Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
4th Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of multiplication.
3rd Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of multiplication.
Learning Targets
Explain how multiplication can compare quantities (Jason is 4 times as old as Ben).
Write equations to show multiplicative comparison.
Represent multiplicative comparisons.
Explain the difference between multiplicative (as many times as) and additive (more) comparisons.
About the Math
Area models, equal groups, and arrays are ways of thinking about multiplication. Multiplication can also be thought of as a comparison. Students should work with multiplicative comparison in basic settings when introduced. As the year progresses, students should work with comparison situations using larger factors.
Explain how multiplication can compare quantities (Jason is 4 times as old as Ben).
Multiplication can be used to compare quantities. For example, John has 4 apples and Jimmy has 3 times more apples than John. Jimmy has 12 apples because 12 is 3 times greater than 4.
Write equations to show multiplicative comparison.
Equations must be connected explicitly to problems and representations. Students should be able to explain where the numbers and operations in an equation originate.
Represent multiplicative comparisons.
Multiplicative comparisons can be represented in a wide range of ways. Students can use physical models like unifix or Katie cubes. Students could use base ten blocks or Cuisennaire rods. The bar diagram to the right is anothe representation students should be comfortable with.
Explain the difference between multiplicative (as many times as) and additive (more) comparisons.
It is critical that students understand the difference between additive and multiplicative comparison.
Additive comparison:
John has 4 apples. Jimmy has 3 more apples. (4 + 3)
Multiplicative comparison:
John has 4 apples. Jimmy has 3 times more than John. (3 x 4)
Essential vocabulary for this standard includes comparison, multiplicative comparison, additive comparisonand equation.
Progression of Standard within Grade 4
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Explain how multiplication can compare quantities (Jason is 4 times as old as Ben).
Write equations to show multiplicative comparison.
Represent multiplicative comparisons.
Explain the difference between multiplicative (as many times as) and additive (more) comparisons.
These tasks can be used with small group or whole group instruction.
Distribute Cuisenaire Rods to students and have students use them to represent multiplicative comparison. See the About the Math tab for a visual. An example: The ash tree is 6 feet tall. The oak tree is 3 times as tall as the ash tree. How can we model the problem using the Cuisenaire Rods? Pointing to a student's representation... what does this rod represent from the scenario? Other possible multiplicative comparison examples: A T-shirt costs $6, a sweatshirt cost $18-- compare the costs of the shirts with the rods. Jose picked 20 apples and Janette picked 5 apples. Jose picked ___ times as many apples as Janette. Siri has 24 inches of ribbon and this is twice as much as she needs for a neckace, how many inches does she need for her necklace?
Show students two rectangles (one of which is three times longer than the other- see pg. 22 in Essential Understanding). How do the sizes of the two rectangles compare? (Multiplicative comparison is when one quantity (factor) is described by a multiple of the other, different than repeated addition and arrays.)
Martin and Kate used star stickers in a picture of the night sky. Kate used four times as many stars as Martin. How many stars could they have each used? Is there another possible answer?
A plant was 2 inches tall on Day 1. It was measured at 10 inches on Day 12. How can you describe the relationship between the two quantities using multiplicative reasoning.
Mark’s recipe calls for three times as many potatoes as carrots. If Mark uses two cups of carrots, how many cups of potatoes will he use?
Anna is 8 years old. Her mom is five times older than she is and her grandmother is eight times older than Anna. What multiplication sentences can be written to represent the relationship between Anna’s age and her mom’s age? between Anna’s age and her grandmother’s age? How old are Anna’s mother and grandmother?
What multiplication equation could you write to match the picture of the pencils?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
