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Math 7 U1-L1 Tools for Problem Solving

A Plan for Problem Solving

Anyone can do the arithmetic once someone hands them the sum. The hard part is working out what the sum is.

Teacher Notes

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Lesson Goal

Students will learn the four-step plan for solving a problem: Explore, Plan, Solve, Examine. The arithmetic in this lesson is easy on purpose. The skill being taught is deciding what to work out and knowing whether the answer makes sense.

Key Concepts

Explore means working out what you already know and what you're being asked. Plan means deciding what to do with those numbers, and estimating roughly what the answer should be. Solve means doing it. Examine means checking the answer against the estimate, and working backwards to see if you land where you started.

Why The Estimate Comes First

This is the part of the lesson worth defending. A student can get the answer to almost any of these from a phone in about four seconds. What a phone will not do is tell him the answer should have been between ten and twenty hours, which is the only thing that catches a wrong answer.

So on this page the calculation stays locked until an estimate is entered. That's not a gimmick. It's the order the textbook itself teaches, and it's the habit that survives after the arithmetic is forgotten.

Where Students Get Stuck

Two places. The first is Explore, where a problem hands you a number you don't need. The second is Examine, which most students skip because they believe the answer as soon as the calculator shows it. If he does the check every time on the easy problems, he still has the habit on the hard ones.

Teaching Suggestion

Ask him to make up a problem of his own before the end of the lesson: something he genuinely wants to know, like how long a drive takes or what a full shopping cart comes to. Proposing the question is half of what this lesson teaches, and it's the half no worksheet can ask for.

Key Vocabulary

Explore
Step one: what do I know, and what am I trying to find?
Plan
Step two: what math should I use, and about what should the answer be?
Estimate
A rough range worked out before the real answer, so you know where it should land.
Examine
Step four: does my answer make sense? Check it against your estimate and work backwards.
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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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