Global Concept Guides:Strategies for multiplying and dividing by 3 and 6, Understanding associative and distributive properties, Strategies for multiplying and dividing by 7 and 9, Strategies for combination problems
Prior Learning:MA.1.A.1.3, MA.1.A.1.2, MA.1.A.1.1,MA.2.A.2.1, MA.2.A.4.1, MA.2.A.6.1, MA.3.A.1.1
Progression Document Link
Show What you Know Task:Use the modified Go Math Show What You Know for Ch. 4 and 6
Next Generation Sunshine State Standards for Mathematical Content
MA.3.A.1.1 Model multiplication and division including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement, partitioning.
MA.3.A.1.2 Solve multiplication and division fact problems by using strategies that result from applying number properties.
MA.3.A.1.3 Identify, describe and apply division and multiplication as inverse operations. / Comments:
Model multiplication and division in MA.3.A.1.1 refers to direct modeling. Direct Modeling is the use of manipulatives or drawings along with counting to represent directly the meaning of an operation or story problem. (Van de Walle 7th ed., 2010,p. 214.)
Notes on Assessments:
Unit 3 (Modified 4 and 6)
See Common Performance Task link below
Unpacking the Standards for this Task: Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.Click here for more info
Common Performance Task for this unit:Goldfish Bowls - Students will utilize concepts learned throughout this Unit of Study. Click here for the Performance Task and rubric.
Future Learning:
In future units, students will use the understanding of multiplication (arrays) to determine the area of geometric shapes. In fourth grade, They extend their understanding of multiplication and division to multi-digit numbers. Students write and solve numeric and algebraic expressions relating to multiplication and division.
3rd / Global Concept 1 of 4 for this Unit of Study: Strategies for multiplying and dividing by 3 and 6 / Projected Time Allotment: 2 days
Sample Essential Questions:
Day 1: How can you use strategies to multiply and divide by 3?
Day 2: How can you use strategies to multiply and divide by 6?
Related Unit 3 Assessment: Go Math Chapter Mod. Ch.4 and 6 #8, 17, 19, 25, 26, 27
Instructional Resources
Manipulatives:
- Unit cubes
- Two color counters
- Snap cubes
- Color tiles
- Number line - Students will use jumps to represent equal groups and the intervals to represent the number in each group. Click here to see how to connect equal groups to the linear model.
- Go Math Lesson 4.1 – Unlock the Problem, p.153, Problem Solving, p. 156, FBP p. 85 # 17 – 18
- Go Math Lesson 4.2 - Unlock the Problem,p. 157, Problem Solving, p. 159 #26 – 29
- Go Math Lesson 6.1 – Unlock the Problem, p. 249, Refer to Other Ways on p.250 to utilize number line, Problem Solving, p. 252 #32 – 35, FBP p. 137 #13 – 14
- Go Math Lesson 6.4 – Unlock the Problem, p. 261, Problem Solving, p. 264, FBP p. 143 #13 - 14
- iTools Number Lines
- Number Line Arithmetic
Sample HOT Questions: Use these to facilitate student discussion.
- How can you use the strategies to multiply and divide by 3 to help you multiply and divide by 6?
- How did the products of 3 compare to the products of 2?
- How did the products of 3 compare to the products of 1?
- What do your manipulatives represent in the equation?
- How did you know what operation to use to solve the equation?
Our students are able to…
- Use multiple tools to represent given situations. (SMP 1,5)
- Directly model given situations and writing expressions to match them. e.g. 7+7+7 or 3X7 (SMP 2)
- Explain what their models represent and justify the models created. (SMP 3)
- Justify the use of strategy used to arrive at a solution. (SMP 3)
- Provide opportunities for students to utilize manipulatives to model problems including equal groups. (SMP 1,5)
- Question student responses and require justification of strategies (SMP 3).
- Examine students’ models to ensure the model and/or expression matches the given situation. (SMP 3)
- Emphasize precise use of vocabulary: addend, sum, factor, and product. (SMP 6)
3rd / Global Concept 2 of 4 for this Unit of Study: Understanding Associative and Distributive properties / Projected Time Allotment: 2 days
Sample Essential Questions:
Day 1: Why is the Associative Property also called the grouping property?
Day 2: How can you use the Distributive Property to find products?
Related Unit 3 Assessment: Go Math Chapter Mod. Ch.4 and 6 #10, 14, 23
Instructional Resources
Manipulatives:
- Unit cubes
- Snap cubes
- Color tiles
- Go Math Lesson 4.3 – Unlock the Problem, p. 161, Problem Solving, p. 164, FBP p. 89 #13 - 14
- Go Math Lesson 4.5 – Unlock the Problem, p. 169, Share and Show, p. 170, On Your Own, p. 171, Problem Solving, p. 172
- Multiplication Properties
- Array Game for Distributive Property
- Matching Expressions to Distributive Property
- For more information on how to teach the distributive property click hereto watch this Professional Development Video.
- Click here to see the implementation of a sample performance task under “task rubric” tab.
Sample HOT Questions: Use these to facilitate student discussion.
- Why would grouping factors make it easier to multiply?
- How would making an array help you group the factors?
- How would knowing your basic facts help you with these properties?
- Does it matter which factors you multiply first and why?
- Did dividing your array change your value? Explain?
- Why do you think it’s called the Distributive Property?
Our students are able to…
- Use multiple tools to represent given situations. (SMP 1,5)
- Directly model given situations and write expressions to match them. Ex: 6 x 4 is the same as (3 x 4) + (3 x 4) (SMP 2, 7)
- Explain and justify the models created. (SMP 3)
- Use multiple models to justify solution (SMP 1)
- Provide opportunities for students to utilize manipulatives to model problems. (SMP 1,5)
- Encourage students to group factors to solve problems efficiently. (SMP 7)
- Examine students’ models to ensure the model (decomposed array) and expression matches the given situation. (SMP 3)
- Emphasize precise use of vocabulary: factor, product, Distributive Property, Associative Property, decompose, compose. (SMP 6)
3rd / Global Concept 3 of 4 for this Unit of Study: Strategies for multiplying and dividing by 7 and 9 / Projected Time Allotment: 4 days
Sample Essential Questions:
Day 1: What patterns help you multiply and divide with the factor 9?
Day 2: What strategies can you use to multiply and divide with the factor 7?
Related Unit 3 Assessment: Go Math Chapter Mod. Ch.4 and 6 #1, 13
Instructional Resources
Manipulatives:
- Unit Cubes
- Two Color Counters
- Snap Cubes
- Color Tiles
- Grid Paper
- Go Math Lesson 4.8 – Unlock the Problem, p. 183, Another Way, p. 184, Problem Solving, p. 185 - 186
- Go Math Lesson 4.9 – Unlock the Problem,p. 187, Share and Show #1, p. 188, Problem Solving, p. 189.
- Go Math Lesson 6.5 – Unlock the Problem, p. 267, Unlock the Problem, p. 270, FBP p. 145 #13 - 14
- Go Math Lesson 6.7 – Unlock the Problem, p. 275, Unlock the Problem, p. 278, FBP p. 149 #13 - 14
- Garden Problem for Distributive Property
- iTools Number Lines
- Number Line Arithmetic
- For more information on how to teach the Distributive Property click hereto watch this Professional Development Video.
Sample HOT Questions: Use these to facilitate student discussion.
- How would making an array help you solve problems involving factors of 7 and 9?
- How would knowing your basic facts help you with these properties?
- Did dividing your array change your value? Explain?
- What facts are you most comfortable with? How would you use those facts to help you solve the problems?
- How can you use a number line to skip count to find how many are in each group?
Our students are able to…
- Use multiple tools to represent given situations. (SMP 1,5)
- Use strategies (tools, pictures, Distributive Property) to solve problems. (SMP 5)
- Directly model given situations, use the Distributive Property to decompose factors, write expressions to solve problems. (SMP 2, 7)
- Explain and justify how you decomposed your models. (SMP 3)
- Encourage students to decompose arrays to solve problems (SMP 1,5)
- Provide opportunities for students to utilize manipulatives to model problems. (SMP 1,5)
- Examine students’ models to ensure the model and/or expression matches the way they decomposed their array (SMP 3)
- Emphasize precise use of vocabulary: factor, product, Distributive Property, associative property, decompose, compose. (SMP 6)
3rd / Global Concept 4 of 4 for this Unit of Study: Strategies for combination problems / Projected Time Allotment: 2 days
Sample Essential Questions:
Day 1: How do combination problems relate to multiplication?
Day 2: What strategies can you use to solve combination problems?
Related Unit 3 Assessment: Go Math Chapter Mod. Ch.4 and 6 #21
Instructional Resources
Manipulatives:
- Unit Cubes
- Two Color Counters
- Snap Cubes
- Color Tiles
- Go Math Lesson 4 .4 – Unlock the Problem, p. 165, Another Way, p. 166, On Your Own p. 167 #10, Problem Solving, p. 168
- The Sundae Challenge
- Illuminations - Combinations
- Illuminations – Pizza Toppings
Sample HOT Questions: Use these to facilitate student discussion.
- How does your model represent the problem?
- How do you know when you have made all possible combinations?
- Why did you organize your combinations in that way?
- Could you have grouped your combinations in any other way? Explain?
- What would happen to your model if you added another choice?
- Is your model the most efficient strategy for solving combination problems?
- How did you organize your thinking to make sure you did not repeat a combination?
Our students are able to….
- Use multiple tools and strategies to represent given situations. (SMP 1,5)
- Directly modeling given situations and writing expressions to match them. (SMP 2)
- Explain what their models represent and justify the models created. (SMP 3)
- Evaluate efficiency of strategies used. (SMP 1,3)
- Provide opportunities for students to utilize manipulatives to model problems (SMP 1,5)
- Have students record thinking to ensure all combinations are created. (SMP 4,6)
- Examine students’ models to ensure the model and/or expression matches the given situation. (SMP 3)
- Emphasize precise use of vocabulary: addend, sum, factor, and product. (SMP 6)