Grade 4 · Measurement & Data · MAT-04-MD-002
Use Relative Sizes of Measurement Units
Represent and solve use relative sizes of measurement units problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve use relative sizes of measurement units problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for use relative sizes of measurement units works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Use Relative Sizes of Measurement Units is a measurement & data idea built from precise quantities, representations, and operations. The mathematical goal is to preserve the meaning of each quantity while choosing a representation that makes the relationship visible.
Represent the idea
The Math Box uses measurement sorter as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Measurement Conversion Lab
Use equivalent units to preserve the same physical length while changing the numerical description.
- Build one example of use relative sizes of measurement units in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
Convert 2 feet to inches.
2 × 12 = 24 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 3 feet to inches.
3 × 12 = 36 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 4 feet to inches.
4 × 12 = 48 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 5 feet to inches.
5 × 12 = 60 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 6 feet to inches.
6 × 12 = 72 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 7 feet to inches.
7 × 12 = 84 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 8 feet to inches.
8 × 12 = 96 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 9 feet to inches.
9 × 12 = 108 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 10 feet to inches.
10 × 12 = 120 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 11 feet to inches.
11 × 12 = 132 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 12 feet to inches.
12 × 12 = 144 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 13 feet to inches.
13 × 12 = 156 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 14 feet to inches.
14 × 12 = 168 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 15 feet to inches.
15 × 12 = 180 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 16 feet to inches.
16 × 12 = 192 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 17 feet to inches.
17 × 12 = 204 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 18 feet to inches.
18 × 12 = 216 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 19 feet to inches.
19 × 12 = 228 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 20 feet to inches.
20 × 12 = 240 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Convert 21 feet to inches.
21 × 12 = 252 inchesEach foot contains 12 inches, so converting feet to inches multiplies by 12.
Practice
Guided practice with hints
01Convert 22 feet to inches.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 22 × 12 = 264 inches
02Convert 23 feet to inches.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 23 × 12 = 276 inches
03Convert 24 feet to inches.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 24 × 12 = 288 inches
04Convert 25 feet to inches.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 25 × 12 = 300 inches
05Convert 26 feet to inches.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 26 × 12 = 312 inches
06Convert 27 feet to inches.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 27 × 12 = 324 inches
Practice
Independent practice
01Convert 28 feet to inches.
Answer: 28 × 12 = 336 inches
02Convert 29 feet to inches.
Answer: 29 × 12 = 348 inches
03Convert 30 feet to inches.
Answer: 30 × 12 = 360 inches
04Convert 31 feet to inches.
Answer: 31 × 12 = 372 inches
05Convert 32 feet to inches.
Answer: 32 × 12 = 384 inches
06Convert 33 feet to inches.
Answer: 33 × 12 = 396 inches
07Convert 34 feet to inches.
Answer: 34 × 12 = 408 inches
08Convert 35 feet to inches.
Answer: 35 × 12 = 420 inches
Common mistakes
Learn to catch the error, not just the answer.
Identify what each number represents and how the quantities are related before selecting an operation.
Estimate, use an inverse operation, or compare with a second representation.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use use relative sizes of measurement units when solving multi-step problems in measurement, data, money, design, or everyday quantitative decisions.
- Explain the result with units and a second check so another person can audit the reasoning.
Challenge problems
Convert 36 feet to inches.
36 × 12 = 432 inches
Convert 37 feet to inches.
37 × 12 = 444 inches
Convert 38 feet to inches.
38 × 12 = 456 inches
Convert 39 feet to inches.
39 × 12 = 468 inches
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain use relative sizes of measurement units problems accurately, then check each result with a second method.
Practice
Mastery check
01Convert 40 feet to inches.
Answer: 40 × 12 = 480 inches
02Convert 41 feet to inches.
Answer: 41 × 12 = 492 inches
03Convert 42 feet to inches.
Answer: 42 × 12 = 504 inches
04Convert 43 feet to inches.
Answer: 43 × 12 = 516 inches
05Convert 44 feet to inches.
Answer: 44 × 12 = 528 inches
06Convert 45 feet to inches.
Answer: 45 × 12 = 540 inches
07Convert 46 feet to inches.
Answer: 46 × 12 = 552 inches
08Convert 47 feet to inches.
Answer: 47 × 12 = 564 inches
Terminology
Words to know
- representation
- A diagram, model, equation, table, graph, or other form showing a mathematical idea.
- strategy
- A purposeful method chosen to solve or analyze a problem.
- estimate
- A nearby value used to judge size or reasonableness.
- verify
- To confirm a result using a second calculation, representation, or logical check.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.