🔢 MathGrade 4Lesson 34
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Operations Challenge
Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).
Learning Objectives
- 1Review multiplication and division of multi-digit numbers
- 2Apply fraction and decimal concepts to solve problems
- 3Use inverse operations to check answers
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Mini Lesson
This challenge reviews Unit 3 skills: multiplication, division, fractions, decimals, and order of operations. Use everything you have learned to show your operations mastery.
Multi-Step Problems
- Work through one operation at a time — never rush to the answer.
- Follow the order of operations: brackets first, then multiplication and division, then addition and subtraction.
- Estimate your answer first so you can check whether your result is reasonable.
Inverse Operations
- Multiplication and division undo each other: if 8 × 9 = 72, then 72 ÷ 9 = 8.
- Use the inverse operation to check your answer after every calculation.
- Addition and subtraction are also inverse operations: 45 + 23 = 68, so 68 − 23 = 45.
Fractions and Decimals
- Fractions and decimals both represent parts of a whole.
- Key equivalents: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2.
- To add fractions, the denominators must be the same: 3/4 + 1/4 = 4/4 = 1.
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Tip: memorize the key fraction-decimal pairs (1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75) — they appear in many problems.
Vocabulary
inverse operation
An operation that undoes another (multiplication ↔ division, addition ↔ subtraction).e.g. Check 8 × 9 = 72 by computing 72 ÷ 9 = 8.
order of operations
The agreed order for evaluating an expression: brackets, then ×/÷, then +/−.e.g. 6 + 2 × 3 = 6 + 6 = 12, not 24.
estimate
A rough answer used to check that a calculation is reasonable.e.g. Estimate 412 × 9 as 400 × 10 = 4,000.
fraction
A number that represents part of a whole, written as numerator/denominator.e.g. 3/4 means 3 of 4 equal parts.
decimal
A number that uses a decimal point to show parts smaller than one.e.g. 0.25 is the decimal form of 1/4.
denominator
The bottom number of a fraction, showing how many equal parts make a whole.e.g. In 3/4, the denominator is 4.
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