Grade 5 · Mathematical Practice & Problem Solving · MAT-05-MP-003
Estimate, Check, and Select Efficient Strategies
Represent and solve estimate, check, and select efficient strategies problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve estimate, check, and select efficient strategies problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for estimate, check, and select efficient strategies 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.
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
Estimate, Check, and Select Efficient Strategies is a mathematical practice & problem solving 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 number line 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.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- Build one example of estimate, check, and select efficient strategies 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.
Estimate 198 + 302, then compare with the exact sum.
Estimate ≈ 500; exact = 500Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 209 + 309, then compare with the exact sum.
Estimate ≈ 500; exact = 518Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 220 + 316, then compare with the exact sum.
Estimate ≈ 500; exact = 536Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 231 + 323, then compare with the exact sum.
Estimate ≈ 500; exact = 554Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 242 + 330, then compare with the exact sum.
Estimate ≈ 500; exact = 572Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 253 + 337, then compare with the exact sum.
Estimate ≈ 600; exact = 590Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 264 + 344, then compare with the exact sum.
Estimate ≈ 600; exact = 608Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 275 + 351, then compare with the exact sum.
Estimate ≈ 700; exact = 626Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 286 + 358, then compare with the exact sum.
Estimate ≈ 700; exact = 644Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 297 + 365, then compare with the exact sum.
Estimate ≈ 700; exact = 662Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 308 + 372, then compare with the exact sum.
Estimate ≈ 700; exact = 680Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 319 + 379, then compare with the exact sum.
Estimate ≈ 700; exact = 698Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 330 + 386, then compare with the exact sum.
Estimate ≈ 700; exact = 716Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 341 + 393, then compare with the exact sum.
Estimate ≈ 700; exact = 734Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 352 + 400, then compare with the exact sum.
Estimate ≈ 800; exact = 752Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 363 + 407, then compare with the exact sum.
Estimate ≈ 800; exact = 770Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 374 + 414, then compare with the exact sum.
Estimate ≈ 800; exact = 788Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 385 + 421, then compare with the exact sum.
Estimate ≈ 800; exact = 806Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 396 + 428, then compare with the exact sum.
Estimate ≈ 800; exact = 824Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Estimate 407 + 435, then compare with the exact sum.
Estimate ≈ 800; exact = 842Estimation provides a reasonableness check; the exact calculation should be close to the rounded benchmark.
Practice
Guided practice with hints
01Estimate 418 + 442, then compare with the exact sum.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Estimate ≈ 800; exact = 860
02Estimate 429 + 449, then compare with the exact sum.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Estimate ≈ 800; exact = 878
03Estimate 440 + 456, then compare with the exact sum.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Estimate ≈ 900; exact = 896
04Estimate 451 + 463, then compare with the exact sum.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Estimate ≈ 1000; exact = 914
05Estimate 462 + 470, then compare with the exact sum.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Estimate ≈ 1000; exact = 932
06Estimate 473 + 477, then compare with the exact sum.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Estimate ≈ 1000; exact = 950
Practice
Independent practice
01Estimate 484 + 484, then compare with the exact sum.
Answer: Estimate ≈ 1000; exact = 968
02Estimate 495 + 491, then compare with the exact sum.
Answer: Estimate ≈ 1000; exact = 986
03Estimate 506 + 498, then compare with the exact sum.
Answer: Estimate ≈ 1000; exact = 1004
04Estimate 517 + 505, then compare with the exact sum.
Answer: Estimate ≈ 1000; exact = 1022
05Estimate 198 + 302, then compare with the exact sum.
Answer: Estimate ≈ 500; exact = 500
06Estimate 209 + 309, then compare with the exact sum.
Answer: Estimate ≈ 500; exact = 518
07Estimate 220 + 316, then compare with the exact sum.
Answer: Estimate ≈ 500; exact = 536
08Estimate 231 + 323, then compare with the exact sum.
Answer: Estimate ≈ 500; exact = 554
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 estimate, check, and select efficient strategies 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
Estimate 242 + 330, then compare with the exact sum.
Estimate ≈ 500; exact = 572
Estimate 253 + 337, then compare with the exact sum.
Estimate ≈ 600; exact = 590
Estimate 264 + 344, then compare with the exact sum.
Estimate ≈ 600; exact = 608
Estimate 275 + 351, then compare with the exact sum.
Estimate ≈ 700; exact = 626
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain estimate, check, and select efficient strategies problems accurately, then check each result with a second method.
Practice
Mastery check
01Estimate 286 + 358, then compare with the exact sum.
Answer: Estimate ≈ 700; exact = 644
02Estimate 297 + 365, then compare with the exact sum.
Answer: Estimate ≈ 700; exact = 662
03Estimate 308 + 372, then compare with the exact sum.
Answer: Estimate ≈ 700; exact = 680
04Estimate 319 + 379, then compare with the exact sum.
Answer: Estimate ≈ 700; exact = 698
05Estimate 330 + 386, then compare with the exact sum.
Answer: Estimate ≈ 700; exact = 716
06Estimate 341 + 393, then compare with the exact sum.
Answer: Estimate ≈ 700; exact = 734
07Estimate 352 + 400, then compare with the exact sum.
Answer: Estimate ≈ 800; exact = 752
08Estimate 363 + 407, then compare with the exact sum.
Answer: Estimate ≈ 800; exact = 770
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.