New
New
Year 8

Checking understanding of algebraic notation

I can represent situations using algebra.

New
New
Year 8

Checking understanding of algebraic notation

I can represent situations using algebra.

Lesson details

Key learning points

  1. Missing numbers can be found in context.
  2. Missing number problems can be expressed algebraically.
  3. Pairs of numbers that satisfy an equation with two unknowns can be found.
  4. Real life situations can be expressed using algebra.

Common misconception

When converting English to algebra, pupils can mix up 4x + 2 and 4(x + 2)

Reviewing priority of operations and expanding brackets may be helpful. The multiplier operates on all terms in the bracket.

Keywords

  • Integer - An integer is any positive or negative whole number or zero

  • Expression - An expression contains one or more terms, where each term is separated by an operator.

  • Equation - An equation is used to show 2 expressions that are equal to each other.

In learning cycle 1, the problems are worked through in steps. You may wish to adapt the amount of information you give pupils before allowing them chance to try the problems. Pupils could make up their own problems to consolidate understanding.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Here is a number line with two numbers shown. What calculation will work out the length of the arrow?
An image in a quiz
$$98 + 134$$
$$98 - 134$$
Correct answer: $$134 - 98$$
$$134\div 98$$
$$134\times 98$$
Q2.
Which calculation represents a half of 8?
Correct answer: $${1\over 2} \times 8 $$
$${1\over 2} \div 8 $$
$$8\div {1\over 2} $$
Correct answer: $$8\over 2$$
$$8\times 2$$
Q3.
Which of these are integers?
Correct answer: $$-3$$
$$-{1\over 5}$$
Correct answer: 0
3.6
Correct answer: 101
Q4.
A bag of sweets costs 5 p, which of these could represent the cost of buying any number of bags of sweets?
$$a + 5$$
Correct answer: $$5a$$
$$a5$$
$$a^5$$
$$a\over 5$$
Q5.
Match each calculation to its answer.
Correct Answer:$$5 + 3\times 2 + 1$$,12

12

Correct Answer:$$(5 + 3)\times 2 + 1$$,17

17

Correct Answer:$$(5 + 3)\times (2 + 1)$$,16

16

Correct Answer:$$5 + 3\times (2 + 1)$$,14

14

Q6.
Match each calculation to its answer.
Correct Answer:$${10-4\over 2} + 1$$,4

4

Correct Answer:$$10-{4\over 2} + 1$$,9

9

Correct Answer:$$10-4\over 2 + 1$$,2

2

Correct Answer:$$10-{4\over 2 + 1}$$,$$26\over 3$$

$$26\over 3$$

6 Questions

Q1.
Which equations are represented by this bar model?
An image in a quiz
$$y = 4x + 7$$
Correct answer: $$4x = y + 7$$
$$4x + y = 7$$
$$x = y + 7$$
Correct answer: $$y + 7 = 4x$$
Q2.
Which diagram could represent a rectangle that has a length 3 times its width?
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q3.
Match up equivalent terms.
Correct Answer:$$-{x\over 4}$$,$$-{1\over 4} x$$

$$-{1\over 4} x$$

Correct Answer:$$4x\over- 5$$,$$-{4\over 5} x$$

$$-{4\over 5} x$$

Correct Answer:$$-5x\over 4$$,$$-{5\over 4} x$$

$$-{5\over 4} x$$

Correct Answer:$$-x\over -4$$,$${1\over 4} x$$

$${1\over 4} x$$

Correct Answer:$$-10x\over -8x$$,$$\frac{5}{4}$$

$$\frac{5}{4}$$

Q4.
Match each expressions to its description.
Correct Answer:$$3b - 7$$,a number multiplied by 3 then subtract 7

a number multiplied by 3 then subtract 7

Correct Answer:$$3(b - 7)$$,a number subtract 7 then multiplied by 3

a number subtract 7 then multiplied by 3

Correct Answer:$$b - 7 \times 3$$,a number subtract the product of 7 and 3

a number subtract the product of 7 and 3

Correct Answer:$$7 - 3b$$,a number multiplied by 3 then subtracted from 7

a number multiplied by 3 then subtracted from 7

Correct Answer:$$3(7 - b)$$,a number subtracted from 7 then multiplied by 3

a number subtracted from 7 then multiplied by 3

Q5.
Select the values of $$a$$ and $$b$$ that satisfy the equation $$2a + 6b = 12$$.
$$a=-3, b = -1$$
$$a = 2, b = 10 $$
Correct answer: $$a = 3, b = 1$$
Correct answer: $$a = 4.5, b = 0.5$$
$$a = 15, b = -0.5$$
Q6.
Andeep has 2 blocks, one block is 5 cm smaller than the other. The blocks have a combined height of 121 cm. How tall is the larger block? cm
Correct Answer: 63, 63 cm, 63cm