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# KS3 Numeracy Year 8 Consolidating Numeracy

Use these Consolidating Numeracy sessions to check that your students' numeracy is and remains secure and fluent through Key Stage 3. Each session has additional teaching material in case you find they need some revision of concepts and procedures.

Each Unit consists of three ‘starters’ - two slides in a PowerPoint presentation designed to provide some quick numeracy revision to be done at the start of the maths lesson. This revision takes no more than 10-12 minutes. This revision can be done at the beginning of each maths lesson in the week.

If the students show that they have not mastered this aspect of numeracy and are not demonstrating fluency, there are further slides which may be used to teach and consolidate the topic. This further teaching can be used on that day, replacing the planned lesson, or can be factored in to the medium term planning to be taught at a later time.

## Unit 1 Place Value and Decimals 1 (free)

### Objectives

Day 1

• Explore the Place Value (PV) chart from thousands to hundredths;
• Carry out PV addition and subtraction.

KS3 Objective

• Understand and use place value for integers of any size.

Day 2

• Explore the Place Value of large numbers by ordering and comparing on a number line.

KS3 Objective

• Order decimals and use the number line as a model for ordering of the real numbers.

Day 3

• Explore the Place Value of 2-place decimals by ordering and comparing on a number line.

KS3 Objective

• Order decimals and use the number line as a model for ordering of the real numbers.

### Planning and Activities

Day 1

Check-up

Identify the value of each digit in numbers with up two decimal places. Use place value to add and subtract.

Follow-up

Use the place value grid and chart to consolidate understanding of the value of each digit, then use place value to change one digit at a time in a number.

Day 2

Check-up

Compare, order and place whole numbers on a number line between multiples of 10,000.

Follow-up

Use the most significant digits in 5-digit numbers to compare and place between multiples of 10,000 on number lines.

Day 3

Check-up

Order numbers with one or two decimal places. Place numbers with two decimal places between multiples of 0.1 on a number line.

Follow-up

Use the place value grid to compare numbers with one or two decimal places.

## Unit 2 Place Value and Decimals 2

### Objectives

Day 1

• Explore the PV chart from 1s to 10,000s: multiplying and dividing by 10.

KS3 Objective

• Understand and use place value for integers of any size.

Day 2

• Explore the PV chart from 100 to hundredths: Multiplying and dividing by 10.

KS3 Objective

• Understand and use place value for decimals and integers of any size.

Day 3

• Explore the PV chart from 10,000s to hundredths: Multiplying and dividing by 10 and 100.

KS3 Objective

• Understand and use place value for decimals and integers of any size.

### Planning and Activities

Day 1

Check-up

Multiply and divide by 10 (answers with up to one decimal place).

Follow-up

Use the place value grid to multiply and divide by 10 (answers with up to one decimal place).

Day 2

Check-up

Multiply and divide by 10 (answers with up to two decimal places).

Follow-up

Use the place value grid to multiply and divide decimals by 10 (answers with up to two decimal places).

Day 3

Check-up

Multiply and divide by 100 (answers with up to two decimal places).

Follow-up

Use the place value grid to multiply and divide by 100 (answers with up to two decimal places).

## Unit 3 Addition and Subtraction: Mental Strategies

### Objectives

Day 1

• Number bonds to 100: addition and subtraction; counting up.

KS3 Objectives

• Use the four operations applied to integers.
• Recognise and use relationships between operations including inverse operations.

Day 2

• Mental addition of 2-digit numbers, including decimal numbers.

KS3 Objective

• Use the four operations applied to integers and decimals.

Day 3

• Mental subtraction of 2-digit numbers, including decimal numbers, by counting up.

KS3 Objective

• Use the four operations applied to integers and decimals.

### Planning and Activities

Day 1

Check-up

Use pairs to 100 (addition and subtraction).

Follow-up

Use the 1-100 grid to find complements to 100.

Day 2

Check-up

Use mental strategies to add pairs of 2-digit whole numbers and 2-digit numbers with one decimal place.

Follow-up

Focus on three different mental strategies to add pairs of 2-digit whole numbers and 2-digit numbers with one decimal place.

Day 3

Check-up

Use ‘counting up’ to subtract pairs of 2-digit whole numbers and 2-digit numbers with one decimal place.

Follow-up

Use ‘counting up’ on the number line to subtract pairs of 2-digit whole numbers and 2-digit numbers with one decimal place.

## Unit 4 Multiples and Factors

### Objectives

Day 1

• Know times tables;
• Identify multiples and factors.

KS3 Objective

• Use the concepts and vocabulary of factors (or divisors) and multiples.

Day 2

• Double and halve 2-digit numbers by partitioning.

KS3 Objective

• Use relationships between operations.

Day 3

• Multiply 2-digit numbers by 1-digit numbers by partitioning.

KS3 Objective

• Use the four operations, including formal written methods.

### Planning and Activities

Day 1

Check-up

Answer times tables questions, recognise multiples and find factors.

Follow-up

Focus on ways to remember the 6 and 9 times tables and tricky facts. Use factor bugs and arrays to find factors. Recognise multiples.

Day 2

Check-up

Double and halve 2-digit numbers.

Follow-up

Partition using place value cards to double and halve 2-digit numbers.

Day 3

Check-up

Use partitioning to multiply 2-digit numbers by 1-digit numbers.

Follow-up

Partition using place value cards to multiply 2-digit numbers by 1-digit numbers, record steps in a grid.

## Unit 5 Multiplication and Division: Mental Strategies

### Objectives

Day 1

• Understand division as the reverse of multiplication: factors.

KS3 Objective

• Use the concepts and vocabulary of factors (or divisors).

Day 2

• Use efficient mental doubling and halving strategies.

KS3 Objective

• Use relationships between operations.

Day 3

• Carry out division for numbers greater than tables facts.

KS3 Objective

• Use the four operations, including formal written methods applied to integers.

### Planning and Activities

Day 1

Check-up

Write related multiplication and division facts. Find factors of 2-digit numbers.

Follow-up

Multiplication and division facts for the 6 times table, using arrays to see how they link. Use factor bugs to find factors of 2-digit numbers.

Day 2

Check-up

Use doubling and halving to multiply and divide whole numbers and amounts of money by 4, 5 and 8.

Follow-up

Use images such as towers of cubes and dividing cakes to show how doubling and halving can be used to multiply and divide by 4, 5 and 8.

Day 3

Check-up

Divide numbers above the times tables (no remainders), including word problems.

Follow-up

Use a context and the number line to support dividing numbers above the times tables (no remainders).

## Unit 6 Fractions 1

### Objectives

Day 1

• Identify equivalent fractions;
• Reduce fractions to their simplest form.

KS3 Objective

• Extend understanding of the number system including fractions.

Day 2

• Use fraction families to compare fractions.

KS3 Objective

• Extend understanding of the number system including fractions.

Day 3

• Change improper fractions to mixed numbers and vice versa.

KS3 Objective

• Extend understanding of the number system including fractions.

### Planning and Activities

Day 1

Check-up

Identify equivalent fractions. Simplify fractions.

Follow-up

Use pies and fractions walls to show equivalent fractions.

Day 2

Check-up

Compare and order fractions with different denominators.

Follow-up

Use pies and fractions walls to compare fractions.

Day 3

Check-up

Change improper fractions to mixed numbers and vice versa. Compare improper fractions.

Follow-up

Use pies and fractions walls to show mixed numbers and improper fractions.

## Unit 7 Place Value and Decimals 3

### Objectives

Day 1

• Compare and round whole numbers.

KS3 Objective

• Round numbers and measures to an appropriate degree of accuracy.

Day 2

• Compare and round decimal numbers.

KS3 Objective

• Round numbers and measures to an appropriate degree of accuracy.

Day 3

• Derive decimal and fraction equivalents.

KS3 Objective

• Work interchangeably with terminating decimals and their corresponding fractions.

### Planning and Activities

Day 1

Check-up

Round whole numbers to the nearest 10, 100 or 1000.

Follow-up

Place numbers on the number line to round them to the nearest 100 or 1000.

Day 2

Check-up

Place numbers with one two decimal places on number lines. Round decimals to the nearest whole or tenth.

Follow-up

Place numbers with one or two decimal places on the number line to round them to the nearest whole or tenth.

Day 3

Check-up

Identify equivalent fractions and decimals. Use equivalent with decimals to compare fractions.

Follow-up

Mark fractions and decimals on a number line to find equivalent fractions and decimals.

## Unit 8 Written Addition and Subtraction

### Objectives

Day 1

• Revise counting up to solve decimal subtraction.

KS3 Objective

• Use the four operations, including formal written methods, applied to integers and decimals.

Day 2

• Relate the addition and subtraction of decimals.

KS3 Objectives

• Use the four operations, including formal written methods, applied to integers and decimals.
• Recognise and use relationships between operations including inverse operations.

Day 3

• Consolidate counting up to complete ‘missing- number’ problems.

KS3 Objectives

• Use the four operations, including formal written methods, applied to integers and decimals.
• Recognise and use relationships between operations including inverse operations.

### Planning and Activities

Day 1

Check-up

Use mental strategies to add and subtract pairs of numbers with one decimal place.

Follow-up

Use ‘counting up’ on the number line to subtract pairs of numbers with one decimal place.

Day 2

Check-up

Use ‘counting on’ and number facts to add pairs of numbers with one decimal place.

Follow-up

Use ‘counting on’ on a number line to add pairs of numbers with one decimal place and ‘counting up’ to work out missing numbers in additions.

Day 3

Check-up

Use ‘counting up’ to solve missing number problems (whole numbers and amounts of money).

Follow-up

Use ‘counting up’ on the number line to solve missing number problems and find change.

## Unit 9 Multiplication and Division 2

### Objectives

Day 1

• Revise grid multiplication for 2-digit numbers and for 1-place decimals.

KS3 Objective

• Use the four operations, including formal written methods, applied to integers and decimals.

Day 2

• Perform division with remainders, mainly within times tables facts or just above.

KS3 Objectives

• Use the four operations.
• Consolidate numerical and mathematical capability from key stage 2 and extend understanding of the number system.

Day 3

• Relate multiplication and division.

KS3 Objectives

• Use the four operations.
• Consolidate numerical and mathematical capability from key stage 2 and extend understanding of the number system.

### Planning and Activities

Day 1

Check-up

Use the grid method to multiply 2-digit whole numbers and 2-digit numbers with one decimal place by 1-digit numbers.

Follow-up

Show how to use the grid method to multiply 2-digit whole numbers and 2-digit numbers with one decimal place by 1-digit numbers.

Day 2

Check-up

Divide numbers within or above the times tables, with remainders.

Follow-up

Use a context and the number line to support dividing numbers above the times tables, with remainders.

Day 3

Check-up

Write multiplications and divisions to link given numbers.

Follow-up

Write multiplications and divisions to go with arrays to help students to see the link between multiplication and division.

## Unit 10 Division: Written Strategies

### Objectives

Day 1

• Use short division to divide up to 4-digit numbers by a single-digit number.

KS3 Objectives

• Use the four operations, including formal written methods.
• Consolidate numerical and mathematical capability from Key Stage 2 and extend understanding of the number system.

Day 2

• Use short division to divide up to 4-digit numbers by a 2-digit number.

KS3 Objective

• Consolidate their numerical and mathematical capability from Key Stage 2 and extend their understanding of the number system.

Day 3

• Rehearse strategies for dividing decimals.

KS3 Objectives

• Understand and use place value for decimals, measures and integers of any size.
• Use the four operations, including formal written methods, applied to integers and decimals.

### Planning and Activities

Day 1

Use short division to divide 3-digit and 4-digit numbers by single-digit numbers, including word problems.

Follow-up

Use base 10 equipment to show how to use short division to divide 3-digit and 4-digit numbers by single-digit numbers.

Day 2

Check-up

Use short division to divide 3-digit and 4-digit numbers by 2-digit numbers.

Follow-up

List multiples of the divisor to help students to use short division of 3-digit and 4-digit numbers by 2-digit numbers.

Day 3

Use division of whole numbers, then divide by 10 or 100 to divide numbers/measures with one or two decimal places by single-digit numbers, including one place decimals.

Follow-up

Use efficient grouping to divide whole numbers, then divide by 10 or 100 to divide numbers/measures with one or two decimal places by single-digit whole numbers.

## Unit 11 Fractions 2

### Objectives

Day 1

• Identify equivalent fractions;
• Reduce fractions to their simplest form.

KS3 Objective

• Move freely between different numerical equivalent fractions.

Day 2

• Compare and order fractions, including mixed numbers.

KS3 Objective

• Move freely between different numerical equivalent fractions.

Day 3

• Find fractions of amounts and relate to division.

KS3 Objective

• Use the four operations with proper fractions.

### Planning and Activities

Day 1

Check-up

Identify equivalent fractions. Simplify fractions.

Follow-up

Identify ‘fraction families’. Use pies to identify equivalent fractions and simplify fractions.

Day 2

Check-up

Order fractions, including mixed numbers.

Follow-up

Use fraction walls and factors to compare fractions, including mixed numbers and improper fractions.

Day 3

Check-up

Find unit and non-unit fractions of amounts.

Follow-up

Use pies, a bar model and the link with division to find a unit fraction of amount and then a related non-unit fraction of the same amount.

## Unit 12 Mental Calculations and Money

### Objectives

Day 1

• Use inverse operations to check calculations and to solve missing number calculations.

KS3 Objective

• Recognise and use relationships between operations including inverse operations.

Day 2

• Revise adding amounts of money and finding change.

KS3 Objective

• Use standard units of mass, length, time, money and other measures, including with decimal quantities.

Day 3

• Revise multiplying and dividing amounts of money by a single digit number.

KS3 Objective

• Use standard units of mass, length, time, money and other measures, including with decimal quantities.

### Planning and Activities

Day 1

Check-up

Use inverse operations to solve missing number calculations.

Follow-up

Use function machines to help students see that inverse operations do the opposite of each other.

Day 2

Check-up

Use mental strategies to add amounts of money and find change.

Follow-up

Focus on the three mental strategies to add amounts of money, and ‘counting up’ to find change.

Day 3

Check-up

Multiply and divide amounts of money by single-digit numbers to solve problems, choosing a strategy.

Follow-up

Look at a range of mental and written strategies to multiply and divide amounts of money by single-digit numbers.