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Operations and Algebraic Thinking
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Due to formatting limitations, standards are abbreviated. Full text of standards are listed on tab "Complete Standards"
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StandardsPracticesActivitiesResourcesAssessmentTimeframeDuration
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Interpret products of whole numbers - e.g interpret 5 Ã— 7 as the total number of objects in 5 groups of 7 objects each.2. Reason abstractly and quantitatively.1. Use whiteboards and manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers
2. Display multiplication table and discuss patterns with factors and products
3. Use fingers to show groups and count-by numbers (ex. 9s trick)
4. Represent equal groups with drawings (Equal Shares Drawings)
5. Create function tables to show patterns in repeated addition
6. Daily student multiplication practice through check-up sheets
7. Create and understand arrays with rows and columns (drawings, unifix cubes)
8. Students choose appropriate multiplication strategies to solve single and multi-step word problems and also create their own
9. Using array drawings to identify the communative property of multiplication
10. Use number lines to show skip counting
11. Use repeated addition and subtraction strategies to find products
12. Use known multication families to solve more complex problems
13. Play multiplcation and division games
14. Focus on math practices by relating math to photography
15. Fill in scrambled multiplication tables
16. Use place value blocks to show multiples of 10
17. Focus on math practices by relating math to recipes and zoo animals

1. Math Expressions 1.1-1.10, 1.12-1.14, 1.16, 1.18, 1.19, 2.2, 2.4, 2.7, 2.9-2.11, 2.13, and 2.15
2. Student whiteboards
3. Strategy cards
4. Student fluency check-up sheets
5. Multiplication tables
6. Place value blocks
7. Unifix cubes
8. Fingers
9. Number lines
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 2, 3,and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
September 2-November 21 52 Days
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Interpret whole-number quotients of whole numbers - e.g interpret 56 Ã· 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.2. Reason abstractly and quantitatively.1. Use cups, counters, students, and unifix cubes to show division into equal groups
2. Relate multiplication and division by showing division as an unknown factor
3. Use equal shares drawings to show the missing factor
4. Use fingers to show the number of groups
5. Use diagrams to equally partition the count-by number into the group number
6. Use manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers to find the division partner
1. Math Expressions Unit 1.4-1.7, 1.9-1.10, 1.12-1.19, 2.2, 2.4, 2.7, 2.9-2.11, 2.13, and 2.15
2. Student whiteboards
3. Strategy cards
4. Student fluency check-up sheets
5. Multiplication tables
6. Place value blocks
7. Unifix cubes
8. Fingers
9. Cups, counters, hula hoops,and various manipulatives
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 2, 3,and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
September 8-November 2148 Days
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Use multiplication and division within 100 to solve word problems in situations involving equal groups; arrays; and measurement quantities - e.g by using drawings and equations with a symbol for the unknown number to represent the problem.2. Reason abstractly and quantitatively.1. Use equal groups drawings to solve one step word problems
2. Use plates and counters to represent word problems
3. Identify types of word problems and create equal groups drawings and arrays to find the product or factor
4. Use unifix cubes to represent factors in word problems
5. Use cups and counters to find missing factors in problems
6. Use various manipulatives to represent word problems
7. Introduce the idea of using letters as variables for the unknown number
8. Focus on math practices by relating math to photography
9. Use everyday objects to identify an appropriate measurement tool to solve word problems
1. Math Expressions Unit 1.2-1.4, 1.6-1.7, 1.9-1.10, 1.12-1.14, 1.16, 1.18-1.19, 2.2, 2.4, 2.7, 2.9-2.11, 2.13, 2.15, 3.2-3.5, 3.14, 5.2, 5.3, 5.7-5.9, and 5.11
2. Counters and cups
3. Measurement containers
4. Plates to show equal groups
5. Whiteboards to demonstrate student work
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 3, and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
9. Unit 3 Quick Quiz 1
10. Unit 3 Test
September 4-December 460 Days
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Determine the unknown whole number in a multiplication or division equation relating three whole numbers.1. Make sense of problems and persevere in solving them.1. Create equal share drawings to identify unknown factors
2. Display multi-operation problems and lead student discussions on solving them
3. Introduce and understand order of operations
4. Use equal groups drawings to solve one step word problems
5. Use plates and counters to represent word problems
6. Identify types of word problems and create equal groups drawings and arrays to find the product or factor
7. Use unifix cubes to represent factors in word problems
8. Use cups and counters to find missing factors in problems
9. Use various manipulatives to represent word problems
10. Introduce the idea of using letters as variables for the unknown number
11. Focus on math practices by relating math to photography
1. Math Expressions Unit 1.1, 1.4-1.14, 1.16, 1.18-1.19, 2.1-2.11, 2.13-2.15, 5.3
2. Unifix cubes
3. Student whiteboards
4. Cups and counters
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 2, 3,and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
9. Unit 5 Quick Quiz 1
September 2-November 21, March 253 Days
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Apply properties of operations as strategies to multiply and divide. Examples: If 6 Ã— 4 = 24 is known then 4 Ã— 6 = 24 is also known. (Commutative property of multiplication.) 3 Ã— 5 Ã— 2 can be found by 3 Ã— 5 = 15 then 15 Ã— 2 = 30 or by 5 Ã— 2 = 10 then 3 Ã— 10 = 30. (Associative property of multiplication.) Knowing that 8 Ã— 5 = 40 and 8 Ã— 2 = 16 one can find 8 Ã— 7 as 8 Ã— (5 + 2) = (8 Ã— 5) + (8 Ã— 2) = 40 + 16 = 56. (Distributive property.)7. Look for and make use of structure.1. Display multi-operation problems and lead student discussions on solving them
2. Introduce and understand order of operations
3. Use square tangram pieces to show distributive property
4. Create arrays both vertically and horizontally to show the Communative Property of multiplication
5. Select students to represent picture drawings for basic whole numbers that are bing multiplied and demonstrate the Communative, Associative, and Distributive Properties
6. Discuss the use of parenthesese
1. Math Expressions Unit 1.3, 1.6, 1.11-1.12, 1.14-1.15, 1.19, 2.1, 2.8, 2.12, and 2.15
2. Student and teacher whiteboards
3. Document camera
4. Tangram squares
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1
2. Unit 1 Test
3. Smarter Balanced questions
4. Unit 2 Quick Quiz 1
5. Unit 2 Test
September 12-November 215 Days
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Understand division as an unknown-factor problem.2. Reason abstractly and quantitatively.1. Use cups, counters, students, and unifix cubes to show division into equal groups
2. Relate multiplication and division by showing division as an unknown factor
3. Use equal shares drawings to show the missing factor
4. Use fingers to show the number of groups
5. Use diagrams to equally partition the count-by number into the group number
6. Use manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers to find the division partner
1. Math Expressions Unit 1.4-1.18, 2.1-2.14
2. Student whiteboards
3. Strategy cards
4. Student fluency check-up sheets
5. Multiplication tables
6. Place value blocks
7. Unifix cubes
8. Fingers
9. Cups, counters, hula hoops,and various manipulatives
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 2, 3,and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
September 8-November 2124 Days
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Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (e.g knowing that 8 Ã— 5 = 40 one knows 40 Ã· 5 = 8) or properties of operations.2. Reason abstractly and quantitatively.1. Use whiteboards and manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers
2. Display multiplication table and discuss patterns with factors and products
3. Use fingers to show groups and count-by numbers (ex. 9s trick)
4. Represent equal groups with drawings (Equal Shares Drawings)
5. Create function tables to show patterns in repeated addition
6. Daily student multiplication practice through check-up sheets
7. Create and understand arrays with rows and columns (drawings, unifix cubes)
8. Students choose appropriate multiplication strategies to solve single and multi-step word problems and also create their own
9. Using array drawings to identify the communative property of multiplication
10. Use number lines to show skip counting
11. Use repeated addition and subtraction strategies to find products
12. Use known multication families to solve more complex problems
13. Play multiplcation and division games
14. Focus on math practices by relating math to photography
15. Fill in scrambled multiplication tables
16. Use place value blocks to show multiples of 10
17. Focus on math practices by relating math to recipes and zoo animals
18. Use cups, counters, students, and unifix cubes to show division into equal groups
19. Relate multiplication and division by showing division as an unknown factor
20. Use equal shares drawings to show the missing factor
21. Use fingers to show the number of groups
22. Use diagrams to equally distribute the count-by number into the group number
23. Use manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers to find the division partner
1. Math Expressions Unit 1.1-1.19, 2.1-2.15
2. Student whiteboards
3. Strategy cards
4. Student fluency check-up sheets
5. Multiplication tables
6. Place value blocks
7. Unifix cubes
8. Fingers
9. Number lines
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 2, 3,and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
September 2-November 2152 Days
12
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.1. Make sense of problems and persevere in solving them.1. Use counters and unifix cubes to represent the steps of problems
2. Identify questions to the first step of multi-step word problems
3. Underline key vocabulary in word problems
4. Omit numbers initially to help students identify the appropriate operation to be used
5. Use comparison bars
6. Place parenthesese in appropriate locations in equations
7. Use pictures, graphs, and diagrams to represent problems
8. Students implement variables as unknown numbers in equations
9. Round numbers to ten or hundred in problem on student whiteboard to estimate answers
1. Math Expressions Unit 2.9-2.11, 2.13, 4.17, 5.7-5.11
2. Student whiteboards
3. Counters
4. Unifix cubes
5. Place value blocks
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 2 Quick Quiz 2
2. Unit 2 Test
3. Smarter Balanced question
4. Unit 4 Quick Quiz 2 and 3
5. Unit 4 Test
6. Smarter Balanced questions
8. Unit 5 Quick Quiz 1 and 2
9. Unit 5 test
10. Smarter Balanced questions
October 27-November 21, March 16-April 1020 Days
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Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.8. Look for and express regularity in repeated reasoning.1. Play count-by games to understand patterns
2. Use and understand function tables
3. Use counters to create groups
4. Use boards to circle groups
5. Student led discussions on patterns in multiplication tables and hundred charts
1. Math Expressions Unit 1.1, 1.5-1.8, 1.10, 1.12, 1.15, 1.19, 2.1, 2.3, 2.5, 2.6, 2.8, 2.14, 2.15, and 4.17
2. Student whiteboards
3. Multiplication table
4. Hundreds chart
5. Counters
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1 and 2
2. Unit 1 Test
4. Unit 2 Quick Quiz 1 and 2
5. Unit 2 Test
7. Smarter Balanced questions
September 2-November 2152 Days
14
By the end of Grade 3 - know from memory all products of two one-digit numbers.2. Reason abstractly and quantitatively.1. Use whiteboards and manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers
2. Display multiplication table and discuss patterns with factors and products
3. Use fingers to show groups and count-by numbers (ex. 9s trick)
4. Represent equal groups with drawings (Equal Shares Drawings)
5. Create function tables to show patterns in repeated addition
6. Daily student multiplication practice through check-up sheets
7. Create and understand arrays with rows and columns (drawings, unifix cubes)
8. Students choose appropriate multiplication strategies to solve single and multi-step word problems and also create their own
9. Using array drawings to identify the communative property of multiplication
10. Use number lines to show skip counting
11. Use repeated addition and subtraction strategies to find products
12. Use known multication families to solve more complex problems
13. Play multiplcation and division games
14. Focus on math practices by relating math to photography
15. Fill in scrambled multiplication tables
16. Use place value blocks to show multiples of 10
17. Focus on math practices by relating math to recipes and zoo animals
18. Use cups, counters, students, and unifix cubes to show division into equal groups
19. Relate multiplication and division by showing division as an unknown factor
20. Use equal shares drawings to show the missing factor
21. Use fingers to show the number of groups
22. Use diagrams to equally distribute the count-by number into the group number
23. Use manipulatives to make groups of 5s, 2s, 10s, 9s, 3s, 4s, 1s, 0s, 6s, 8s, 7s, square numbers to find the division partner
1. Math Expressions Unit 1.1-1.19, 2.1-2.15
2. Student whiteboards
3. Strategy cards
4. Student fluency check-up sheets
5. Multiplication tables
6. Place value blocks
7. Unifix cubes
8. Fingers
9. Number lines
(MobyMax, Odyssey, BrainPop(jr), Math Writing Prompts)
1. Unit 1 Quick Quiz 1, 2, 3, and 4
2. Unit 1 Test
4. Smarter Balanced questions
5. Unit 2 Quick Quiz 1 and 2
6. Unit 2 Test
8. Smarter Balanced questions
September 2-November 2152 Days
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