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Math 7 U1-L11 Tools for Problem Solving

Unit 1 Review: Tools for Problem Solving

Ten lessons can feel like ten separate tricks. They aren't; every one of them fits into the plan from the very first lesson.

Teacher Notes

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Lesson Goal

Bring the ten Unit 1 lessons together under the four-step plan from U1-L1, check which tools hold, and find the ones that need a second read.

This is a diagnostic, not a test. Every question's hint names the lesson to reopen, so a wrong answer is a pointer rather than a grade.

How to Use It

Read the review through once, then do the questions. For every miss, open the lesson the hint names and read just the section it points to, then come back.

If the student misses two or more questions from the same step, that step is the one to re-teach before Unit 2 starts.

Where Students Get Stuck

🚨 The two most common misses in this unit are reading 3⁴ as 3 x 4, and doing addition before multiplication in an expression like 3 + 7 x 4 - 6. Both come from working left to right without checking the order.

The Examine step gets skipped more than any other. If the student gets an answer and stops, ask what it should have been about, before looking at the answer key.

Key Vocabulary

Explore
Step one: what do I know, and what am I trying to find?
Examine
Step four: does my answer make sense? Check it against your estimate.
Estimate
A quick, rounded answer that tells you roughly where the real one should land.
Reasonable
Close enough to your estimate that the answer is probably right.
Order of Operations
The agreed hierarchy that tells us which operations to do first.
Variable
A letter that holds the place of a number that can change or is not known yet.
Exponent
The small raised number that counts how many times the base is used as a factor.
Equation
A math sentence with an equals sign in it. It can be true or false.
Solution
The number that makes an equation true.
Sentence 1 of 26 Tap any sentence to start reading there
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Before You Start

The Words

The words this lesson uses. Tap a card to see what it means, then come back to them whenever a question uses one.

Part One

The Questions

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Questions about the story you just read. Pick your answer straight off, or press Find it in the story if you would rather hunt for the sentence first.

Part Two

Vocabulary Check

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The word cards are at the top of this page. Look back at them as often as you need, then answer.

When you finish: write the answers out in your own words — not copied word for word from the choices. Saying it your own way is the part that proves you understood it. Then use Print Answer Sheet for a one-page record of what was answered and scored.
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