Courseversity

Lesson

Numerical expressions

Primary EducationGrade 5MathematicsCV-PRI-G05-MATH-NUM-U01-L0745–60 min

You will learn

  • Translate words into expressions.
  • Use parentheses.
  • Evaluate simple expressions.
  • Compare expressions.

Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

The lesson in 60 seconds

  1. An expression has numbers and operations but no equals sign.
  2. Do the brackets first.
  3. Translate words into expressions.
  4. Evaluate to find the value.

Words to know

expression
Numbers and operations without =.
parentheses
Brackets that group.
evaluate
Find the value.
operation
Add, subtract, multiply, divide.

1. Discover: words to numbers

“Add 8 and 7, then multiply by 2.” How do you write that with numbers?

2. Understand: expressions

  • “Add 8 and 7, then multiply by 2” is 2 × (8 + 7) = 2 × 15 = 30.
  • 3 × (4 + 5) = 3 × 9 = 27.
  • “Subtract 5 from 20, then divide by 3”: (20 − 5) ÷ 3 = 5.

Parentheses show what to do first.

Idea 1: Brackets

4 × (6 + 2): 6 + 2 = 8, then 4 × 8 = 32. 10 − (3 + 2) = 10 − 5 = 5.

Idea 2: Division

(15 − 3) ÷ 4 = 12 ÷ 4 = 3. 2 × (9 − 4) = 2 × 5 = 10.

Idea 3: Words

“Add 6 and 4, then multiply by 3” is 3 × (6 + 4).

Why brackets? They show what to do first.

Remember: Parentheses first, then the rest.

3. Worked examples

Example 1 (I show you): Evaluate

4 × (6 + 2)

  1. Brackets first.

Answer: 32

Example 2 (We do it together): Evaluate

(15 − 3) ÷ 4

  1. 15 − 3 = 12.

Answer: 3

Example 3 (You try): Write

Add 6 and 4, then multiply by 3

Show the steps and answer
  1. Brackets around the add.

Answer: 3 × (6 + 4)

Did you know?

Brackets change the order in which we calculate.

Why this matters

Expressions let us write calculations clearly for others and for computers.

4. Explore: translate

You need paper.

  1. Write “add 8 and 7, then multiply by 2”.
  2. Use parentheses.
  3. Evaluate.
  4. Compare with 8 + 7 × 2.
Think about it: what did you notice?

30 vs 22.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • First I work out ___.
  • Then I ___.
  • The value is ___.
  • In words it says ___.

Guided practice

Question 1. 2 × (8 + 7)?

30.

Question 2. 3 × (4 + 5)?

27.

Question 3. (20 − 5) ÷ 3?

5.

Independent practice

Level 1: Start

  1. 4 × (6 + 2)
  2. (15 − 3) ÷ 4
  3. Write: add 6 and 4, then multiply by 3
  4. 10 − (3 + 2)
  5. 2 × (9 − 4)

Level 2: Grow

  1. 6 × (2 + 3)
  2. (24 − 4) ÷ 5
  3. Write: add 5 and 7, then divide by 3

Level 3: Stretch

  1. 3 × (10 − 4) + 2
  2. Write: multiply 4 by the sum of 3 and 5
  3. Ana says 10 − (3 + 2) = 9. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

Ada buys 3 packs. Each pack has 4 pens and 5 books. Write the total number of items as an expression.

Show a sample answer

3 × (4 + 5) = 27.

Another one. A box has 6 red and 4 blue pens. Ana buys 3 boxes. Write an expression and find the total.

Show a sample answer

3 × (6 + 4) = 30 pens

7. Common mistakes

Mistake: Ignoring parentheses.
Fix: Do parentheses first.
Another mistake: Ignoring the brackets.
Fix: Do the brackets first.
Another mistake: Writing an expression without brackets when needed.
Fix: Use brackets to show the first step.

8. Lesson summary and revision card

I can…

  • I can translate words into expressions.
  • I can use parentheses.
  • I can evaluate simple expressions.
  • I can compare expressions.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. 2 × (8 + 7) =

2. 3 × (4 + 5) =

3. (20 − 5) ÷ 3 =

4. 4 × (6 + 2) =

5. 10 − (3 + 2) =

6. 5 × (3 + 4) =

7. (18 − 6) ÷ 3 =

8. 20 − (4 + 6) =

9. Subtract 3 from 10, then multiply by 2 is…

10. 3 × (9 − 2) =

11. (7 + 5) × 2 =

12. 2 × (3 + 4) __ 2 × 3 + 4

Challenge 1. Add 6 and 4, then multiply by 3:

Challenge 2. (12 + 8) ÷ (7 − 3) =

Your result appears here after you answer every question.

10. Key takeaways

  • Words to symbols.
  • Parentheses first.
  • Evaluate stepwise.

11. Next lesson

Next lesson: Multidigit multiplication. Keep going with the next idea in this course.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

  1. Find 4 × (6 + 2). [2 marks]
  2. Find (15 − 3) ÷ 4. [2 marks]
  3. Write: add 6 and 4, then multiply by 3. [2 marks]
  4. Find 10 − (3 + 2). [2 marks]
  5. Ben says 2 × (9 − 4) = 14. Is he right? Explain. [3 marks]

Total: 11 marks.

Marking guide and model answers
  1. Brackets first: 8 [1]; 32 [1]
  2. 15 − 3 = 12 [1]; 3 [1]
  3. Brackets round the add [1]; 3 × (6 + 4) [1]
  4. 3 + 2 = 5 [1]; 5 [1]
  5. No [1]. Brackets first: 9 − 4 = 5 [1]. 2 × 5 = 10 [1].

Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.

Printable worksheet

  1. 4 × (6 + 2)
  2. (15 − 3) ÷ 4
  3. Add 6 and 4 then multiply by 3
  4. 10 − (3 + 2)
  5. 2 × (9 − 4)
  6. 2 × (8 + 7) =
  7. 3 × (4 + 5) =
  8. (20 − 5) ÷ 3 =
  9. 4 × (6 + 2) =
  10. 10 − (3 + 2) =

Homework

Write five word problems as expressions.

Answer key and marking scheme

Question Expected response Marks
4 × (6 + 2) 32 2
(15 − 3) ÷ 4 3 2
Add 6 and 4 then multiply by 3 3 × (6 + 4) 2
10 − (3 + 2) 5 2
2 × (9 − 4) 10 2
Total 10

Practice answers: Worksheet: 1 32; 2 3; 3 3 × (6 + 4); 4 5; 5 10.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.

Extra worksheet answers (items 6 onward): 6 30; 7 27; 8 5; 9 32; 10 5.

Independent practice answers. Level 1: 1 32; 2 3; 3 3 × (6 + 4); 4 5; 5 10. Level 2: 1 30; 2 4; 3 (5 + 7) ÷ 3. Level 3: 1 20; 2 4 × (3 + 5); 3 She did 10 − 3 + 2. Brackets first: 3 + 2 = 5 and 10 − 5 = 5..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Translate words into expressions Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Use parentheses Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Evaluate simple expressions Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Compare expressions Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Ignoring parentheses. Do parentheses first.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Practise two-step computations.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child writes and evaluates expressions with brackets. You do not need to be good at mathematics to help.

  • Write shopping calculations as expressions.
  • Ask: what do we do first?
  • Read an expression aloud in words.
  • Ask “how do you know?” after each answer, and listen.
  • Praise effort, not only right answers. Mistakes are how we learn.
  • Ten to fifteen minutes a day is better than one long session.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: translate words into expressions; use parentheses; evaluate simple expressions; compare expressions.

Prerequisite knowledge. Grade 4 operations.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 45–60 minutes. It can be split into two shorter sessions.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Key questions. What is in the brackets? What comes next?

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Ignoring parentheses. Do parentheses first.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Practise two-step computations. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.

Research used to shape this lesson. Common Core 5.OA.A.1 and 5.OA.A.2; Cambridge Primary Mathematics Stage 5 (expressions). These sources informed the lesson; no official alignment is claimed.

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