Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
Students are able to…
- Solve multiplicative comparison problems using words, symbols, numbers, counters or pictures.
- Represent multiplicative comparison problems with equations.
- Model the information in the problem using concrete models or drawings.
Students are able to…because teachers…
- Help students make connections between models, equations and multiplicative comparison problems.
- Facilitate mathematical discussion to help students make connections between problems, equations and models.
- Provide both additive and multiplicative comparison problems to help students determine the differences.
Questions to ask students:
- What is the difference between additive comparisons and multiplicative comparisons?
- Sample answer that indicates understanding: Additive comparisons focus on the difference between two values. Ex. how many more? or how many less? Multiplicative comparisons compare values where one value is a specified number of times greater or less than the given value.
- Jeremy has 8 puppies. This is 4 times as many as Beth. How many puppies does Beth have? How could you model the problem and record it as an equation?
- Sample answer that indicates understanding: Student lays out 8 counters to illustrate Jeremy’s puppies. Student then breaks up the counters into 4 groups or times. There are 2 counters in each equal group, so Beth has 2 puppies.
- How could you use multiplication to solve the problem? How could you use division to solve the problem? How do division and multiplication relate?
- Sample answer that could indicate understanding: 4 x ? = 8 so I can divide 8 divided by 4 to get 2. Both multiplication and division deal with equal groups, but multiplication is when I know the number of groups and number in each group, but not the total. Division is when I know the total and either the number of groups OR how many in each group.
FSA Notes
Cognitive Complexity Level: 2-Basic Application of Skills & Concepts
Achievement Level Descriptors:
2-multiplies or divides to solve word problems involving multiplicative comparison (where the unknown is the product or quotient)
3-multiplies or divides to solve word problems involving multiplicative comparison (where the unknown is in a variety of positions)
4-creates and solves a multiplication equation with a symbol for the unknown number to represent a word problem involving multiplicative comparison
5-[intentionally left blank]
Assessment Limits:
Multiplication situation must be a comparison (e.g., times as many).
Limit multiplication and division to 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit.
Additional Resources:
Additional in-depth content knowledge
Video: Multiplicative comparisons
Khan Academy – Comparing with multiplication exercise
Sample Formative Assessment Tasks:
Resources/Tasks to Help Your Child at Home:
Discuss and draw bar models of real world examples of multiplicative comparison problems, then extend to have your child record equations and solve. Remind them to reflect to make sure the answer is reasonable and they used the correct part of the bar model or equation to answer the problem.
Use it to help your child budget: If they have $5 and want to purchase an item that is $40, how many times greater is the cost of the item than what you have? 5 x 8 = 40 or 40 ÷ 5 = 8. So the item is 8 times the amount they have.
Khan Academy: Comparing with Multiplication Basics https://goo.gl/78hja4
Khan Academy: Comparing With Multiplication, Age https://goo.gl/QvwD6G