Model. Model solving as the students follow along and solve on their Student Handouts. a. Read the story problem. b. Say: Look at the first box on the Student Handout. This first box is where we write important information from the problem. 6. Ask the following questions: ‘a. What information do we know from the problem?  b. What information are we trying to find out?’ 7. Model filling in the first box of the Problem-Solving Model. Numbers, names, and important words will be written here. a. Say: ‘Now we need to complete the second box in our Problem-Solving Model. This is where we decide what strategy to use to solve the problem. What are some strategies we could use to solve this problem?’ b. Allow students time to discuss with their partners. Possible strategies include using a bar model, picture, number line, ten frame, etc. 8. Model filling in the second box of the Problem-Solving Model by using one of the strategies suggested by students. a. Say: ‘Now we need to complete the third box in our Problem-Solving Model. This is where we show our solution or write our answer.’ 9. Model writing the answer to the problem in this box. a. Say: ‘Our last step is to complete the fourth box in our Problem-Solving Model. This is where we justify our answer. How can we prove we are correct?’ b. Allow students time to discuss with their partners. Possible strategies include writing a number sentence to check their work, drawing a picture, explaining how they solved in words, etc. 10. Repeat steps 5–9 using the remaining story problems from the Story Problem Cards. Challenge students to complete the fourth problem without your help. Check work as a whole group. 11. Monitor and facilitate discussions as the students work to complete the problem-solving model by asking the following questions: a. Why do you think this strategy is important? b. Can you explain to me what you did during this strategy? c. What was your favorite part of the Problem-Solving Model? 12. As students work through the Explores in this scope, allow them to have access to the Problem-Solving Model Explanation Sheet to use as a reference when solving story problems. 13. When this activity is complete, move on to Explore 1 for students to apply their knowledge of the skills just learned.” (2.OA.1)

• Scope 8: Money, Evaluate, Decide and Defend, students apply understanding denominations of money alongside conceptual understanding as they solve problems involving money. “Michelle wanted to save her money to buy new crayons. She counted the money she had saved. She had 2 quarters, 2 dimes, 3 nickels, and 3 pennies. Her work is below. Did she count and label her money correctly?” Students see 2 quarters, 2 dimes, 3 nickels, and 3 pennies.  The dimes, however, are identified as worth 1 cent and the pennies are worth 10 cents. “Make your claim and describe your reasoning below.” (2.MD.8)

• Scope 14: Time, Explore, Explore 4–Digital and Analog Clocks, Exit Ticket, students apply understanding on telling time on a digital or analog clock alongside conceptual understanding as they work with time. Given 4 analog clocks and 4 digital clocks, “Match the correct digital clock to the correct analog clock.” (2.MD.7)

The materials reviewed for STEMscopes Math Grade 2 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 are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the scopes. 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 the support of the teacher and independently throughout the scopes. Examples include:

• Scope 7: Addition and Subtraction Problem Solving, Explore, Explore 2–Represent and Solve Multistep Word Problems, Standards of Mathematical Practice, “Students explain the meaning of a problem and look for ways to solve it. They check their thinking by asking if the answer makes sense, and if not, they try other approaches.” Water Park Ride Cards, “Lazy River, Word Problem: 92 people were floating in the lazy river. 37 of them were boys, 23 were adults, and the rest were girls. How many of the people floating in the lazy river were girls? Pictorial Model: Students are shown a bar model with 92 in the top and the bottom labeled 37, ?, 23.”

• Scope 8: Money, Standards of Mathematical Practice and Explore 5–Solving Word Problems Involving Bills and Coins, students make sense of word problems involving money and persevere to solve as they analyze and make sense of problems. Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students use coins and bills to solve problems involving money and communicate their strategies for solving them.” Exit Ticket, “Read each word problem. Solve each problem by showing your work in the space provided using an equation or pictorial model. Write your solution. 1. Customer 7 spent 48 cents on fruit. What is one combination of coins that equals this amount? Solution:___, 2. Customer 8 spent 71￠ on a tangerine and pear. The pear cost 24￠. How much did the tangerine cost? Solution:___, 3. Customer 9 bought five cases of fruit. The customer handed you 2 ten-dollar bills, 1 twenty-dollar bill, and 6 one-dollar bills. How much money did the customer spend on fruit altogether? Solution:___”

• Scope 15: Data Analysis, Explore, Explore 3–Solving Problems Using Bar Graphs, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them. Students use a variety of graphs to visually conceptualize and to represent and solve problems.” Students work in groups to solve problems using bar graphs, “1. Read the following scenario: Each second-grade class has been working hard to present facts about their class on their class website. Today you will look at bar graphs showing information from other second-grade classes. Can you use the data presented in each bar graph to solve problems? 2. Divide the class into six groups and assign each group a Bar Graph to begin working. Give each student a copy of the Student Journal. 3. Instruct students to analyze the Bar Graph and discuss the title, intervals, and categories. They will use the information presented in each bar graph to answer the questions. 4. Monitor and talk with students as needed to check for understanding by using guiding questions. a. DOK-1 What is the title of this graph? b. DOK-1 What are the intervals of this graph? c. DOK-1 What are the categories shown on this graph? d. DOK-2 What information do you need to find out? e. DOK-3 How will you solve for the missing information? f. DOK-3 How could you solve using a pictorial model? g. DOK-3 What number sentence could you write to solve for the missing information? h. DOK-1 What operation are you using to solve this problem? 5. Have students solve the problems related to each bar graph by showing a pictorial model and writing a number sentence to show their solutions on the Student Journal. Have students rotate through each Bar Graph…”

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 the support of the teacher and independently throughout the scopes. Examples include:

• Scope 2: Represent Numbers to 1,000, Explore 3–Representing Numbers in Different Ways, while not labeled by STEMscopes as applying MP.2, students reason abstractly and quantitatively while working with place value, as they attend to the meaning of quantities within each place. Procedure and Facilitation Points, “8. Ask students to use the Place Value Chart to help determine the total number of blocks they used for their structures. Ask the following guiding questions as students are organizing their blocks: a. DOK-3 What do you notice about your amount of blocks? b. DOK-2 If one place value has more than ten blocks, what do you need to do to that amount? 9. Encourage students to borrow what they need from the extra blocks available to regroup their blocks. Once all the blocks have been regrouped, students should find the total hundreds, tens, and ones, and write this number at the bottom of their Place Value Charts. 10. Give each student a copy of the Student Journal, and ask students to write their numbers in four ways: standard form, pictorial model (of their original blocks or the regrouped version), expanded form, and word form in their group number’s section of the handout.”

• Scope 4: Compare Numbers to 1,000, Explore, Explore 2–Comparing Numbers, Standards of Mathematical Practice, “Students make comparisons between numbers and represent these comparisons using the symbols >, =, and <.” Procedure and Facilitation Points, “1. Read the following scenario: The school’s spelling bee is complete, and the scores are in! The principal needs our help deciding the winner of each round and determining the overall winner of the contest. Can we help the principal find the winner of the spelling bee? 2. Divide the class into pairs. Give each pair a set of base ten blocks and a set of Spelling Bee Scorecards. 3. Direct students' attention to the Spelling Bee Scorecards and base ten blocks. Allow students a few moments to discover the manipulatives and experience how they could build the score with their partners. 4. Instruct students to look at the Round 1 scorecard from the Spelling Bee. Challenge students to build each number using their blocks and then compare the two scores.” Student Journal, “Comparing Numbers, Compare the number of words each student spelled correctly in more than one way by using the symbols <, >, and = and comparative language: greater than, less than, or equal to. Circle the name of the student who won each round.”

• Scope 13: Area, Explore, Explore 2–Partitioning Rectangles into Squares, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: As students work with the area of a rectangle, they must consider the square units involved and gain the ability to reason and focus on the meaning of the unit quantities.” Exit Ticket, students see a representation of trays of brownies. They then partition the brownies into the appropriate number of equal pieces. “Partition each rectangle and record the number of equal squares in each pan of brownies. Brownies, Rows: 2 Columns: 3, The brownies are partitioned into ___ equal squares.  Brownies, Rows: 3 Columns: 5, The brownies are partitioned into ___ equal squares.”

The materials reviewed for STEMscopes Math Grade 2 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.

The materials provide opportunities for student engagement with MP3 that are both connected to the mathematical content of the grade level and fully developed across the grade level. Mathematical practices are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. Students construct viable arguments and critique the reasoning of others, in connection to grade-level content, as they work with support of the teacher and independently throughout the Scopes. Examples include:

• Scope 3: Numbers on a Number Line, Explore, Explore 3–Representing Addition and Subtraction on a Number Line, students construct viable arguments by using a number line as a concrete referent. “Frog Problem-Solving Cards, CARD 1, Jamaal watched a large bullfrog hop across 24 lily pads. Then he saw a little frog hop across 16 lily pads. How many lily pads did the two frogs hop across altogether?” Student Journal, “Use the number line and counter to act out addition and subtraction for each problem-solving card. Draw the solution for each card and write the number sentence that describes it.”

• Scope 5: Fractions, Explore, Explore 2–Examples and Non-examples, Student Journal, students construct viable arguments by analyzing given representations and recognizing examples and counterexamples as they work with fractions. “Draw a model of each candy bar or cup. Write how many parts it is partitioned into and decide if the parts are equally sized. Explain whether the model is an example or nonexample of halves, thirds, or fourths.” Given an empty circle in the Student Journal and a picture of a circle chocolate cup divided into thirds , “Candy Cup 1, How many parts make one whole candy cup? Are the parts equal in size? This is a(n) ___ of ___ because ___.” 

• Scope 6: Addition and Subtraction Strategies, Explain, Show What You Know, Part 4: Explaining Addition and Subtraction Strategies, students critique the reasoning of others by distinguish correct reasoning from that which is flawed and explain the flaw as they work with addition and subtraction strategies. Student Journal, “Estimate and solve the word problem. Study the two possible strategies. Decide which strategy would not correctly solve the word problem and explain why the strategy is incorrect. James and Amber went digging in their garden for worms to take fishing. Amber found 21 worms, and James found 45 worms. How many worms did they have altogether to take fishing? Strategy 1, The student added 20 and 45 to get 65, and then added 1 more to get 66. The student says James and Amber found 66 worms. Strategy 2, The student added 21 to 50 and got 71, and then counted 5 more to get to 76. The student says James and Amber found 76 worms. Estimate. Solve. Strategy ___ does not work to find the correct answer because ___.” 

• Scope 15: Data Analysis, Elaborate, Fluency Builder–Data Analysis Match, students critique the reasoning of others by deciding if the reasoning of their partner makes sense as they work with graphs. Procedure and Facilitation Points, “2. Model playing the game with a student. a. The first player flips over two cards to try to find a match. b. If the player matches a table to a corresponding picture graph or bar graph, the player keeps the matched set. c. If the player does not find a match, he or she places the turned cards face down again, and it is the next player’s turn. d. Continue taking turns until all the matches have been found. e. The player who collects more cards wins. f. At the end of the game, have each player record two of the matches he or she made on the Student Recording Sheet. Have students record the letters on the bottom of the cards on their Student Recording Sheet. Then, have students draw a different type of graph to represent the same data from the card. For example, if the card shows a picture graph, they draw a bar graph to represent the same data. Students can trade papers with their partner to check each other’s work.”

The materials reviewed for STEMscopes Math Grade 2 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 across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 2: Represent Numbers to 1,000, Explain, Show What You Know, Student Handout,  Represent Numbers to 1,000, Part 1: Grouping Hundreds and Tens to Count Collections, students model the situation by drawing a pictorial model with representations for groups of hundreds and tens. (Students see 160 beads in total.) “Count the collection of beads shown below. Write how many hundreds and tens there are for the total number of beads. Write how many groups of ten are in this number. Draw a pictorial model of how you grouped the beads. There are ___ beads. ___ hundred ___ tens There are ___ groups of ten in ___.”

• Scope 6: Addition and Subtraction Strategies, Explore, Explore 3–Addition and Subtraction with 3-Digit Numbers, Student Journal, students use concrete and pictorial models to solve addition and subtraction word problems with three-digit numbers. “Estimate and solve each task card. Record your solution. Check your strategy using base ten blocks and draw a pictorial model. A, Estimation, Solutions, Number Sentence: ___, Mental Math Strategy:, Pictorial Model”

• Scope 9: Arrays, Show What You Know, Part 1: Arrays with Concrete Objects, students draw a model to represent the number of carrots in the garden and create two equations to represent how they determined the total numbers of carrots. Student Journal, “There are 3 rows of carrot plants in the garden. Each row has 5 carrots. What is the total number of carrots in the garden? Draw your model using circles. Write two equations to show your work. ___ rows with ___ in each row equals ___.”

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 7: Addition and Subtraction Problem Solving, Explore, Explore 4–Represent Addition and Subtraction within 1,000 Using Pictorial Models, students utilize manipulatives and visuals to solve problems. Exit Ticket, “Draw a pictorial model of base ten blocks and a bar model or number line to help solve the problem. Write a number sentence with a symbol for the unknown and a number sentence with the solution. Rayna was at the arcade with her friend Benji. Rayna won 514 tickets. When she combined her tickets with the tickets Benji won, they had a total of 892 tickets. How many tickets did Benji win? Pictorial Model Base Ten Blocks, Pictorial Model Bar Model/Number Line, Number Sentence with Symbol for Unknown, Solve, Answer, Describe the strategy you used to solve the problem. ___” 

• Scope 12: Length, Explore, Explore 2–Inverse Relationships, students build experience with MP5 as they correctly use a ruler to determine the length of their foot in inches and centimeters. Students need to know which side of the ruler represents each unit of measure. Student Journal, “Use a ruler to measure the length of your foot in both centimeters and inches. Draw a number line representing centimeters and a number line representing inches to model your findings. Answer the question to reflect. Centimeters, Inches, Reflect What is the relationship between the size of the unit and the number of units? ____.”

• Scope 15: Data Analysis, Evaluate, Student Journal, students gain experience with MP5 as they use a line plot correctly to answer questions about data collected. “The line plot below shows the length of various pencils measured in the classroom. Use the line plot to answer the questions. 7. How many pencils were measured in all? 8. How many more 8-inch pencils were found than 6-inch pencils?”

The materials reviewed for STEMscopes Math Grade 2 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.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP6 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students attend to precision as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 4: Compare Numbers to 1,000, Explore, Explore 2–Comparing Numbers, Math Chat, students build experience with MP6 as they compare numbers using precise language and symbols to complete the comparisons. “DOK-1 What does the < symbol mean? DOK-1 What does the = symbol mean? DOK-1 What does the > symbol mean? DOK-3 When comparing the two scores on each scorecard, what was the same or different? DOK-3 When might you need to compare two numbers outside of school?”

• Scope 6: Addition and Subtraction Strategies, Explore, Explore 4–Explaining Addition and Subtraction Strategies, Exit Ticket, students attend to precision and the specialized language of mathematics as they explain the reasoning and strategies used to solve problems. “Estimate and solve the word problem. Study the two possible strategies. Decide which strategy would not correctly solve the word problem and explain why the strategy is incorrect. Raquel and Katrina bought a piñata that cost $25. Katrina handed the cashier $32. How much change did Katrina receive from the cashier? Strategy 1 The student added 20 and 30 to get 50, and then added 5 and 2 to get 7. The student says Katrina received $57 from the cashier. Strategy 2 The student started at 25, counted up 5 to get to 30, and then counted 2 more to get to 32. The student added 5 and 2 to get 7. The student says Katrina received $7 from the cashier. Estimate. Solve. Strategy ___ does not work to find the correct answer because ___.”

• Scope 14: Time, Show What You Know - Part 3: Hour- and Minute-Hand Clocks, Student Journal, students attend to precision and the specialized language of mathematics as they practice reading and writing time to the nearest five minutes on an analog clock. Given an analog clock showing 7:45, “Write the time that is shown on each clock. Maria went to school at the time shown below. What time did Maria go to school?”

The materials reviewed for STEMscopes Math Grade 2 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 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 are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 4: Compare Numbers to 1,000, Evaluate, Skills Quiz, Questions 1, 2, 5, and 6, students build experience with MP7 as they look for and use structure with their understanding of place value to compare numbers. “Put a <, >, or = in the circles below to make the statements true. 1. 598, 543; 2. 109, 142; 5. What number is 10 more than 562? ___; 6. What number is 10 less than 195? ___” 

• Scope 5: Fractions, Explore, Explore 1–Partitioning Objects, Math Chat, students build experience with MP7 as they use structure to notice as a shape is partitioned into more equal pieces, each individual piece is smaller in size. “DOK-3 Ask students to observe each group’s quilt. What do you notice about the red pieces of fabric? DOK-1 How many halves equal one whole? DOK-1 How many thirds equal one whole? DOK-1 How many fourths equal one whole?DOK-4 How do we use fractions in everyday life? DOK-2 What do you notice about the size of each part as you partition your object into more and more parts? DOK-1 What is a new vocabulary word for the whole thing that you are cutting into equal shares? DOK-1 What do we call a whole that is partitioned into two equal shares? DOK-1 What do we call a whole that is partitioned into three equal shares? DOK-1 What do we call a whole that is partitioned into four equal shares? DOK-2 Is there more than one way a rectangle can be partitioned into 4 equal parts? What are the different shapes that can be made from these fourths?” 

• Scope 15: Three-Dimensional Solids, Explore, Explore 2–Classifying 3-D Solids, Exit Ticket, students build experience with MP7 as they use structure and attributes to identify shapes. “I am a 3-D solid with 6 rectangular faces. The 4 angles on my faces are right angles. I have 8 vertices and 12 edges. What solid am I? I am a 3-D solid with 1 face that is a circle and 1 apex. I have no edges. What solid am I? I am a 3-D solid with 2 triangular faces with acute angles and 3 rectangular faces with right angles. I have 6 vertices and 9 edges. What solid am I? I am a curved solid with no faces, vertices, or edges. What solid am I? I am a 3-D solid with 6 square faces. Each face has 4 right angles. I have 8 vertices and 12 edges. What solid am I? I am a solid with 2 circular faces. I have no vertices or edges. What solid am I?”

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with the support of the teacher and independently throughout the Scopes. Examples include:

• Scope 2: Represent Numbers to 1,000, Explore, Explore 4–Counting and Place Value Patterns, Exit Ticket, students build experience with MP8 as they use repeated calculations and patterns when counting by different numbers. “Start at the given number. Skip count by fives, tens, or hundreds to find the next five numbers in the pattern. Answer the questions. Given Number, 49, Skip count by FIVES to find the missing numbers. 49 ___, ___, ___, ___, ___, Is the number 83 part of this pattern? Why or why not? Given Number, 121, Skip count by TENS to find the missing numbers. 121 ___, ___, ___, ___, ___, Is the number 531 part of this pattern? Why or why not? Given Number, 273, Skip count by HUNDREDS to find the missing numbers. 273 ___,____, ___, ___, ___, Is the number 873 part of this pattern? Why or why not?” 

• Scope 6: Addition and Subtraction Strategies, Explain, Show What You Know Part 1: Addition and Subtraction with Two 2-Digit Numbers, Student Handout, students build experience with MP8 as they explain pictorial strategies to efficiently add numbers. “Part 1: Addition and Subtraction with Two 2-Digit Numbers Estimate, and then use your mental math strategies to solve the problems below. Use base ten blocks to check your strategy. Draw a pictorial model. 1. Peter had 24 toy cars and 33 toy motorcycles. How many toy cars and motorcycles did he have? Estimation: Solution: Pictorial Model: Explain your strategy. 2. Mark had 85 toy cars. He gave Peter 24 of his toy cars. How many toy cars does Mark have now? Estimation: Solution: Pictorial Model: Explain your strategy.”

• Scope 9: Arrays, Evaluate, Skills Quiz, Question 1 and 8, students build experience with MP8 as they notice and use repeated addition as they count the items in each row and column of an array. Question 1, students see stars in a four by three array. “Use repeated addition to find the total number of objects in each set. Write a repeated addition equation to show the total.” Question 8, “Carly had 8 dot stickers. She arranged them in an array. Draw two different ways she could have arranged them. Write a repeated addition equation to show the total.”