The materials reviewed for STEMscopes Math Grade 1 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 3: Add and Subtract within 20, Explore, Skill Basics-Strategies to Use to Add and Subtract (to 20), Procedure and Facilitation Points, students develop conceptual understanding as they use strategies to add and subtract to 20. “Part II: Making Ten, 1. Give a dry-erase marker and whiteboard to each student. 2. Ask students to write the equation $8+6=$? on their whiteboards. 3. Instruct students to use the Double Ten Frame mat to model this problem and learn the strategy of how to make ten. 4. Have students put 8 counters in the first ten frame. In the second ten frame, have them put 6 counters. Ask the following questions: a. How many total counters are on the double ten frame mat? 14, b. How can we move some of the counters from our second ten frame to fill the first ten frame to make 10? We can move 2 counters from the number 6 in the second ten frame to the number 8 in the first ten frame to make 10. (Model how to do this step using counters, a double ten frame mat, and a document camera or projector.) c. How many counters are now in the first ten frame? 10, d. How many counters are now in the second ten frame? 4, e. Did our total of 14 change? No, f. What number sentence can we write to describe our model now? $10+4=14$, 5. Say, ‘This is called the make ten strategy. You can use this strategy when you are adding numbers whose sum is greater than 10. You have to take some from the second number in the number sentence and add it to the first number to make 10. Once you have made 10, you can add the leftover second number.’ 6. Model how to write the new number sentence beside $8+6=$?. Write $8+6=10+4=14$ 7. Have students erase their whiteboards and clear their Double Ten Frames. 8. Repeat steps 2–7 with the following number sentences. Have students practice the “Make Ten” strategy by taking some of their counters from the second addend and adding them to the first addend to make ten, and then solving. a. $7+8$, b. $5+9$, c. $9+3$, d. $8+8$” (1.OA.6)

• Scope 4: Addition and Subtraction Strategies, Explore, Explore 3 - Properties of Operations, Procedure and Facilitation Points, Math Chat, with teacher guidance, students develop conceptual understanding of operations as strategies to add and subtract. “DOK-3 Is $6+7$ the same as $7+6$? Why? Answers will vary but may include the following: Yes, even though the order of the numbers being added is different, you are still adding the same numbers and will get the same answer.” (1.OA.3)

• Scope 9: Fractions, Explore, Explore 2–Sharing Equally–Partitioning Circles, Procedure and Facilitation Points, Math Chat, with teacher guidance, students develop an understanding of how the size of fractional pieces changes depending on the number pieces. “DOK-3 What happens to the size of the shares as you partition the paper plate into more shares?” Sample student response is as follows, “As you partition the paper plate into more shares, the size of the shares gets smaller.” (1.G.3)

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

• Scope 5: Addition and Subtraction Problem Solving, Explain, Show What You Know–Part 1: Represent and Solve All Problem Types Involving Two Whole Numbers, students draw models to solve additive reasoning problems. “Read the following problem. Draw a model (picture, strip diagram, or number line) and solve. Write a number sentence to represent your model. Michael had some candies. His brother gave him 3 more, and now he has 12. How many candies did Michael start with?” (1.OA.1)

• Scope 12: Represent Numbers to 100, Explain, Show What You Know–Part 2: Sums of Tens and Ones–Tens and Ones to Standard Form, students understand that the two digits of a two-digit number represent amounts of tens and ones. “Write the numbers in standard form. 5 tens and 3 ones = ___, $30+9=$ ___, 6 tens and 0 ones = ___, $80+4=$ ___, (Given 4 lines representing tens and 3 dots representing ones)  = ___, (Given 3 lines representing tens and 4 dots representing ones) = ___” (1.NBT.2)

• Scope 13: Compare Numbers to 100, Explain, Show What You Know–Part 4: Relationships of 10 More and 10 Less, students mentally find 10 more or 10 less than the number. Student Handout, given the starting number of and pictorial model for 54, “Write the number that is 10 less than and the number that is 10 more than the starting number. Draw a pictorial model for each number.” (1.NBT.5)

The materials reviewed for STEMscopes Math Grade 1 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:

• Scope 2: Add and Subtract within 10, Explore, Explore 1–Counting to Add and Subtract (to 10), Procedure and Facilitation Points, students build procedural fluency with adding and subtracting numbers within 10. “6. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-3 Since you can’t look at the acorns in the bag, what strategies do you use to figure out how many acorns are in the pile now?” (1.OA.6)

• Scope 4: Addition and Subtraction Strategies, Explore, Explore 1–Basic Fact Strategies– Using 10 for Addition, Procedure and Facilitation Points, students develop fluency as they make groups of 10. “2. Divide the class into pairs and direct students’ attention to the rekenrek. Allow students a few moments to discover the manipulatives and experience how they work with their partner. 3. Instruct students to come up to the “Orders Table” and choose one lemonade order from the plastic cup to complete correctly and quickly. Encourage students to think of the fastest way to add the two ingredients by leading them to make a ten with the rekenrek. 4. Monitor and talk with students as needed to check for understanding.” (1.OA.6)

• Scope 11: Length, Explore, Skill Basics–The Rules of Measurement, Procedure and Facilitation Points, students develop procedural skill, with teacher support, as they measure. “1. Explain to students they will be practicing the correct way of measuring the length of items. Tell students you have some rules to remind them how to measure. 2. Recite the following poem (Optionally, write it on chart paper so it is visible to the class): Make it straight, if you can.Then always measure end to end. Just remember not to leave gaps, but not too close, so you do not overlap. 3. Give one index card and seven paper clips to each student. 4. Model for students how to measure the length of the index card using the paper clips. As you model, explain the rules from the poem. Instruct the students to use the paper clips to measure the length of their index cards. 5. Chorally recite the poem as the students work to measure the index cards. 6. Guide students in discussion about what steps they took to measure.” (1.MD.2)

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

• Fact Fluency: Addition and Subtraction, Related Facts within 10, Fact Fluency–Game 1, Game Instructions, students demonstrate procedural skill as they find related addition and subtraction facts within 10. “2. Present the following game instructions: a. Player 1 is the red of the counter, and player 2 is the yellow side of the counter. b. Player 1 spins the Addition Fact Spinner. c. Player 1 identifies a related subtraction fact. d. Player 1 covers the fact with a counter on the Addition Fact Game board. e. Player 2 takes his or her turn, repeating the process. f. Play continues until one of the players has placed four adjacent counters of his or her own horizontally, diagonally, vertically, or in a square. g. If the fact is already covered, the player loses his or her turn. h. When one player has four adjacent counters, the game ends.” (1.OA.6) 

• Scope 2: Add and Subtract within 10, Elaborate, Fluency Builder–Go Fish, students match number sentences to visual representations. “Description, Students work in small groups to play a Go Fish card game in which the goal is to match addition and subtraction ten frames or part-part-whole models with number sentences.” (1.OA.6)

• Scope 12: Represent Numbers to 100, Explore, Explore 3–Addition Using Place Value, Exit Ticket, students independently demonstrate procedural skill as they add within 100. “Add the numbers. $49+40=$ ___; $27+50=$ ___” (1.NBT.5)

The materials reviewed for STEMscopes Math Grade 1 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 3: Add and Subtract within 20, Elaborate, Math Story–Monster Starts First Grade, students solve both routine and non-routine problems with teacher support. Non-routine: “Ms. Montez asks for someone to help put supplies in groups. Monster volunteers and promises no oops. The first things to put together are the erasers that were bought. There are twelve students, and one or two erasers that each one brought. Who can help? Look at the picture, won’t you please? Count the erasers. Write the number with ease. ___” (1.OA.1) Routine: “One more student brings a package of three. How many erasers will that be? ___ Next are the hand sanitizers, which are important, too. He counted ten of them and then needed to add two. How many are there to clean hands and fight off the flu? ___” (1.OA.6)

Engaging routine applications of mathematics include:

• Scope 4: Addition and Subtraction Strategies, Engage, Hook–The Basketball Game, Procedure and Facilitation Points, students solve routine problems with teacher support as they add and subtract within 20. “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? How many more points did Steven score than James? 3. Give each student a copy of the Student Handout to model James’s and Steven’s points in the ten double frames. Instruct students to use the space at the bottom of the page to compare the two boys’ scores. Students get to decide how they want to solve the problem. 4. Discuss the following questions: a. DOK-3 What strategies did you use to solve for the number of points James scored? b. DOK-3 What strategies did you use to solve for the number of points Steven scored? c. DOK-3 How did you determine how many more points Steven scored than James?” (1.OA.3)

• Scope 10: Time, Evaluate, Skills Quiz, Question 1 and 2, students independently solve routine problems as they tell time to half hours. For each question, students see an analog clock set to a time either on the hour or half hour. “Write the time shown for each clock. Question 1, (analog clock shows 1:30), Question 2, (analog clock shows 8:00)” (1.MD.3)

Engaging non-routine applications of mathematics include:

• Scope 11: Length, Explain, Show What You Know Part 3: Measuring the Same Thing with Different Units, Student Handout, students independently solve non-routine problems as they measure objects and organize data. “Estimate how many small paper clips and large paper clips it will take to measure the length of the journal. Fill in the My Estimations table. Use small paper clips and large paper clips to measure the length of the journal below, and then fill in the Actual Length table.” (1.MD.2)

• Scope 13: Compare Numbers to 100, Explore 4-Relationships of 10 More or 10 Less, Procedure and Facilitation Points, students solve non-routine problems with teacher support as they develop understanding of numbers 10 more or 10 less. “Part I: Creating Concrete and Pictorial Representations, 1. Read the following scenario: Phillip went to a friend’s birthday party at an arcade. He earned a lot of tickets while playing the games. He had a hard time holding all of his tickets in his ticket cup, so he kept going to the prize booth to spend his tickets after every few games he played. He had to count his tickets and decide what prizes to pick. Some prizes cost 10 fewer tickets than he had, and some cost 10 more tickets than he had, which meant he had to keep playing the games to earn more tickets. Can you help him figure out how many tickets each prize will cost him and if he has enough to get the prize? 2. Give a Student Journal to each student. 3. Divide the class into 6 groups. Give each group a bag of tickets and a set of Ten Frames. 4. Direct students’ attention to the bag of tickets and Ten Frames. Allow students a few moments to discover the manipulatives and experience how they work with their group. 5. Instruct students to look at Part I of their Student Journal. Students look at the given starting number and count out that many tickets from their bag. Students can put the tickets on the ten frames provided for additional counting support. Once the starting number has been counted, students work together to determine a number that is ten less and a number that is ten more. They draw a pictorial model of each of the three numbers (10 less, starting number, 10 more) and answer the questions. 6. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 How many tickets does Phillip have to spend? b. DOK-3 How did you show this number on your ten frames? c. DOK-1 How many ones do you need to make a ten? d. DOK-3 How did you find the number that is 10 less/more?.” (1.NBT.5)

The materials reviewed for STEMscopes Math Grade 1 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:

• Fact Fluency: Addition and Subtraction, Doubles, Fact Fluency–Mini Lesson, Procedure and Facilitation Points, students develop procedural fluency as they work with addition and doubles facts. “1. Write the fact $5+5$ on the board. Hold up 5 fingers on one hand, and 5 fingers on the other hand. 2. Ask students the following questions: ‘a. What are 5 and 5? 10, b. What are doubles facts? They are facts that add the same two numbers together. c. How can doubles help us answer other addition problems?’ Answers will vary. ‘We can add more quickly if we can double a number. We can use doubles to help us find the answers to other facts. d. How can we use a ten frame to help us find the sum of a doubles fact?’ Answers will vary.  ‘We can place the counters for the first number on the top ten frame. Then we can place counters for the second number on the bottom ten frame. Then we can count them.’ 3. Pair students up, and distribute a double ten frame, 24 counters, 1 set of crayons, and a piece of white paper to each pair of students. 4. Instruct Partner 1 to place between 0 and 12 counters on the double ten frame. 5. Instruct Partner 2 to place the same number of counters on the double ten frame. 6. Instruct students to count the total number of counters and record their work on a blank piece of paper. 7. Have students continue to model doubles facts on their double ten frame, and then record their work on a blank piece of paper.”

• Scope 3: Add and Subtract within 20, Explore, Explore 1–Counting to Add and Subtract (to 20), Procedure and Facilitation Points, students develop conceptual understanding, with teacher guidance, of addition and subtraction strategies. “3. Divide the class into 6 groups. Direct students’ attention to the Order Cards. Allow students a few moments to look through the Order Cards and experience how they work with their group. 4. Instruct students to read Order Card 1 and use a counting on or counting back strategy to figure out the total.” (1.OA.6)

• Scope 6: Data Analysis, Explore, Explore 3–Collecting and Organizing Data with Picture Charts, Part III: Drawing Conclusions, Student Handout, students apply their understanding as they solve problems while representing and interpreting data. “Use your picture chart to answer the questions. 1. How many students chose chocolate? ___ 2. How many students chose vanilla? ___ 3. How many students chose strawberry? ___ 4. Circle the type of ice cream that had the most votes. Chocolate, Vanilla, Strawberry, 5. Circle the type of ice cream that had the least votes. Chocolate, Vanilla, Strawberry 6. How many more votes did the favorite type of ice cream have than the least-favorite type of ice cream? ___ “ (1.MD.4)

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 4: Addition and Subtraction Strategies, Explore, Explore 4–The Equal Sign, Exit Ticket, students apply understanding of equations alongside procedural fluency as they solve problems working with the meaning of the equal sign. “Look at each pair of number sentences. Write true if they are equal, or false if they are not equal.” Given a chart labeled “Number Sentence 1, True/False, Number Sentence 2” and the True/False column is blank. $11-7$ ___ $8-4$, $8-1$ ___ $6+5$, $7+3$ ___ $2+9$, $5+4$ ___ $12-3$” (1.OA.7)

• Scope 5: Addition and Subtraction Problem Solving, Explore 1, Exit Ticket, students apply understanding of addition and subtraction alongside conceptual understanding as they solve word problems involving addition and subtraction. “Read each problem. Draw a model to solve. 1. Jamie bought 16 pieces of candy, and 9 were chocolate. How many pieces of candy were not chocolate? 2. Jorgé had 10 lollipops. His brother gave him 4 more. How many lollipops does he have now?” (1.OA.1)

• Scope 12: Represent Numbers to 100, Elaborate, Problem-Based Task-Football Frenzy, Student Handout, students show conceptual understanding of numbers alongside procedural skill and fluency as they represent a two-digit number using tens and ones. Students complete several scenarios independently. A box is provided for each scenario for students to show their work. “Football Frenzy, You have been chosen to be the equipment manager for the local high school football team. You’re in charge of organizing so many different pieces of equipment! Read the prompts to help the team. Your first task is to organize 96 water bottles. Draw how you would organize these, using tens and ones. Your second task is to combine 40 blue uniforms and 32 red uniforms in one box. Draw how you would organize these in groups of tens and ones. How many uniforms are in the box all together? Explain how you solved this problem. Your third task is to organize the footballs. The team had 90 footballs, but 10 footballs were old and had to be thrown away. Draw how you could organize the remaining footballs in groups of tens and ones. How many footballs are left? Explain how you solved this problem.” (1.NBT.1 and 1.NBT.2)

The materials reviewed for STEMscopes Math Grade 1 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 2: Add and Subtract within 10, Explore, Explore 2–Adding to/Taking from-Unknown in all Positions (to 10), Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: 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.” In the Exit Ticket, students determine if it is an addition or subtraction problem, and then use a strategy to solve it. “Adding to/Taking from–Unknowns in All Positions (to 10) Exit Ticket Read the problem. Alli gave her puppy 9 treats. He only ate some of the treats. There were 6 treats left. How many treats did her puppy eat? What type of problem is this? Circle your answer. Add to, Take from, Use the ten frame to solve, and then write a number sentence. ___ ___ = ___, The puppy ate ___ treats.”

• Scope 9: Fractions, Explore, Explore 2 - Sharing Equally–Partitioning Circles, students make sense of problems and persevere in solving them while they analyze and make sense of problems. Procedure and Facilitation Points, “6. Provide a new paper plate, and invite students to look at the pizza again. 7. Read the following scenario: Oh no! I forgot. Nicole and Heather invited 2 friends to join them for lunch, and they only have enough ingredients to make 1 pizza. Now they will have to divide their pizza into 4 equal shares. Can you help the girls decide how to divide the pizza into four fair shares, or equal shares? 8. Instruct students to decide how they are to partition the pizza into four fair shares, or equal shares. Encourage students to discuss and explore many different ways of partitioning with their group. Once they have decided how to partition, ask students to fold the paper plate and draw lines where the pizza needs to be divided. 9. Ask students to share how they partitioned the pizza into four equal shares with their group. Students record their partitions on the Student Journal.”

• Scope 13: Compare Numbers to 100, Explore, Explore 2–Comparing Numbers with Place Value, students make sense of problems and persevere in solving them as they reflect on their strategy. Exit Ticket, “Part I: The Jaguars and the Wildcats made it to the playoffs. Draw a model of the two teams’ scores. Write how many tens and ones are in each score. Compare the scores, and circle the team that won the game numbers.” Students are given a 2-cell table. In one cell is a picture of a Jaguar “= 34, ___ tens ___ ones.” In the 2nd cell is a picture of a Wildcat “= 76, ___ tens ___ ones.” Below the table are the following: “1. ___ is greater than ___. I know this because ___ tens is more than ___ tens. 2. ___ is less than ___. I know this because ___ tens is less than ___ tens. Part II, Use the phrases less than, equal to, or greater than to compare the  89 is ___ 89. 50 is ___ 70. 98 is ___ 89.”

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 4: Addition and Subtraction Strategies, Show What You Know–Part 2: Basic Fact Strategies–Using 10 for Subtraction, students build experience with MP.2. Although not labeled by STEMscopes as applying MP.2, students reason abstractly and quantitatively while working with subtraction strategies. Student Handout, students are given subtraction problems with 2 ten frames for each problem. “Addition and Subtraction Strategies Part 2: Basic Fact Strategies – Using 10 for Subtraction, Use your strategy of decomposing leading to a 10 to solve the  problems below. Write your number sentence and create a pictorial model for each equation using the double ten frames.  18 - 11= ____, 16 - 10= ____, 19 - 14= ____, 17 - 13= ____”

• Scope 5: Addition and Subtraction Problem Solving, Explore, Explore 2–Represent and Solve Problem Types Involving Three Whole Numbers, students build experience with MP.2. Although not labeled by STEMscopes as applying MP.2, students reason abstractly and quantitatively while problem solving. Exit Ticket, “Read each problem. Draw a model to solve. 1. Silvia loved the circus and said clowns were her favorite part. She saw 6 happy clowns. Then she saw 4 sad clowns. Then she saw 5 surprised clowns. How many clowns did she see?”

• Scope 10: Time, Explore 2–Analog Clocks (Hour and Minute Hands), Standards of Mathematical Practice and Procedure and Facilitation Points, students build experience with MP2. In Standards for Mathematical Practice, the program connects work done to MP2. “MP.2 Reason abstractly and quantitatively: Students connect the passage of time to the representation provided on an analog or digital clock.” In Procedure and Facilitation Points, “1. Read the following scenario: The Museum of Natural Science just received a set of 8 fossils to add to its fossil exhibit. These fossils were found by paleontologists. The time they were discovered was recorded. The museum wants to include a small clock image on each fossil card in their exhibit, but they are really busy prepping the fossils so they are behind on getting the fossil information cards ready for the public. They need your help drawing the hour and minute hands on clock images to include on their information cards. Can we help the museum prepare the cards? 2. Divide the class into groups of 2 or 3 and direct students’ attention to the geared analog clock. Allow students a few moments to discover the manipulatives and experience how they work with their group. 3. Instruct each group to begin working at a different fossil card found around the room. Students study the card to find out when that particular fossil was discovered. Using the geared analog clock, they manipulate the hour and minute hands to show the time on the card. Encourage students to compare and discuss the time on their clock. 4. Monitor and talk with students as needed to check for understanding by using the guiding questions below. a. DOK-1 What does the short hand on the clock represent? b. DOK-1 What does the long hand on the clock represent? c. DOK-2 What time are you showing on the clock? d. DOK-3 What is the hour in this time? e. DOK-2 Where will the hour hand point? f. DOK-3 What are the minutes in this time? g. DOK-2 Where will the minute hand point? h. DOK-3 Why is your hour hand between two numbers on the clock? i. DOK-3 What is a different way to write or say that time? j. DOK-3 How can you use the geared clock as a tool to determine the time?”

The materials reviewed for STEMscopes Math Grade 1 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: Add and Subtract within 20, Explore, Explore 5–Solving Word Problems Involving Three Whole Numbers (to 20), students  construct viable arguments as they solve word problems. “Task Cards, Task Card 1, Carlos the cat fed the fish 9 orange flakes of food. He then fed him 3 brown and 4 green flakes of food. How many flakes did Carlos the cat feed the fish in all?” Student Journal, “Draw a pictorial model of your counters and double ten frame mat. Write a number sentence in three different ways to show the total number of fish food flakes.” Students are given 2 ten-frames for the Pictorial Model and Does the order of the numbers you added in each number sentence for each task matter? Explain. ____What strategy could you use to make adding the numbers for Task Number 5 easier and faster?____” (1.OA1)

• Scope 4: Addition and Subtraction Strategies, Explore, Explore 2–Basic Fact Strategies – Using 10 for Subtraction, students critique the reasoning of others by deciding whether guesses make sense as they work with addition and subtraction strategies. Procedure and Facilitation Points, “1. Read the following scenario: Kate’s little brother is always taking cookies out of the cookie jar without asking, so Kate has decided to catch him in the act. The only way she can do that is by counting how many cookies are in the jar in the beginning, and then guessing how many cookies her little brother took from the jar. Can you help Kate count the cookies and decide how many cookies her little brother took from each jar? 2. Direct students’ attention to the Task Cards, Double Ten Frame Mat, and linking cubes. Allow students a few moments to discover the manipulatives and experience how they work with their partner. 3. Instruct students to read each task card and use the linking cubes to act out the problem on the Double Ten Frame Mat. Encourage students to discuss what they notice about the ten frame and the answer each time Kate makes a guess. 4. Monitor and talk with students as needed to check for understanding by using guiding questions: a. DOK-2 How many total cookies did Kate count in the jar at the beginning? b. DOK-3 How did you show the total number of cookies on the double ten frame? c. DOK-3 How did the double ten frame change each time Kate made a guess? 5. Give each student a copy of the Student Journal and ask students to look at the number of cookies left to determine which guess was correct. Students draw a pictorial model and write the number sentences showing how they decomposed leading to a ten. They write the correct guess for each task card.”

• Scope 6: Data Analysis, Standards for Mathematical Practice and Explore, Explore 3–Collecting and Organizing Data with Picture Charts, Math Chat, Standards for Mathematical Practice, “MP.3 Construct viable arguments and critique the reasoning of others: Students analyze data by asking questions, listening to explanations, and deciding if they are in agreement or not.” Math Chat, “DOK-3 How did the survey help you create your picture chart? I counted how many tally marks there were for each flavor, and that told me how many pictures of ice cream I needed for each flavor on my chart. DOK-3 How are your survey and picture chart similar? DOK-3 How are the data represented on the survey different from the data represented on the picture chart? DOK-3 What information can we learn from our chart? DOK-3 What are some questions you could ask about the data on the picture chart?” 

• Scope 13: Compare Numbers to 100, Explore, Explore 4, Relationships of 10 More and 10 Less, students construct viable arguments as they mentally find 10 more and 10 less. Student Journal, “Part I Count out the number of tickets Phillip earned. Find the number that is 10 less and the number that is 10 more to determine how many tickets each prize will cost. Draw a pictorial model and answer the questions.” Given a table with the columns labeled, “10 Less, Starting Number, 10 More,” students fill in the rows. “The pencil costs ___ tickets. Draw this number. Phillip has 51 tickets to spend. Draw this number. The spider ring costs ___ tickets. Draw this number. Can Phillip buy the spider ring? Explain. ___”

The materials reviewed for STEMscopes Math Grade 1 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: Add and Subtract within 10, Explore, Explore 1–Counting to Add and Subtract (to 10), students use the math they know to solve problems. Student Journal, “Complete the task cards in order. Draw a pictorial model and check off the strategy you used. Write a number sentence to explain the action. Complete the sentence with the number of acorns after each task card.” 

• Scope 9: Fractions, Explain, Show What You Know, Part 1: Sharing Equally–Partitioning Rectangles, students model their thinking with pictures as they partition fractions. Student Journal, “Fractions, Part 1 How can you partition the shapes into 2 and 4 equal shares? Fill in the blanks and model how to partition the shapes.” Given 2 rectangles. “The ___ can be partitioned into ___ and ___. Model your thinking.” Given 2 squares. “The ___ can be partitioned into halves and ___. Model your thinking.”

• Scope 13: Compare Numbers to 100, Explore, Explore 1–Generating Numbers Greater Than and Less Than with Objects and Pictures, students create pictorial models of numbers as they compare numbers. Student Journal, “Write the given number for each station. Draw a pictorial model of a number less  than and a number greater than, and then write the number. Station 1, Given Number: ___, Less Than, Draw a model. Write the number. ___, Greater Than, Draw a model. Write the number. ___”

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 4: Addition and Subtraction Strategies, Evaluate, Skills Quiz, Question 6, provides students experience with MP5 as they choose a tool or model to solve an addition problem and explain their strategy. “Renee grew flowers in her garden. She grew 7 mums and 8 daisies. How many flowers did Renee grow in her garden? Draw a picture to show your strategy and solve.”

• Scope 5: Addition and Subtraction Problem Solving, Explore, Explore 1–Represent and Solve All Problem Types Involving Two Whole Numbers, students choose a pictorial model to help them solve  problems. Student Journal, “Read the scenario card. Draw a model (picture, bar model, number line, number path, or number bond) and solve. Record your solution using a number sentence.”  

• Scope 11: Length, Explore, Explore 3–Measuring the Same Thing with Different Units, students use tools to measure, recognizing both the insight to be gained and the limitations. Student Journal, Exit Ticket, “Estimate how many small paper clips and how many large paper clips it will take to measure the length of the fork. Fill in the table and answer the question. My Estimations, ___ small paper clips, ___ large paper clips 1. Do you think it will take more small or large paper clips to measure the length of the fork? Explain. ___ Measure the length of the fork using small paper clips and then large paper clips. Fill in the table and answer the question. Actual Length, ___ small paper clips ___ large paper clips 2. Did it take fewer of the small or large paper clips to measure the length of the fork? Why? ___”

The materials reviewed for STEMscopes Math Grade 1 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 5: Addition and Subtraction Problem Solving, Explore, Skill Basics–Ways to Represent Addition and Subtraction, Procedure and Facilitation Points, students attend to precision and the specialized language of mathematics as they use a bar model, a number line, a number bond, and a number path to assist them with solving addition and subtraction problems. “3. Model creating a bar model and guide students as they learn how. Explain that this model is similar to a part-part-whole mat. The diagram has three sections: part, part, and whole. For the first flash card, explain that both parts are known, 7 and 2. The whole, or total, needs to be found. 4. Instruct students to stack seven linking cubes and place them in the Bar Model WorkSpace on the Strategy Work Mat. Model tracing around the seven connected linking cubes with a dry-erase marker and label this group with the number seven. Guide students in discussion by asking the following questions: a. Is 7 a part or whole? Part b. Now that I have a bar model drawn to show one part is 7, what do you think the next step should be? We still need to add 2 more. 5. Support students as they connect 2 more cubes and then label and trace them. Ask the following questions: a. Now that you have drawn the parts that are being added in the bar model, what can we do to solve for the total? Answers may vary as students explain problem-solving strategies. We can count how many total cubes are in the stack. b. How does drawing a bar model help solve the problem? It allows you to see (or visualize) the problem and solve it. It allows you to see what you need to find to solve the problem. c. What is the total amount of this whole bar model? 9”

• Scope 6: Data Analysis, Explore, Skill Basics–T.A.L.K. About Your Chart, students attend to precision and the specialized language of mathematics as they analyze charts and ensure that they have all the key components. Procedure and Facilitation Points, “3. Direct students’ attention to the chart on the Student Handout. 4. Say, “Let’s T.A.L.K. about this chart (emphasizing the word talk. There are a few things that are missing. These are very important parts to a chart, so it is important that we talk about them. In fact, I have a trick called T.A.L.K. to help you remember the missing parts. 5. Hold up the letter T card from the T.A.L.K. Cards and say, “T stands for title. Each chart should have a title. Find where the title should go, and point to it on your chart.” Tape this card onto the board or somewhere easily visible to students. 6. Actively monitor as students point to the space for the missing title, and facilitate a discussion by asking the following questions: a. How do you know this is where the title would go? It is at the top, and the title would go at the top of the chart. b. What do you think a good title would be? A good title might be Favorite Pets. 7. Guide students as they write in a title. 8. Instruct students to check off the box by the letter in the T.A.L.K. acronym beside their charts. 9. Continue to review the T.A.L.K. acronym by repeating the methodology in steps 5–8. Remember to allow students to stop and discuss each letter of the acronym and check it off as they add it to the chart.”

• Scope 7: Two-Dimensional Shapes, Evaluate, Skills Quiz, Question 3 and 4, students build experience with MP6 as they use precise language and vocabulary to identify 2-D shapes. Question 3, students see pictures of a rhombus, trapezoid, triangle and rectangle. “3. Circle the rectangle. How do you know it is a rectangle?” On question 4, students see a square and triangle next to one another. “4. Lily made the shape below by putting together two different shapes with pattern blocks. What two shapes did Lily put together?”

The materials reviewed for STEMscopes Math Grade 1 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 7: Two-Dimensional Shapes, Explore, Explore 2–Identifying and Classifying 2-D Shapes, Exit Ticket, students build experience with MP7 as they use structure and attributes to classify 2-D shapes. Students match the shape to its name and identify the number of sides and vertices for the shape. “Cut out each of the shapes and glue it in the correct box. Complete the sentence to describe the attributes. Special Rectangle (Square), A square has ___ vertices and ___ sides. Triangle, A triangle has ___ vertices and ___ sides. Trapezoid, A trapezoid has ___ vertices and ___ sides. Hexagon, A hexagon has ___ vertices and ___ sides. Rectangle, A rectangle has ___ vertices and ___ sides. Circle, A circle has ___ vertices and ___ straight sides.”

• Scope 8: Three-Dimensional Solids, Explore, Explore 2–Identifying 3-D Solids, Exit Ticket, students build experience with MP7 as they use structure and attributes to classify 3-D solids. Students are given five solids to match with their names and determine the number of vertices, faces, and edges. “Cut out each of the solids and glue each solid in the correct box. Complete the sentence to describe the attributes. Sphere A: sphere has ___ faces, ___ vertices, and ___ edges. Cone A: cone has ___ faces, ___ apex, and ___ edges. Cylinder A: cylinder has ___ faces, ___ vertices, and ___ edges. Cube A: cube has ___ faces, ___ vertices, and ___ edges. Rectangular Prism A: rectangular prism has ___ faces, ___ vertices, and ___ edges. Are the attributes describing each solid helping to name the solids or not helping? Why?”

• Scope 9: Fractions, Explore, Explore 2–Sharing Equally-Partitioning Circles, Exit Ticket, students build experience with MP7 as they use structure and note the pattern that a shape partitioned into more equal pieces will have smaller pieces. “Partition the circles, and fill in the answers. Word Bank, halves, half of, fourths, fourth of, quarters, quarter of circle, shares, Partition this circle into two equal shares. Is there a different way to partition this circle into two equal shares? These equal shares are called ___. Partition this circle into four equal shares. Is there a different way to partition this circle into four equal shares? These equal shares are called ___.Partition one circle into halves and the other into fourths. What do you notice about the size of halves in comparison to fourths? ___”

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:

• Fact Fluency: Addition and Subtraction, Doubles, Fact Fluency-Mini Lesson, Procedure and Facilitation Points, students build experience with MP8 as they use strategies and use repeated reasoning to solve addition problems up to 12 plus 12. “1. Write the fact $5+5$ on the board. Hold up 5 fingers on one hand, and 5 fingers on the other hand. 2. Ask students the following questions: a. What are 5 and 5? 10, b. What are doubles facts? They are facts that add the same two numbers together. c. How can doubles help us answer other addition problems? Answers will vary. We can add more quickly if we can double a number. We can use doubles to help us find the answers to other facts. d. How can we use a ten frame to help us find the sum of a doubles fact? Answers will vary.  We can place the counters for the first number on the top ten frame. Then we can place counters for the second number on the bottom ten frame. Then we can count them. 3. Pair students up, and distribute a double ten frame, 24 counters, 1 set of crayons, and a piece of white paper to each pair of students. 4. Instruct Partner 1 to place between 0 and 12 counters on the double ten frame. 5. Instruct Partner 2 to place the same number of counters on the double ten frame. 6. Instruct students to count the total number of counters and record their work on a blank piece of paper. 7. Have students continue to model doubles facts on their double ten frame, and then record their work on a blank piece of paper. 8. Ask the following discussion questions: a. How did you model your doubles facts? Answers will vary. I placed my counters on the top ten frame for both numbers. If I ran out of room, I moved to the bottom ten frame. I placed 6 counters on the top ten frame, and 6 on the bottom ten frame. Then I moved some to fill up the top ten frame. b. What do you notice about your doubles facts? Answers will vary. All of the sums are even. c. What is the sum of 6 and 6? How do you know? 12, because I placed 6 counters on the ten frame and then filled in 6 more, and I saw that I had 1 full ten frame and 2 more. d. How did you record your work on your paper? Answers will vary. I wrote: $2 + 2 = 4$. I drew a ten frame with 2 circles and then drew 2 more circles to make 4 in all. e.What did you notice when you filled up your double ten frame? I had to place the extra counters below the double ten frame. It was a fact that was more than 10 plus 10. The answer was greater than 20.  8. Use benchmarks to help students remember their doubles facts: a. Eyes: $1+1=2$, b. Wheels on a car: $2+2=4$, c. Six-pack of soda: $3+3=6$, d. Spider legs: $4+4=8$, e. Hands: $1+1=2$, f. Dozen eggs: $6+6=12$, g. Two weeks of a calendar: $7+7=14$, h. 16-pack of crayons: $8+8=16$, i. Eighteen-wheeler: $9+9=18$, j. Fingers and toes: $10+10=20$”

• Scope 4: Addition and Subtraction Strategies, Explore, Explore 3–Properties of Operations, Procedure and Facilitation Points, students build experience with MP8 as they find and use efficient strategies for addition and subtraction and assess the reasonableness of their answers. “1. Read the following scenario: Your friend just spent eight days enjoying the great outdoors. She drew pictures in her Camper’s Journal of the different things she wanted to share with you. The pages from your friend’s journal are posted around the room. At the bottom of each journal page, you will see one or two number sentences that your friend created using the pictures. She was trying to keep track of the number of things she saw. Can you help your friend determine the answer for those number sentences? 2. Divide the class into groups of 2 or 3, and direct students’ attention to the linking cubes. Allow students a few moments to discover the manipulatives and experience how they work with their group. 3. Give each student a copy of the Student Journal. Place each group at a page from the Camper’s Journal hung around the room. Ask students to go there with the linking cubes and their Student Journal. 4. Instruct students to build a concrete model of the number sentence(s) with the linking cubes. Students write the number sentence, draw a pictorial model, and answer the question in the box under the same day on the Student Journal. 5. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 What did your friend see on this day? b. DOK-3 How could you represent that using your linking cubes?. c. DOK-3 Is there another way to represent the same problem? d. DOK-3 Do you get the same answer? Why? e. DOK-3 What picture did you draw to represent this day?”

• Scope 12: Represent Numbers to 100, Explore, Explore 1–Counting and Organizing Collections Up to 120, Math Chat, students build experience with MP8 as they find patterns in the place value system and develop efficient strategies for counting and adding. “DOK-1 Which digit(s) in a number tell(s) us how many groups of ten there are? DOK-1 What does the last digit in each number tell us? DOK-3 How could you utilize your Ten Frame Mat to help you count your candies more quickly? DOK-1 How many cubes fill a ten frame? DOK-2 How many cubes will I have if I take those same 10 cubes off the ten frame? DOK-2 Starting at the number of candies for ___ (insert one of the names of the people from the Candy Bag Answer Key), count until you reach the number of candies for ___ (insert one of the names of the people from the Candy Bag Answer Key). DOK-3 Which person had the most candies? DOK-2 If you had 70 candies, how many tens and ones would you have? DOK-3 When we were counting in Part II, what did you notice about the answers you were getting in relation to what you found in Part I? DOK-3 Was it easier to count with ten frames or without? Explain.”

The materials reviewed for STEMscopes Math Grade 1 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 3: Add and Subtract within 20, Elaborate, Spiraled Review–Fast Food Fun, Procedure and Facilitation Points, provides teacher guidance. “1. You may need to provide reading assistance in order for some students to complete this activity. 2. Read the story on the first page to engage student interest before moving on to the questions. 3. Use this spiraled review as a warm-up in class, or send it home for homework, but be sure to discuss answers and strategies with the class as a whole group. 4. Refer to the standard in the lower right-hand corner of each question box to assess the students’ content knowledge or need for further intervention.”

• Scope 7: Two-Dimensional Shapes, Explain, My Math Thoughts, Preparation, guides the teacher while preparing for the lesson. “Print a copy of the My Math Thoughts handout for each student. Gather any mathematical tools and models used in this Scope to aid students in the writing process.”

• Scope 10: Time, Explore, Skills Basics–Reading/Saying/Writing Time on Digital and Analog Clocks, Preparation. Teachers “prepare to have students work as a whole group to complete this activity. Print the Clock Mat for each student. Laminate or place it in a plastic sheet protector to use with a dry-erase marker. Separate 2 colors of about $\frac{1}{8}$of a container of modeling clay for each student. Re-create the printed Clock Mat on a whiteboard for all students to see.”

The materials reviewed for STEMscopes Math Grade 1 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 2: Add and Subtract within 10, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states, “In second grade, students expand their knowledge of base-ten numbers by forming units of 100 by bundling groups of 10. Students solve one- and two step problems by adding and subtracting numbers up to 100 using a variety of strategies. Second graders begin to represent the location of numbers on a number line and represent whole-number sums and differences on a number line.”

• Scope 5: Addition and Subtraction Problem Solving, Home, Content Support, Coming Attractions. It states, “Knowledge gained about patterns within base-ten numbers between kindergarten and Grade 5 builds an essential foundation that is used to support algebraic thinking in later grades. Sixth graders become proficient using all 4 operations with decimals and fractions. In Grades 6 and 7, students begin to work with negative numbers. Sixth-grade students identify the bases and heights of triangles and parallelograms, and they apply shape composition and decomposition to derive and understand the formulas for area and volume. In Grade 8, students begin work with irrational numbers. From Grade 6 on, the domain “Number and Operations in Base Ten” is replaced with the domain “Ratios and Proportional Reasoning.””

• Scope 7: Two-Dimensional Shapes, Content Support, Current Scope. It states, “Students distinguish between defining attributes and non defining attributes, and they draw shapes to possess defining attributes. Students compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) to create composite shapes.”

• Scope 10: Length, Home, Content Overview, Teacher Guide, Current Scope. It states, “Students use nonstandard measuring tools to measure length. They illustrate that the length of an object 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.”

The materials reviewed for STEMscopes Math Grade 1 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 provides 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 5: Addition and Subtraction Problem Solving, Home, Scope Overview, Teacher Guide,  states, “Vertical Alignment, Background Knowledge, In Kindergarten, students modeled the action of joining to represent addition and the action of separating to represent subtraction. They solved contextual word problems involving familiar scenarios with sums up to 10 and differences within 10. Students used the process of decomposition to find number pairs that add to the total amount. Students explained the strategies they used to solve addition and subtraction problems using spoken words, concrete and pictorial models, and equations. Future Expectations, In second grade, students expand their knowledge of base-ten numbers by forming units of 100 by bundling groups of 10. Students solve one- and two step problems by adding and subtracting numbers up to 100 using a variety of strategies. Second graders begin to represent the locations of numbers on a number line and represent whole-number sums and differences on a number line.”

• Scope 11: Length, Home, Content Unwrapped, Vertical Alignment, Grade K, Standard. It states to “Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.” Grade 1, “Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlap.” Grade 2, “Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.” Grade 3, “Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.” Grade 4, “Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),...”

The materials reviewed for STEMscopes Math Grade 1 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, states, “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 Grade 1 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 3: Add and Subtract within 20, Explore, Explore 1–Counting to Add and Subtract (to 20), Materials, “Printed, 1 Student Journal (per student), 1 Display Case (per teacher, optional), 1 Set of Order Cards (per group), 1 Exit Ticket (per student), Reusable, 1 Projector or document camera (per teacher), 1 Resealable bag (per group)”

• Scope 7: Two-Dimensional Shapes, Elaborate, Fluency Builder–Go Fish, Materials, “Printed, 1 Instruction Sheet (per group), 1 Set of Go Fish Cards (per group), 1 Student Recording Sheet (per student), Reusable, 1 Envelope or resealable bag (per group)”

• Scope 11: Length, Explore, Explore 1–Length Concept, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), Reusable, 1 Pair of scissors (per teacher), Consumable, 1 Roll of red string (per teacher), 1 Roll of blue string (per teacher), 1 Roll of black string (per teacher), 1 Roll of white string (per teacher), 1 Roll of yellow string (per teacher)”

The materials reviewed for STEMscopes Math Grade 1 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 1, an Observation Checklist is provided for teachers to utilize as students complete work within the Explore activities of each Scope. Each Scope provides a Show What You Know, Procedure and Facilitation Points, “This element can be used to assess whether intervention is needed for each student.” In addition, students complete Show and Tell assessments, and an Interview Rubric for the teacher to use with each student. 

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 5: Addition and Subtraction Problem Solving, Evaluate, Observation Checklist.  Procedure and Facilitation Points states,“1. As students are working through the Explores for each Scope, take note of what you observe for each standard breakout. 2. This is a good place to document accommodations/modifications used during the Explores, as well as documentation for standards-based report cards.” Observation Checklist provides a table with the headings, Skill, Where to Observe, and Notes. The following is provided:  “Skill, Where to Observe, Notes, Use addition and subtraction within 20 to solve word problems involving situations of adding to and taking from with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Explore 1, Explore 2, Use addition and subtraction within 20 to solve word problems involving situations of putting together and taking apart with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Explore 1, Explore 2, Use addition and subtraction within 20 to solve word problems involving situations of comparing with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Explore 1” (1.OA.1)

• Scope 10: Time, Evaluate, Show and Tell, Procedure and Facilitation Points and Interview Rubric, provide teachers with opportunities to evaluate student learning. In Procedure and Facilitation Points, “1. Meet with each student or group of students at a table separate from the class. 2. Read each Teacher Prompt card, and observe each student as they follow the directions. 3. Ask students to record their thinking on the Student Cards if applicable. 4. Evaluate each student’s performance of the task using the rubric.” The Interview Rubric provides the teacher with a checklist of the work students are to complete as well as points assigned to each item students complete. The rubric also provides intervention tips as needed. “1. Read an analog clock and write the time to the hour and half hour. Student reads an analog clock and correctly writes the time (8 points–2 points for each time). 2. Match a digital clock to an analog clock. Student matches the analog clock to the digital clock (6 points–2 points for each match). Score: ____/ 14, Interventions, If the concern is reading a clock to the hour or half hour, take the following steps: Discuss times (on the half hour) when different events occur during the day. Read clocks only on the hour, and then look at and discuss the difference between a half hour and an hour. Practice with clock manipulatives. Just focus on hour-hand clocks, and discuss what happens to the hour hand when the minutes are passing by.” (1.MD.3)

• Scope 12: Represent Numbers to 100, Intervention, Small-Group Intervention, Procedure and Facilitation Points, provides the following: “Part I, 1. Prior to beginning the activity, ask students to tell you everything they know about numbers up to 120. As students answer, check to see if they understand the concept of place value and how to count groups of ten. Identify student misconceptions. 2. Have students work in pairs. 3. Give bag 1 containing 58 linking cubes to each pair. Do not tell students how many cubes are in the bag. 4. Instruct students to carefully empty their bags and count the cubes. 5. Watch and listen to how students group and count their cubes.”

The materials reviewed for STEMscopes Math Grade 1 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, Observation Checklists, Show What You Know, Skills Quiz, Technology-Enhanced Questions,and Show-and-Tell Assessments. 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 4: Addition and Subtraction Strategies, Explore, Explore 3–Properties of Operations, Exit Ticket, allows students to demonstrate the full intent of 1.OA.3, Apply properties of operations as strategies to add and subtract. Examples: If $8+3=11$ is known, then $3+8=11$ is also known. (Commutative property of addition.) To add $2+6+4$, the second two numbers can be added to make a ten, so $2+6+4=2+10=12$. (Associative property of addition.) “Look at the picture and number sentences below. Draw a picture to show how you would answer each number sentence. $5+4+5=$? $5+5+4=$ ? What do you notice? ____” 

• Scope 5: Addition and Subtraction Problem Solving, Explore, Explore 2–Represent and Solve Problem Types Involving Three Whole Numbers, allows students to demonstrate the full intent of MP1, “Make sense of problems and persevere in solving them: 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.” Explain, Show What You Know Part 2, “Part 2: Represent and Solve Problem Types Involving Three Whole Numbers, Read the problem. Draw a pictorial model to solve and write a number sentence that includes the solution to the problem. 1. Oliver loved kayaking. On his last kayaking trip, he saw 7 fish, 8 turtles, and 2 snakes. How many animals did he see on his trip? Number Sentence ____”

• Scope 12: Represent Numbers to 100, Evaluate, Observation Checklist, allows students to demonstrate the full intent of 1.NBT.4, “Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.” Procedure and Facilitation Points, “As students are working through the Explores for each scope, take note of what you observe for each standard breakout. This is a good place to document accommodations/modifications used during the Explores, as well as documentation for standards-based report cards.” Observation Checklist is a table with columns labeled, “Skill, Where to Observe, Notes” For example, “Add within 100, including adding a two-digit number and a one-digit number, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explore 2, Explore 3, ___”

The materials reviewed for STEMscopes Grade 1 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 4: 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. Description: Students apply basic fact strategies such as counting on, making ten, using the relationship between addition and subtraction, and applying properties of operations. Students determine the unknown in an addition or subtraction equation and understand the meaning of the equal sign to determine if an equation is true or false.”

• Scope 12: Represent Numbers to 100, Explore, Explore 4–Subtracting Using Place Value, Instructional Supports states, ”1. Assign at least one strong reader to each group to read the Task Cards aloud. 2. If students are struggling with organizing their cubes on the Place Value Chart, suggest labeling their stacks of ten cubes and single cubes using the dry-erase marker. 3. Allow students to have a scribe or to work with partners to help with the drawing part of the experience. This allows an increase in peer interaction and eliminates the need for drawing quickly.”

The materials reviewed for STEMscopes Math Grade 1 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 4: Addition and Subtraction Strategies, Acceleration, Math Today–A World-Record Bubble, Question 1 states, “The bubble artist needs to have an equal number of people standing on each section of the floor. He asked 13 people to stand in the first section. Then he asked 9 people to stand in the second section. How many more people does he need to ask to stand on the second section? Solve the problem using mental math to help show how many more people the artist needs to ask to stand on the second section. Write your strategy below.  The artist needs to ask ___ more people to stand on the second section.” 

• Scope 9: Fraction, Acceleration, Math Today–Pakistan Holi Festival, Question 1 states, “Moor put color on half of her mother’s face. Show what her mother looked like by partitioning the circle into halves and then coloring half of the circle.” Question 2, “Tahir put color on one-fourth of Ali’s shirt. Partition the rectangle below into fourths, and then color one-fourth to show what Ali’s shirt looked like.” 

• Scope 12: Represent Numbers to 100, Acceleration, Math Today–Norman, the Scooter Dog, Question 1 states,  “Norman can ride a scooter for 98 feet by himself. Draw a pictorial model of 98. Include the number of tens and ones. Pictorial Model: $10=|1=\square$ Tens ___ Ones ___” Question 2, “Draw another way to represent 98. Include the number of tens and ones that are used in the pictorial model. Tens ___ Ones ___”

The materials reviewed for STEMscopes Math Grade 1 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 6: Data Analysis, Engage, Foundation Builder, Possible Misconceptions, provides guidance for challenging words in English. “The English language has many words that have multiple meanings. Suggested Solution: To eliminate any confusion, ensure students have an understanding of the following words:Word, Possible Student Thinking, Our Intention, In Context, Label, A sticker you put on something to identify the content The words that tell the facts about groups of data, What are the labels for these groups?

• Scope 10: Time, Explore, Explore 1–Hour Hand Clocks, Instructional Supports, provides guidance for teachers with challenging words. “The words hour and our are homophones. Ensure students understand the context of the word hour while engaging in this lesson.The word hand is used in this lesson as a part of an analog clock. Ensure students understand the context and meaning of the word hand while engaging in this lesson. If students are struggling to show the time on the Event Cards on their analog clock, consider revisiting and reviewing the Skill Basics lesson to practice showing times with only the hour hand.”

• Scope 13: Compare Numbers to 100, Engage, Foundation Builder, Possible Preconceptions, provides situations where students may need assistance with words. “Students may confuse the terms more/greater than with less/fewer than. Suggested Solution: Using hand motions, say the words more/greater than with arms wide open and less/fewer than with hands close together. Work with students to make vocabulary posters with examples of more/greater than and less/fewer than.”

The materials reviewed for STEMscopes Math Grade 1 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 4: Addition and Subtraction Strategies, Explore, Virtual Manipulative–Rekenrek, provides a virtual rekenrek students can use to add and subtract accurately. 

• Scope 10: Time, Explore, Skills Basics–How to Use a Geared Clock, Procedure and Facilitation Points states, “1. Give a small geared clock to each student. 2. Gather students into a whole group, and discuss the basics of using a geared clock. Show students a 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 hand on the clock? By moving the blue (minute) hand to the right. b. What happens to the hour hand as I am moving 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 by 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 group with your guidance, tell students that you will now ask them questions and they must share their answers with their partners. Remind students that they should demonstrate a time to the closest hour or half hour. If they are not sure, they will make their best guesses.”

• Scope 12: Represent Numbers to 100, Intervention, Supplemental Aids–Number Charts, Procedure and Facilitation Points states, “Number charts are a tool that can be used for a variety of mathematical concepts, including the following: Whole numbers, Addition and subtraction, Comparing numbers, Ordering numbers, Rounding, A number chart can be used as a supplemental aid for students who need assistance visualizing numerical concepts. Display the number chart provided on the Student Handout that is applicable to the concepts being taught. Model how to use the chart. Examples include the following: Coloring in numbers while counting, Skip counting by twos, fives, tens, etc., Identifying evens and odds, Counting nickels or dimes, Recognizing multiples, Identifying prime numbers, Rounding to the nearest ten, If possible, provide a laminated copy of the number charts for each student. The students may then use dry-erase markers to utilize the charts to solve a variety of problems. Students may also write their own numbers on the blank versions of the Student Handouts for additional practice.”