standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Activity
This activity is an opportunity to apply insights from the previous activity in a different context. In this activity, students convert between pounds and kilograms. The conversion factor is not given as a unit rate. As a result of the work in the previous activity, some students may compute and use unit rates, and some may still reason using various representations of equivalent ratios. The numbers are also purposely chosen such that the unit rate
\(\frac{10}{22}\)
does not have a convenient decimal equivalent, suggesting that fractions are sometimes much more convenient to work with than decimals. Students should have learned efficient methods for multiplying fractions in grade 5 (5.NF.B.4a), but may need support. Additionally, while all measurements within this activity are accurate with rounding to the nearest integer, you may choose to point out before or after the task that
\(\frac{10}{22}\)
is a common approximation of the conversion factor from pounds to kilograms and not the true conversion factor.
As students work, identify those who computed and used the unit rates
\(\frac{10}{22}\)
and
\(\frac{22}{10}\)
. Highlight these strategies in the discussion, while continuing to refer to other representations to make sense of them as needed.
Launch
Ask students to recall which is heavier: 1 pound or 1 kilogram? (1 kilogram is heavier.) Tell them that in this activity, they will be given weights in pounds and asked to express it in kilograms, and also the other way around. The pairs of measurements in pounds and kilograms for a set of objects are all equivalent ratios. Encourage students to consider how finding unit rates—how many kilograms in 1 pound and how many pounds in 1 kilogram—can make their work more efficient.
Give students quiet think time to complete the activity, and then time to share their explanation with a partner. Follow with whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organization and problem solving. For example, ask students to first draw a table or double number line to organize their thinking and then find a ratio for converting pounds to kilograms. Next, ask students to convert the weight of each dog separately. After that, ask students to complete the last question.
Supports accessibility for: Organization; Attention
Student Facing
A veterinarian uses weights in kilograms to figure out what dosages of medicines to prescribe for animals. For every 10 kilograms, there are 22 pounds.
Calculate each animal’s weight in kilograms. Explain or show your reasoning. If you get stuck, consider drawing a double number line or table.
Fido the Labrador weighs 88 pounds.
Spot the Beagle weighs 33 pounds.
Bella the Chihuahua weighs
\(5\frac12\)
pounds.
A certain medication says it can only be given to animals over 25 kilograms. How much is this in pounds?
Student Response
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Anticipated Misconceptions
Students working with the unit rate
\(\frac{10}{22}\)
may want to convert it to a decimal and get bogged down. Encourage them to work with the fraction, reviewing strategies for multiplying by a fraction as necessary.
Activity Synthesis
Invite one or more students to share who used the unit rates
\(\frac{10}{22}\)
and
\(\frac{22}{10}\)
as part of their work. Display a table of equivalent ratios as needed to help students make sense of this approach, including attending to the meaning of these numbers and the rationale for any operations used.
Listening, Speaking: MLR2 Collect and Display.
As students share their explanations for the first and second questions with a partner followed with whole class discussion, listen for and scribe the words and phrases that students used when converting between pounds and kilograms. Some students may convert to decimals and find this method more challenging, while others may show reasoning using the unit rates
\(\frac{10}{22}\)
and
\(\frac{22}{10}\)
. Highlight key vocabulary that students use in the discussion, while continuing to refer to other representations to make sense of them as needed. This will help students increase sense-making while simultaneously support meta-awareness of language.
Design Principle(s): Support sense-making; Maximize meta-awareness


aligns: no