Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Students are able to…
- Use concrete materials to model various multiplication situations.
- Identify the number of groups and the number of items in each group with maipulatives.
- Connect representations to numeric expressions.
- Use appropriate vocabulary (factor, product, multiplication, groups of) to describe their work.
Students are able to…because teachers:
- Provide students with a variety of multiplication situations to model using concrete materials such as chips, counters, straws to represent the items, and cups, egg carton, paper to represent groups.
- Ask students to identify the number of groups and the number of items in each group and then the total number of items.
- Introduce multiplication terminology and symbols as students are ready. Add these terms and symbols to the class multiplication and division word wall: factors, product, groups, multiplication, x.
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Questions to ask students:
- Ask students to tell you what the symbol “x” means.
- Sample answer/s that indicate understanding: “The “x” means or can be read as “groups of” (3 x 5 is three “groups of” five). Students may also say that this is the multiplication symbol and can explain that multiplication is related to repeated addition (of the same value/number)
- Sample answer that indicates partial understanding or a misconception: the “x” stands for times. Student can’t explain what “times” means other than reciting a times table.
- The problem scenarios in this unit should center around “groups of” objects and repeated addition.
- “Times” is an interpretation of multiplication that is focused on in 4th grade rather than 3rd. (Multiplicative comparison: Jose ran 3 laps around the field. Jane ran 4 times as many laps as Jose. How many laps did Jane run?)
- It is not incorrect if students refer to the “x” symbol as times, but it is a very abstract concept for them to use as the basis for learning about multiplication. The “groups of” interpretation should be focused on first.
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- As students are solving simple word problems involving multiplication ask them to identify the number of groups and the number in each group. Example, There are 3 seats in the van and each seat can hold 4 people. Ask student to identify the number of groups and the number of items in each group and then the total number of items. How people can sit in the van?
- If students are using manipulatives, ask them to model the scenario.
Sample answer that indicates understanding: 3 is the number of groups, 4 is the number in each group and 12 is the total number of people. If students are modeling with cubes, they should be able to build three groups with four cubes in each group. The students should be able to tell you that the cubes represent the people and the groups represent the seats.
Ask student to write an expression or equation that represents the van problem above. They should be able to explain their expression.
- Sample answer that indicates understanding: 3×4 or 3×4=12 because the I have 3 groups of seats and 4 people on each seat for a total of 12 people.
- 4 x 3 is incorrect as this equation is read as “four groups of three” which is a different scenario with a much different looking van.
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FSA Notes :
Cognitive Complexity Level: 1 – Recall
Achievement Level Descriptions:
Level 2: interprets products of single-digit whole numbers (using factors of 1, 2, or 5) using equal groups of objects and arrays of objects
Level 3: interprets products of single-digit whole numbers (using factors up to 10)
Level 4: interprets products of whole numbers within 100, representing context with numbers and words
Level 5: [intentionally left blank]
Assessment Limits:
- Whole number factors may not exceed 10 x 10.
- Students may not be required to write an equation to represent a product of whole numbers.
Context: Allowable
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Additional Resources:
Additional in depth content knowledge:
Blog Post: Understanding Multiplication
Learn Zillion Video:Interpret products by drawing pictures
Multiplication Progressions Video
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Sample Formative Assessment Tasks:
Tom told Mary he planted 4 x 5 flowers. How might Mary describe the
arrangement of flowers in Tom’s rectangular‐shaped garden?
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Draw a picture and write an equation for each part of the task.
Part 1: Zeke’s dog eats 3 cups of food a day. If Zeke goes away for 9 days how much food should he leave?
Part 2: If Zeke is staying away for 3 days less, how much food should he leave?
Part 3: Write a sentence explaining how you know that you are correct.
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Resources/Tasks to Help Your Child at Home:
Look for real-world examples of situations with equal groups. For example: packs of candy, cartons of eggs, six-pack of soda, tires on vehicles, etc. (If we bought 3 six-packs of Pepsi, how many Pepsi cans did we buy?)
LearnZillion Video: The Carrot Patch- Use Equal Groups to Represent Multiplication https://goo.gl/C3M2mR
Task: Sarah is putting 20 cookies on plates. She wants the same number of cookies on each plate. Create as many different equal groups models as you can to represent how Sarah could arrange her cookies. Write a multiplication equation to match each model.
LearnZillion Video: Understand Multiplication Problems: Using Equal Groups https://goo.gl/D3DVt9