Monday, August 3, 2026

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Teacher Abi Study Notebook

I DON’T UNDERSTAND... translating verbal and mathematical phrases.

Learn the vocabulary, follow the order, combine ideas, and translate in both directions—up to the level used in school assessments.

✏️ Teacher Abi’s Note
The easy examples are only the first step. This notebook keeps climbing until you can handle grouped and multi-operation phrases.
Learn in levelsTeacher example → your turn → checkpoint.
Practice your wayGuided, independent, mixed, or school challenge.
Master both directionsWords → algebra and algebra → words.
Start Check

What can you already translate?

The questions climb. Blank answers are allowed.

Translator Card 1

Addition phrases

plus · more than · increased by · added to
+
sum 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?
Practice Studio

Choose the amount and difficulty you need.

The practice now climbs to the same level as the worked examples and mastery.

Practice Workspace

Practice

Ready?

Can you translate at school difficulty?

Seven mixed items. You need 6 out of 7.

Learn From Your Mistakes

Fix only what you missed.

Complete Ready? first. Your correction set will appear here.
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For Students

Guided Practice, Independent Practice, Mixed Review, School Challenge, summary, and answer key.

Student Downloads

For Parents

Skills checklist, home review guide, and signs that a student needs guided help.

Parent Guide

For Teachers & Tutors

Lesson guide, leveled worksheets, matching activity, exit ticket, mini assessment, answer key, and remediation.

Teacher/Tutor Kit
Notebook Updated

I finished this.

Notebook Pocket
↔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
Teacher Abi Review Session

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.

Book a Review Session with Teacher Abi
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