I DON'T UNDERSTAND... Translating Verbal Phrases into Mathematical Expressions (Grade 7 Interactive Notebook)

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I DON’T UNDERSTAND...

Translating English/Verbal Phrases to Mathematical Phrases and Vice Versa

Notebook 1 of 6Grade 7 Algebra

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I DON’T UNDERSTAND...Translating Verbal Phrases into Mathematical Expressions and Vice Versa

Example 1Five more than a numberx + 5

Example 2Three less than twice a number2x − 3

Okay. What are these words actually telling you to do?

That is what this notebook is for. We’ll look for the clues, build the expression one piece at a time, and work up to the kind of phrasing that shows up in school.

Teacher Abi’s Note

Don’t memorize a giant list and hope for the best. Learn what the words are telling you to do, then build the expression one piece at a time.

Learn in levelsTeacher example → your turn → checkpoint.

Practice your wayGuided, independent, mixed, or school challenge.

Master both directionsWords → algebra and algebra → words.

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Translator Card 1

Addition phrases

Look for these words in the phrase. When you see them, they are clues that you will add.

Look forplus · more than · increased by · added to

+

Also means addsum of · total of

+

Level 1 — one operation

Three more than a number

1.

“A number” → x

2.

“Three more” → add 3

Answer

x + 3

The sum of a number and 9

A number → x

The sum of that number and 9 → x + 9

A number increased by 6

A number → x

Increased by 6 → x + 6

Level 2 — combine two ideas

Five more than twice a number

1.

Twice a number → 2x

2.

Five more → + 5

Answer

2x + 5

Seven more than three times a number

Three times a number → 3x

Seven more than that → 3x + 7

The total of four times a number and 8

Four times a number → 4x

The total of that and 8 → 4x + 8

Quick Check

Translator Card 2

Subtraction: normal and reverse order

minus · decreased by · diminished by

−

difference of

−

less than · subtracted from

REVERSE

Level 1 — normal order

A number decreased by 6

1.

A number → x

2.

Decreased by 6 → − 6

Answer

x − 6

A number diminished by 10

A number → x

Diminished by 10 → x − 10

The difference of a number and 4

First quantity → x

Second quantity → 4

Difference → x − 4

Level 2 — reverse order

Eight less than a number

Ask: “Eight less than what?” The number comes first.

1.

The number → x

2.

Take away 8

Answer

x − 8

A number subtracted from 20

Start with 20

Subtract the number → 20 − x

Five less than three times a number

Three times a number → 3x

Five less than that → 3x − 5

Quick Check

Translator Card 3

Multiplication phrases

times · multiplied by · product of

×

twice · double

2x

thrice · triple

3x

Level 1 — one product

The product of 7 and a number

1.

Product means multiplication

Answer

7x

Triple a number

Triple → 3 times

A number → x

Answer → 3x

The product of 6 and a number

The product of 6 and x → 6x

Level 2 — multiply a group

Four times the sum of a number and 2

1.

The sum → x + 2

2.

Four times the whole sum

Answer

4(x + 2)

Five times the difference of a number and 3

Difference → x − 3

Five times the whole difference → 5(x − 3)

Twice the sum of a number and 8

Sum → x + 8

Twice that sum → 2(x + 8)

Quick Check

Translator Card 4

Division phrases

divided by · quotient of · ratio of

÷

Level 1 — one quotient

The quotient of a number and 5

1.

A number comes first

2.

5 comes second

Answer

x / 5

The ratio of a number to 8

A number → x

Ratio to 8 → x / 8

A number divided by 6

A number → x

Divided by 6 → x / 6

Level 2 — divide a group

The quotient of the sum of a number and 6 and 3

1.

The sum → x + 6

2.

Divide the whole sum by 3

Answer

(x + 6) / 3

The quotient of the difference of a number and 4 and 2

Difference → x − 4

Divide the whole difference by 2 → (x − 4) / 2

The quotient of the sum of twice a number and 5 and 4

Twice a number → 2x

Sum with 5 → 2x + 5

Divide the whole sum by 4 → (2x + 5) / 4

Quick Check

Level Up Examples

Combine ideas one step at a time.

Level 3

Three less than twice a number

1.

Twice a number → 2x

2.

Three less than that → 2x − 3

Six more than four times a number

Four times a number → 4x

Six more → 4x + 6

Seven less than five times a number

Five times a number → 5x

Seven less → 5x − 7

Level 4 — grouping

Three times the difference of a number and 7

1.

Difference → x − 7

2.

Three times the whole difference → 3(x − 7)

Twice the sum of a number and 9

Sum → x + 9

Twice the sum → 2(x + 9)

Four times the difference of twice a number and 3

Twice a number → 2x

Difference with 3 → 2x − 3

Four times that difference → 4(2x − 3)

Level 5 — school difficulty

Five less than the quotient of the sum of a number and 8 and 3

1.

Sum → x + 8

2.

Quotient → (x + 8) / 3

3.

Five less than that → (x + 8) / 3 − 5

Four more than the quotient of the difference of a number and 6 and 2

Difference → x − 6

Divide by 2 → (x − 6) / 2

Add 4 → (x − 6) / 2 + 4

Three less than the quotient of the sum of twice a number and 5 and 4

Twice a number plus 5 → 2x + 5

Divide by 4 → (2x + 5) / 4

Three less → (2x + 5) / 4 − 3

Mathematical → Verbal

Read the structure back into words.

Level 1

4x + 5

1.

4x → four times a number

2.

+ 5 → increased by five

Answer

Four times a number increased by five.

3x − 7

3x → three times a number

− 7 → decreased by seven

2x + 9

2x → twice a number

+ 9 → nine more

Level 2 — grouping

5(x + 2)

Inside

x + 2 → the sum of a number and two

Outside

Five times that sum

Answer

Five times the sum of a number and two.

(x − 4) / 2

x − 4 → the difference of a number and four

Divide that difference by 2

3(x + 1) − 5

x + 1 → the sum of a number and one

3(x + 1) → three times that sum

− 5 → decreased by five

More than one wording may be correct

The words may change, but the operation, order, and grouping must stay the same.

School-Style Questions

Now use the skill the way quizzes do.

1. Which expression represents “seven less than twice the sum of a number and 1”?

2. Which verbal phrase matches 3(x − 4) + 2?

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↔Expression TranslatorTeacher Abi Study Notebook

Today I can...

• translate one-operation and multi-operation verbal phrases
• use parentheses for grouped sums and differences
• translate mathematical phrases back into words
• handle “less than” and “subtracted from” correctly

Solving One-Step Equations — Coming Soon

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Still not understanding it?

That is okay.

Sometimes the easy example makes sense, but the grouped or multi-operation phrase does not. That usually means one step in the translation process needs to be rebuilt.

In a review session, we will identify the exact phrase or order that is causing the problem and practise from that level upward.

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