Equivalence is when two or more things have the same value.

Compensation is a mental strategy which involves adjusting parts of an equation while maintaining equivalence.

An unknown is a quantity that has a set value but it is represented by a symbol or letter.

An expression contains one or more values, where each value is separated by an operator.

Use equivalence and compensation strategies to solve problems

Maths

Using redistribution with addition of integers

Using redistribution with addition of decimal fractions

Using balanced equations to calculate redistribution

Use a balanced equation to calculate unknown parts

Explain how adjusting one part affects the sum

Solve addition calculations mentally by using known facts

Solve addition calculations mentally by using known facts in a range of contexts

Solve calculations with missing parts

Use equivalence and compensation strategies to solve addition problems in a range of contexts

In this unit pupils used the concept of same sum to simplify and solve addition problems. In the future unit pupils will solve calculations with missing addends and use the same difference rule to balance equations. They will explain how increasing or decreasing the minuend affects the difference.

In the prior unit pupils identified structures within stories using their knowledge of structures to create stories. They used their knowledge of additive structures to solve problems. In this unit pupils used the concept of same sum to simplify and solve addition problems

In this unit pupils used the concept of same sum to simplify and solve addition problems.

Use equivalence and compensation to simplify and solve addition calculations

Which of the equations below is incorrect and does not contain two equivalent expressions?

Calculate the unknown in this equation.
45 + {{ }} = 97

Calculate the unknown in this equation.
1.3 + {{ }} + 1.7 = 1.1 + 2.1 + 0.8

Calculate the unknown in the empty box of this magic square.

34 + 0.145 + 109.25 > 100 + 9.25 + 34.135

£67.50 + £67.70 + £67.90 < £67.70 + £67.70 + £67.70

9,100,206 + 4,023,128 > 4,023,128 + 9,010,206

234.5 kg + 200 kg < 230 kg + 204 kg + 0.5 kg

Some of the inequality statements below are false. Can you spot them?

What do expressions have if they are equivalent?

What is the unknown in the equation below?
{{ }} + 3 + 8 = 15

What is the unknown in the equation below? {{ }} + 0.6 + 0.8 = 1.5

What is the unknown in the equation below?
{{ }} + 67 = 82 + 18

Which inequality symbol should go between these two expressions?
54 + 98 {{ }} 52 + 101

Which inequality symbol should go between these two expressions?
3.6 + 2.3 {{ }} 3.3 + 2.1

Starter Quiz

What do expressions have if they are equivalent?