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.”

The materials reviewed for STEMScopes Math Grade 2 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Within each Scope, there is a Home dropdown menu, where the teacher will find several sections for guidance about the Scope. Under this menu, the Scope Overview has the teacher guide which leads the teacher through the Scope’s fundamental activities while providing facilitation tips, guidance, reminders, and a place to record notes on the various elements within the Scope. Content Support includes Background Knowledge; Misconceptions and Obstacles, which identifies potential student misunderstandings; Current Scope, listing the main points of the lesson, as well as the terms to know. There is also a section that gives examples of the problems that the students will see in this Scope, and the last section is the Coming Attractions which will describe what the students will be doing in the next grade level. Content Unwrapped provides teacher guidance for developing the lesson, dissecting the standards, including verbs that the students should be doing and nouns that the students should know, as well as information on vertical alignment. Also with each Explore, there is a Preparation list for the teacher with instructions for preparing the lesson and Procedure and Facilitation Points which lists step-by-step guidance for the lesson. Examples include:

• Scope 4: Compare Numbers to 1,000, Engage, Foundation Builder, Preparation. Teachers “plan to have students work with partners to complete this activity. Prepare to project the Slideshow for students. Print the Student Handout for each pair of students. Gather a set of base ten blocks for each pair, and place them in a resealable bag: 1 flat, 20 rods, and 20 units.”

• Scope 9: Arrays, Explore, Explore 1–Arrays with Concrete Objects, Procedure and Facilitation Points. Teachers will do the following:  “Part I, 1. Read the following scenario: The STEMScopes Toy Factory needs to package up the toys to distribute to all the local toy stores in the next week. The Toy Factory noticed that some of the packages don’t have labels that tell the customer how many toys are in each package. Can you help the toy factory prepare to distribute all the toys and meet its deadline? 2. Divide students into groups of 3 to 4, and place each group at a station. 3. Direct students’ attention to the array at their station. Allow students a few moments to discuss the manipulatives without touching or moving the array. 4. Instruct students to count the objects in the array. Encourage students to discuss the different counting strategies that can be used with their group. 5. Monitor and talk with students as needed to check for understanding using guided questions. Ask the following questions: a. DOK-1 How many objects make up your array? Answers will vary. For example, there are 10 buttons. B. DOK-2 How did you count the objects? Answers will vary. For example, we skip counted by twos. C. DOK-3 Is there another way to count the objects? Answers will vary. For example, we could add $5+5$ to get 10. 6. Give each student a copy of the Student Journal, and direct students' attention to Part I. Ask students to write an equation to represent how many total objects are in the array. Remind students to label the package of toys with the total on the Student Journal. 7. Rotate students through each station, and remind students to complete their copy of the Student Journal for Part I.”

• Scope 14: Time, Explore, Skill Basics–How to Use a Geared Clock, Procedure and Facilitation Points. Teachers do the following: “1. Give a small geared clock to each student. 2. Gather students into a whole-class group, and discuss the basics of using a geared clock. Show students your large geared clock. Identify the parts of the geared clock: the face of the clock, the red numbers (hours), the blue numbers (minutes), the red hand (hour), and the blue hand (minute). Ask the following questions: a. How should I move the hour hand on the clock? By moving the blue (minute) hand to the right, b. What happens to the hour hand as I move the minute hand? (demonstrate) The hour hand is slowly moving to the next number, the next hour. 3. Divide the class into pairs. 4. Model showing various times to the nearest hour and half hour using your large geared clock. Have students show the same times on their small geared clocks. Practice saying a time and then modeling it, while students show the same times on their clocks. Then model a time and see if students can say the time shown. 5. Once students have practiced as a whole-class group with your guidance, tell them that you will ask students questions and they must show their answers to their partners. Remind students to demonstrate a time to the closest hour or half hour. Explain that if they are not sure, they can make their best guesses. 6. Demonstrate a question and answer. Say: What time do we eat lunch? For us, it is close to 11 o’clock. (Show 11 o’clock on your large clock.) Let’s say it’s the weekend and you eat lunch at 11:30. (Show 11:30 on your large clock.) Now listen to the questions and then share your answers with your partners. 7. Ask the following questions. Check for understanding. Randomly ask students to show what time it would be 30 minutes later. This is to make sure they are practicing time to both the hour and half hour. a. What time do you go to bed? b. What time do you eat dinner? c. What time do you wake up during the week? d.What time do you wake up on the weekend? e. What time do you have to be at school? f. What time do you get out of school?  g. What is the latest time you have ever stayed up? h. What is the earliest time you have woken up? 8. When this activity is complete, move on to Explore 2 for students to apply their knowledge of the skills just learned.”

The materials reviewed for STEMScopes Math Grade 2 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

Each Scope has a Content Overview with a Teacher Guide. Within the Teacher Guide, information is given about the current Scope and its skills and concepts. Additionally, each Scope has a Content Support which includes sections entitled: Misconceptions and Obstacles, Current Scope, and Coming Attractions. These resources provide explanations and guidance for teachers. Examples include:

• Scope 4: Compare Numbers to 1,000, Content Support, Current Scope. It states, “Students use their understanding of place value to compare numbers within 1,000 and record these comparisons using the >, =, and < symbols. In addition, students use mental math strategies to add 10 or 100 to a given number 100–900, and to subtract 10 or 100 from a given number 100–900.”

• Scope 7: Addition and Subtraction Problem Solving, Content Overview, Future Expectations. It states,  “In third grade, students find efficient strategies for adding and subtracting within 1,000. They apply strategies based on place value, properties of operations, and the relationship between addition and subtraction. Third-grade students solve multistep problems involving all four operations, and they represent the problems using an equation with a variable. Students assess the reasonableness of answers using mental computation and estimation strategies, including rounding.”

• Scope 8: Money, Content Overview, Teacher Guide, Scope Summary. It states,  “Within this Scope, students will master concepts revolving around working with money. Students learn how to solve real-world problems that involve dollar bills, quarters, dimes, nickels, and pennies and record answers using the appropriate money symbols for dollars and cents.” 

• Scope 12: Length, Content Support, Coming Attractions. It states,  “In fourth grade, students use all four operations to solve measurement problems (including distance, time, liquid volume, mass, and money). Conversions within one system of units are required to express larger units of measure to smaller units of measure.”

The materials reviewed for STEMScopes Math Grade 2 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level and can be found in several places including a drop-down Standards link on the main home page, within teacher resources, and within each Scope. Explanations of the role and progressions of the grade-level mathematics are present. Examples include:

• In each Scope, the Scope Overview, Scope Content, and Content Unwrapped provides opportunities for teachers to view content correlation in regards to the standards for the grade level as well as the math practices practiced within the Scope. The Scope Overview has a section entitled Student Expectations listing the standards covered in the Scope. It also provides a Scope Summary. In the Scope Content, the standards are listed at the beginning. This section also identifies math practices covered within the Scope. Misconceptions and Obstacles, Current Scope, and Background Knowledge make connections between the work done by students within the Scope as well as strategies and concepts covered within the Scope. Content Unwrapped again identifies the standards covered in the Scope as well as a section entitled, Dissecting the Standard. This section provides ideas of what the students are doing in the Scope as well as the important words they need to know to be successful.

• Teacher Toolbox, Essentials, Vertical Alignment Charts, Vertical Alignment Chart Grade K-5. It contains the following information:  “How are the Standards organized? Standards that are vertically aligned show what students learn one grade level to prepare them for the next level. The standards in grades K-5 are organized around six domains. A domain is a larger group of related standards spanning multiple grade levels shown in the colored strip below: Counting and Cardinality, Operations and Algebraic Thinking,  Number and Operations in Base Ten, Number and Operations–Fractions, Measurement and Data, Geometry.” Tables are provided showing the vertical alignment of standards across grade levels.

• Scope 3: Numbers on a Number Line, Home, Scope Overview, Teacher Guide,provides the following information:  “Vertical Alignment, Background Knowledge, First-grade students explored relationships within the place value system. Students gained oral proficiency in counting up from any number to 120, used a written numeral to represent the total amount, and used concrete and pictorial models to develop strategies to add within 100. First-grade students also investigated that the length is the number of same-sized units of length that, when laid end to end with no gaps or overlaps, reach from one end of the object to the other. Prior to second grade, students have been introduced to number lines as a  strategy, and they may have also experienced using a number path to find sums and differences. Future Expectations, In third grade, students will represent and interpret data within several categories using scaled picture graphs, bar graphs, line plots, and number lines. Third grade students measure lengths using rulers marked with halves and fourths of an inch.”

• Scope 9: Arrays, Home, Home, Content Unwrapped, Vertical Alignment, Grade 1, Standard, states to “Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.” Grade 2, “Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.” Grade 3, “Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.”

The materials reviewed for STEMscopes Math Grade 2 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The Teacher Toolbox contains an Elementary STEMscopes Math Philosophy document that provides relevant research as it relates to components for the program. Examples include:

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Learning within Real-World, Relevant Context, Research Summaries and Excerpts, 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 the 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. “If the problem context makes sense to students and they know what they might do to start on a solution, they will be able to engage in problem solving.” (Carpenter, Fennema, Loef Franke, Levi, and Empson, 2015).

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, CRA Approach, Research Summaries and Excerpts, states, “CRA stands for Concrete – Representational –Abstract. When first learning a new skill, students should use carefully selected concrete materials to develop their understanding of the new concept or skill. As students gain understanding with the physical models, they start to draw a variety of pictorial representations that mirror their work with the concrete objects. Students are then taught to translate these models into abstract representations using symbols and algorithms. “The overarching purpose of the CRA instructional approach is to ensure students develop a tangible understanding of the math concepts/skills they learn.” (Special Connections, 2005) “Using their concrete level of understanding of mathematics concepts and skills, students are able to later use this foundation and add/link their conceptual understanding to abstract problems and learning. Having students go through these three steps provides students with a deeper understanding of mathematical concepts and ideas and provides an excellent foundational strategy for problem solving in other areas in the future.” (Special Connections, 2005).” STEMscopes Math Elements states, “As students progress through the Explore activities, they will transition from hands-on experiences with concrete objects to representational, pictorial models, and ultimately arrive at symbolic representations, using only numbers, notations, and mathematical symbols. If students begin to struggle after transitioning to pictorial or abstract, more hands-on experience with concrete objects is included in the Small Group Intervention activities.”

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Collaborative Exploration, Research Summaries and Excerpts, “Our curriculum allows students to work together and learn from each other, with the teacher as the facilitator of their learning. As students work together, they begin to reason mathematically as they discuss their ideas and debate about what will or will not work to solve a problem. Listening to the thinking and reasoning of others allows students to see multiple ways a problem can be solved. In order for students to communicate their own ideas, they must be able to reflect on their knowledge and learn how to communicate this knowledge. Working collaboratively is more reflective of the real-world situations that students will experience outside of school. Incorporate communication into mathematics instruction to help students organize and consolidate their thinking, communicate coherently and clearly, analyze and evaluate the thinking and strategies of others, and use the language of mathematics.” (NCTM, 2000)

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Promoting Equity, Research Summaries and Excerpts, states, “Teachers are encouraged throughout our curriculum to allow students to work together as they make sense of mathematics concepts. Allowing groups of students to work together to solve real-world tasks creates a sense of community and sets a common goal for learning for all students. Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics. They remove the polar separation of being a math person or not, and give opportunities for all students to engage in math and make sense of it. “Teachers can build equity within the classroom community by employing complex instruction, which uses the following practices (Boaler and Staples, 2008): Modifying expectations of success/failure through the use of tasks requiring different abilities, Assigning group roles so students are responsible for each other and contribute equally to tasks, Using group assessments to encourage students' responsibility for each other's learning and appreciation of diversity” “A clear way of improving achievement and promoting equity is to broaden the number of students who are given high-level opportunities.” (Boaler, 2016) “All students should have the opportunity to receive high-quality mathematics instruction, learn challenging grade-level content, and receive the support necessary to be successful. Much of what has been typically referred to as the "achievement gap" in mathematics is a function of differential instructional opportunities.” (NCTM, 2012).” STEMscopes Math Elements states, “Implementing STEMscopes Math in the classroom provides access to high quality, challenging learning opportunities for every student. The activities within the program are scaffolded and differentiated so that all students find the content accessible and challenging. The emphasis on collaborative learning within the STEMscopes program promotes a sense of community in the classroom where students can learn from each other.”

The materials reviewed for STEMScopes Math Grade 2 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Teacher Toolbox provides an Elementary Materials List that provides a spreadsheet with tabs for each grade level, K-5. Each tab lists the materials needed for each activity. Within each Scope, the Home Tab also provides a material list for all activities. It allows the teacher to input the number of students, groups, and stations, and then calculates how many of each item is needed. Finally, each activity within a Scope has a list of any materials that are needed for that activity. Examples include:

• Scope 4: Compare Numbers to 1,000, Explore, Explore 2–Comparing Numbers, Materials, “Printed, 1 Student Journal (per student), 1 Set of Spelling Bee Scorecards (per pair), 1 Exit Ticket (per student), Reusable, 1 Set of base ten blocks (per pair), 1 Resealable bag (per pair)”

• Scope 8: Money, Elaborate, Fluency Builder–Money Match, Materials, “1 Instruction Sheet (per pair), 1 Set of Money Match Cards (per pair), 1 Student Recording Sheet (per student), Reusable, 1 Envelope or resealable bag (per pair)”

• Scope 14: Time, Explore, Skills Basics–How to Use a Geared Clock, Materials, “Reusable, 1 Small geared clock (per student), 1 Large geared clock (per teacher)”

The materials reviewed for STEMScopes Math Grade 2 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

In Grade 2, the Assessment section of each Scope has an activity called Decide and Defend, an assessment that requires students to show their mathematical reasoning and provide evidence to support their claim. A rubric is provided to score Understanding, Computation, and Reasoning. Answer keys are provided for all assessments including Skills Quizzes and Technology-Enhanced Questions. Standards-Based Assessment answer keys provide answers, potential student responses to short answer questions, and identifies the Depth Of Knowledge (DOK) for each question. 

After students complete assessments, the teacher can utilize the Intervention Tab to review concepts presented within the Scopes’ Explore lessons. There are Small-Group Intervention activities that the teacher can use with small groups or all students. Within the Intervention, the lesson is broken into parts that coincide with the number of Explores within the Scope. The teacher can provide targeted instruction in areas where students, or the class, need additional practice. The program also provides a document in the Teacher Guide for each Scope to help group students based on their understanding of the concepts covered in the Scope. The teacher can use this visual aide to make sure to meet the needs of each student. Examples include:

• Scope 6: Addition and Subtraction Strategies, Evaluate, Standards-Based Assessment, Answer Key, Question 2, provides a possible way a student might complete the problem. “2. Miguel needs help solving the problem below. $87-53=$ ___ How can Miguel solve this problem using strategies based on place value? Explain your reasoning and write your answer in the box. (DOK 3) 34, Sample reasoning: I used base ten blocks and placed 8 tens in the tens section of the place value chart and 7 ones in the ones section of the place value chart. First I subtracted the ones: 7 ones − 3 ones = 4 ones. Then I subtracted the tens: 8 tens − 5 tens = 3 tens. 30 + 4 = 34, so 87 - 53 = 34.” (2.NBT.7)

• Scope 14: Time, Evaluate, Standards-Based Assessment, Answer Key, Question 10 provides a possible solution a student might provide. Students see an analog clock with 10:15 displayed. “10. Read the time on the clock. None of these Write the time on the clock in the box below. Explain the steps that you use to tell time on a clock. (DOK 3) It is 10:15. I looked at the hour hand first. It is right past the ten, but not yet 11. I looked at the minute hand next. I counted by fives until I got to the 3, which is 15 minutes.” (2.MD.7)

• Scope 15: Data Analysis, Intervention, Small-Group Intervention, Procedure and Facilitation Points states, “Part I, 1. Prior to beginning the activity, ask students to tell you everything they know about data and graphs. As students answer, check to see if they understand the definitions of data, picture graphs, bar graphs, and line plots. Identify student misconceptions. 2. Display Our Favorite Pet Data. Share with students that you’ve collected some data on students’ favorite pets. You have organized your data in a chart. 3. Explain that you’d like some help creating a picture graph using the data from the chart.”

The materials reviewed for STEMscopes Math Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

Assessment opportunities are included in the Exit Tickets, Show What You Know, Skills Quiz, Technology-Enhanced Questions, Standards-Based Assessment, and Decide and Defend situations. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, and short answer. While the MPs are not identified within the assessments, MPs are described within the Explore sections in relation to the Scope. Examples include:

• Scope 3: Numbers on a Number Line, Evaluate, Decide and Defend, allows students to demonstrate the full intent of 2.MD.6, “Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.” “How Many to Feed? There were 52 students in line to get their lunches from the cafeteria. They were later joined by 20 more students whose class was running late. How many students are in the cafeteria line now? Draw and label a number line that shows your thinking. Describe your reasoning below.”

• Scope 10: Two-Dimensional Shapes, Explore, Explore 3–Drawing 2-D Shapes, Exit Ticket, allows students to demonstrate the full intent of MP6, “Attend to precision: Students use geometric language to identify and describe the attributes of given shapes.” “Draw a shape with 5 sides, 5 angles, and 5 vertices. It is called a ___. Draw a shape with 4 equal sides, 4 right angles, and 4 vertices. It is called a ___. Draw a shape with 4 sides, 4 angles, and 4 vertices with opposite sides that are equal. It is called a ___. Draw a quadrilateral with 1 set of parallel sides. It is called a ___.”

• Scope 15: Data Analysis, Show What You Know, allows students to demonstrate the full intent of 2.MD.9, “Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.” “Data Analysis, Part 4: Organizing Data Using Line Plots, Below are the measurements of sticks that were found in a pile outside the school. Use the data to create a line plot and answer the questions.” Given a table with columns labeled, “Length of Sticks, Number of Sticks” and the number of sticks as tally marks, “11 inches $\vert\vert\vert$, 13 inches $\vert\vert\vert\vert\vert$, 16 inches $\vert\vert$, 17 inches $\vert\vert\vert$, 20 inches $\vert\vert\vert\vert$, How many sticks were found outside the school? ___ What size stick did most students find outside the school? ___ What size was the longest stick found outside the school? ___”

The materials reviewed for STEMscopes Grade 2 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics. 

Within the Teacher Toolbox, under Interventions, materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Within each Explore section of the Scopes there are Instructional Supports and Language Acquisition Strategy suggestions specific to the Explore activity. Additionally, each Scope has an Intervention tab that provides support specific to the Scope. Examples include:

• Teacher Toolbox, Interventions, Interventions–Adaptive Development, Generalizes Information between Situations, supplies teachers with teaching strategies to support students with difficulty generalizing information. “Unable to Generalize: Alike and different–Ask students to make a list of similarities and differences between two concrete objects. Move to abstract ideas once students have mastered this process. Analogies–Play analogy games related to the scope with students. This will help create relationships between words and their application. Different setting–Call attention to vocabulary or concepts that are seen in various settings. For example, highlight vocabulary used in a math problem. Ask students why that word was used in that setting. Multiple modalities–Present concepts in a variety of ways to provide more opportunities for processing. Include a visual or hands-on component with any verbal information.”

• Scope 6: Addition and Subtraction Strategies, Intervention, Small-Group Intervention, provides “a reteach activity that supports student understanding of the concept by reviewing a past skill or reteaching the current skill.” Procedure and Facilitation Points, “Part I,1.  Prior to beginning the activity, ask students to tell you everything they know about different strategies that can be used to add and subtract two-digit numbers. As students answer, check to see if they understand how to use the strategies appropriately. Identify student misconceptions. 2. Give a whiteboard, a dry-erase marker, and a set of base ten blocks to each student. 3. Give the students the equation $42+27$. 4. Discuss first how you can estimate a solution before solving the problem. a. What strategy can we use to estimate a solution? Answers will vary. We can use friendly numbers. We can change 42 to 40, and we can change 27 to 30. Then we can mentally  add 40 and 30 to get 70. 5. Instruct students to build each number. Discuss how many rods (tens) and units (ones) there are for each number. Ask the following questions: a. How many tens are in your model of 42? 4 b. What is the value of the group of tens? 40 c. How many ones are in your model of 42? 2 d. What is the  value of the group of ones? 2 e. How many tens are in your model of 27? 2 f. What is the value of the group of tens? 20 g. How  many ones are in your model of 27? 7 h. What is the value of  the group of ones? 7 6. Ask students to write the value of each group of tens and ones under their blocks on the table. Encourage students to group the tens and ones together to  solve the equation. 7. Instruct students to write a number sentence to find the sum of the group of tens and then a  number sentence to find the sum of the group of ones. Add the  two sums to find the total sum. 8. Discuss whether the estimated solution is close to the actual solution.”

• Scope 13: Area, Explore, Explore 1–Covering Rectangles with Squares, Instructional Supports, ”1. Students will need to use their understanding of addition to find the total area. Provide support for adding multi digit numbers as needed or review the skill if necessary. 2. When working, provide short, explicit feedback on errors before misconceptions are developed.”

The materials reviewed for STEMscopes Math Grade 2 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Within each Scope, Scope Overview, Teacher Guide, a STEMscopes Tip is provided. It states,  “The acceleration section of each Scope, located along the Scope menu, provides resources for students who have mastered the concepts from the Scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.” Examples include:

• Scope 3: Numbers on a Number Line, Acceleration, Math Today–Dinosaur Recycled, Question 1 states, “On the number line below, point A shows how many bottles were collected on Saturday, and point B shows how many were collected on Sunday during one weekend. Label the number line to show how many bottles were picked up on Saturday and how many were [picked up on Sunday.”

• Scope  5: Fractions, Acceleration, Math Today–A Cat’s New Leg states, “Sgt. Stubbs lived a hard life as a stray cat before Adam Schofield of Oak Creek, Wisconsin, adopted him. Sgt. Stubbs got an infection in his two back legs, and they had to be amputated, or removed. Engineering students at the University of Wisconsin–Madison used a 3-D printer to create prosthetic legs with strong straps for Sgt. Stubbs. Now he can use his back legs once again! The students used a rectangular piece of fabric to make the straps for Sgt. Stubbs’s new legs. Question 1, The first strap needs a piece that is one-half of the rectangle. Use your pencil to partition the rectangle into two equal shares. Each piece is one-(half, third, fourth) Question 2, The second strap needs a piece that is one-fourth of the rectangle. Use your pencil to partition the rectangle into four equal shares. Each piece is one- (half, third, fourth)” 

• Scope 10: Two-Dimensional Shapes, Acceleration, Math Today–The Shape of Art states, “Tanya created some mosaic-style art pieces of her own. Mosaic art is created using different shapes that eventually become a picture. Question 1, What shapes did Tanya use to create the pictures above? Question 3, Draw and label the shapes in your own piece of art below. You should include two shapes with 4 vertices.”

The materials reviewed for STEMscopes Math Grade 2 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. 

Within the Teacher Toolbox, the program provides resources to assist MLLs when using the materials. The materials state, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” Examples include but are not limited to:

• “Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language.” 

• “Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates.” 

• “Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses.” 

• “Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases.” 

• “Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe–Try This at Home that students can engage in along with their families. This letter is written in two languages.”

• “Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains.” 

• “Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain.” 

• “Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills.” 

• “Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language.” 

• “Distance Learning Videos – Major skills and concepts are broken down in these student- facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math.”

• “My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well.”

Guidance is also provided throughout the scopes to guide the teacher. Examples include:

• Scope 5: Fractions, Engage, Foundation Builder, Possible Preconceptions, provides the teacher with guidance on challenging words. “The English language has many words that have multiple meanings. Suggested Solution, To eliminate any confusion, ensure that students understand the following words. Word, Possible Student Thinking, Our Intention, In Context, Fair, A gathering where products are sold, Dividing or separating equally, Each person got a fair share of the cake because all the pieces were the same size and shape, Fair, According to the rules, Dividing or separating equally, Each person got a fair share of the cake because all the pieces were the same size and shape. Part, A role, as in a play or movie, A separate piece or section of a whole, James got one part of the cookie cake.”

• Scope 10: Two-Dimensional Shapes, Explore, Explore 3–Drawing 2-D Shapes, Language Acquisition Strategy, provides guidance for the teacher.  “The following Language Acquisition Strategy is supported in this Explore activity. See the strategies below for ways to support a student's language development. Students will connect printed text that is routinely used in classroom materials to basic sight vocabulary. Beginner: Provide an illustrated word wall and preview the words being used in the Explore. Model referencing the word wall while completing the Student Journal and Exit Ticket. Allow students to point to the words/visuals in order to answer the questions.”

• Scope 15: Data Analysis, Elaborate, Fluency Builder–Data Analysis Match, Student Recording Sheet, is provided for students that read, write or speak Spanish. “Pareo de Análisis de datos Hoja de registro del estudiante Al final del juego, escoge dos pareos que hayas hecho. Escribe las letras del pareo. Luego, dibuja una gráfica diferente para representar los mismos datos. Por ejemplo, si los datos en la tarjeta están representados en una gráfica pictográfica, dibuja una gráfica de barras para representar los datos.”

The materials reviewed for STEMscopes Math Grade 2 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. Examples include:

• Scope 3: Numbers on a Number Line, Intervention, Supplemental Aids–Open Number Line, Procedure and Facilitation Points states,  “Number lines are a tool that can be used for a variety of mathematical concepts, including the following: Addition and subtraction, Fractions, Comparing numbers, Ordering numbers, Estimation, Rational numbers, A blank number line can be used as a supplemental aid for students who need assistance visualizing numerical concepts. Display the number line provided on the Student Handout that is applicable to the concepts being taught. Model how to add hash marks and numbers to the number line as needed. You may also cut the Student Handout into strips so that students may write on their own number line. If possible, provide a laminated copy of a number line for each student. The students may then use dry-erase markers to utilize the number line in a variety of problems. During assessment, encourage students to draw a number line at the top of their paper or notebook as a strategy to solve problems.”

• Scope 9; Arrays, Explore, Virtual Manipulative–Linking Cubes, provides a variety of colors of cubes that can be linked to one another in preparation for arrays and multiplication.

• Scope 12: Length, Explore, Skills Basics–How to Use Measuring Tools, Procedural and Facilitation Points states,  “1. Share with students that they will be working to measure two items (a pencil and a notebook) using a ruler and measuring tape. 2. Explain to students that there are rules to using measurement tools by saying: When you use a measurement tool to measure the length of an object, you have to keep the measurement tool straight and close to the edge. Line the measurement tool up evenly with one end and measure to the other end. 3. Tell students that they can draw a start line and stop line to help them. 4. Distribute materials to each group. Instruct students to use their rulers and measuring tapes to measure the length of their notebooks and pencils. 5. Support groups and facilitate discussions as they work to measure a pencil by asking the following questions: a. Where did you start measuring? Where did you stop measuring? Encourage students to identify the starting and ending points. Students can be encouraged to draw start and stop lines. b. How do you know you measured correctly? Answers will vary. Allow students to share the rules that they used to measure their objects.  c. Can you explain to me how your group is using the measurement tool? Answers will vary. Allow students to elaborate on the steps to use a measurement tool.”