1st Grade - Gateway 2

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.”