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Math 7 U1-L10 Tools for Problem Solving

Solving Equations Mentally

In Variables and Expressions you had the rule and the number, and you found the answer. This time you have the answer, and the number is missing.

Teacher Notes

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Lesson Goal

By the end of this lesson your student should be able to look at an equation like 2n = 14, find the number that makes it true, and check it by putting that number back in.

It is the reverse of U1-L8. There the student had 2n and a value for n and worked out the answer. Here the answer is known and n is the missing piece.

Start With True or False

Before any letters, write 2 x 5 = 14 and ask whether it's true. Then 2 x 7 = 14. The student should hear an equation as a claim that can be right or wrong.

Then write 2n = 14 and ask the same question. The honest answer is that you can't tell yet, and that answer is the doorway into the lesson.

Where Students Get Stuck

๐Ÿšจ Students often guess once, see it's wrong, and guess again at random. Push them to read the wrong guess: was the result too big or too small? That tells them which way to move.

Some students stop at the number and never check it. The check is the step that makes it an answer rather than a guess, so make it a habit: put the number back in and see if the sentence is true.

Teaching Suggestion

Keep a small table as you guess: the guess, what it gives, and whether it's too big, too small or right. Writing the verdict down is what turns guessing into a method.

When a fact solves it outright, like 12r = 120, ask the student what times table fact they used. Naming the fact is the mental math.

Key Vocabulary

Equation
A math sentence with an equals sign in it. It can be true or false.
Solve
To find the number that makes an equation true.
Solution
The number that makes an equation true.
Guess and Check
Trying a number, seeing whether it is too big or too small, and using that to choose the next try.
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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