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Teacher Abi Study Notebook

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.

Still completely lost?You don’t have to figure it out alone. Book a review session with Teacher Abi.

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What do you already know?

Don’t study anything yet. Just try these. It’s completely fine to leave something blank.

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

“A number” → x

“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

Twice a number → 2x

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

A number → x

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.

The number → x

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

thrice · triple

Level 1 — one product

The product of 7 and a number

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

The sum → x + 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

A number comes first

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

The sum → x + 6

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

Twice a number → 2x

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

Difference → x − 7

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

Sum → x + 8

Quotient → (x + 8) / 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`

4x → four times a number

+ 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. Aim for 6 out of 7. Your score helps you decide what to review — it does not block the rest of the notebook.

Download Center

Use this notebook again.

For Students

Practice sheets, mastery sheets, challenge sheets, complete answer key, and printable review resources.

Student Downloads

For Parents

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

Parent Guide

For Teachers & Tutors

Lesson guide, matching activity, exit ticket, mini assessment, answer key, teaching tips, 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

Solving One-Step Equations — Coming Soon

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.

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Teacher Abi Study Notebook

I DON’T UNDERSTAND...

Translating Verbal Phrases into Mathematical Expressions

A printable practice path for verbal phrases and mathematical expressions — from one-operation practice to mixed mastery, challenges, and translation in both directions.

These free worksheets are the printable companion to Teacher Abi’s interactive study notebook on translating verbal phrases into mathematical expressions and vice versa. They are organized by skill rather than grade level, so students can begin where they are ready and move forward at their own pace.

The learning path follows the same Teacher Abi system: learn the idea → practice with support → mix the skill → work independently → try a challenge. Students do not need to complete every sheet if a skill is already secure.

Start with the interactive notebook

If the wording still feels confusing, begin with the interactive notebook. It teaches the keywords, order, reverse-order subtraction, combined expressions, and mathematical-to-verbal translation with worked examples and guided practice.

Open the Interactive Notebook

Practice divided by, quotient of, and common division wording.

Download PDF

Reverse the process by writing verbal phrases for mathematical expressions.

Download PDF

Translate multi-operation mathematical expressions back into words.

Download PDF

Parent, Teacher & Tutor Resources

The worksheets are one part of the Teacher Abi Study Notebook system. These companion guides help adults support the same skills without having to recreate the lesson from scratch.

FOR PARENTS

Parent Guide

Use this if a student is reviewing at home and you want to know what to practice, what mistakes to watch for, and when guided help may be useful.

Skills checklist
Simple home review plan
Signs a student may need guided support
Easy ways to practice without another worksheet
Which practice sheet to repeat for a specific difficulty

Download Parent Guide PDF

FOR TEACHERS & TUTORS

Teacher & Tutor Guide

A ready-to-use teaching companion for classroom instruction, tutoring, intervention, homeschool, or review sessions.

Learning objectives and suggested teaching sequence
Ready-to-photocopy matching activity
5-item exit ticket
10-item mini assessment
Answer keys
Remediation map
Teaching tips for common errors

Download Teacher & Tutor Guide PDF

Choose your next step

You do not have to use every resource in order. Start with the first stage that matches what the student can already do, then move forward when the skill feels secure.

Interactive Notebook — learn the wording, see worked examples, and practice with immediate feedback.
Practice Sheets 1–5 — focus on one operation at a time: addition, subtraction, reverse-order subtraction, multiplication, and division.
Mastery Sheets A–C — mix the operations, reduce the hints, and practice translating in both directions.
Challenge Sheets A–C — work with combined phrases and multi-operation expressions.
Complete Answer Key — check mistakes immediately and return only to the skill that needs more practice.

Complete Answer Key

The complete answer key covers all Practice, Mastery, and Challenge Sheets in this pack.

For mathematical-expression-to-verbal-phrase items, equivalent wording is accepted when it represents the same mathematical meaning and order.

Download Complete Answer Key

Still not confident in one part?

Go back only to the skill that needs more attention. Reopen the interactive notebook for the explanation, or repeat the matching practice sheet before moving on to mastery or challenge work.

Return to the Interactive Notebook

Still getting stuck on the wording?

If the easy examples make sense but “less than,” “subtracted from,” reverse-order subtraction, or combined phrases still cause trouble, Teacher Abi can work through the exact pattern that is confusing you.

The goal is not to repeat the entire lesson. Guided review can focus only on the skill that is still causing mistakes.

Book a Review Session with Teacher Abi

Friday, August 7, 2026

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

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

What do you already know?

Addition phrases

Three more than a number

The sum of a number and 9

A number increased by 6

Five more than twice a number

Seven more than three times a number

The total of four times a number and 8

Subtraction: normal and reverse order

A number decreased by 6

A number diminished by 10

The difference of a number and 4

Eight less than a number

A number subtracted from 20

Five less than three times a number

Multiplication phrases

The product of 7 and a number

Triple a number

The product of 6 and a number

Four times the sum of a number and 2

Five times the difference of a number and 3

Twice the sum of a number and 8

Division phrases

The quotient of a number and 5

The ratio of a number to 8

A number divided by 6

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

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

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

Combine ideas one step at a time.

Three less than twice a number

Six more than four times a number

Seven less than five times a number

Three times the difference of a number and 7

Twice the sum of a number and 9

Four times the difference of twice a number and 3

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

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

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

Read the structure back into words.

4x + 5

3x − 7

2x + 9

5(x + 2)

(x − 4) / 2

3(x + 1) − 5

Now use the skill the way quizzes do.

Choose the amount and difficulty you need.

Practice

Can you translate at school difficulty?

Use this notebook again.

For Students

For Parents

For Teachers & Tutors

I finished this.

Still not understanding it?

That is okay.

FREE Grade 7 Algebra Worksheets PDF | Translating Verbal Phrases into Mathematical Expressions

Translating Verbal Phrases into Mathematical Expressions

Start with the interactive notebook

Practice — Build One Skill at a Time

Addition Verbal Phrases

Subtraction Verbal Phrases

Reverse-Order Subtraction

Multiplication Verbal Phrases

Division Verbal Phrases

Mastery — Mix the Skills

Mixed Verbal Phrases

Independent Mixed Mastery

Mathematical Expressions to Verbal Phrases

Challenge — Put the Skills Together

Combining Verbal Phrases

Combining Verbal Phrases — Independent

Combined Expressions to Verbal Phrases

Parent, Teacher & Tutor Resources

Parent Guide

Teacher & Tutor Guide

`4x + 5`

`3x − 7`

`2x + 9`

`5(x + 2)`

`(x − 4) / 2`

`3(x + 1) − 5`