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# KS3 Numeracy Year 7 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.

Day 2

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

Day 3

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

### Teaching and Activities

Day 1

Check-up

Write numbers with up two decimal places as words and figures. Use place value to add and subtract, changing one digit at a time.

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 in a number.

Day 2

Check-up

Order whole numbers and place 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.

Day 2

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

Day 3

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

### Teaching 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.

Day 2

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

Day 3

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

### Teaching 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

• Times tables: multiples and factors.

Day 2

• Double and halve 2-digit numbers by partitioning.

Day 3

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

### Teaching and Activities

Day 1

Check-up

Multiplication and division facts. Find factors of 2-digit numbers.

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.

Day 2

• Use efficient mental doubling and halving strategies.

Day 3

• Carry out division for numbers greater than tables facts.

### Teaching and Activities

Day 1

Check-up

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 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

Dividing numbers above the times tables, no remainders.

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.

Day 2

• Use fraction families to compare fractions.

Day 3

• Change improper fractions to mixed numbers and vice versa.

### Teaching 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 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.

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.

Day 2

• Compare and round decimal numbers.

Day 3

• Derive decimal and fraction equivalents.

### Teaching and Activities

Day 1

Check-up

Compare and round whole numbers.

Follow-up

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

Day 2

Check-up

Write missing numbers with 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.

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.

Day 2

• Relate the addition and subtraction of decimals.

Day 3

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

### Teaching and Activities

Day 1

Check-up

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

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 (whole numbers and amounts of money).

## Unit 9 Multiplication and Division 2

### Objectives

Day 1

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

Day 2

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

Day 3

• Relate multiplication and division.

### Teaching 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

Dividing numbers 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.

Day 2

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

Day 3

• Rehearse strategies for dividing decimals.

### Teaching and Activities

Day 1

Check-up

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

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

Use lists of multiples of the divisor to help divide 3-digit and 4-digit numbers by 2-digit numbers

Day 3

Check-up

Use division of whole numbers, then divide by 10 to divide numbers with one or two decimal places by single-digit numbers.

Follow-up

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

## Unit 11 Fractions 2

### Objectives

Day 1

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

Day 2

• Compare and order fractions.

Day 3

• Understand mixed numbers and improper fractions;
• Convert from improper fractions to mixed numbers and vice versa.

### Teaching and Activities

Day 1

Check-up

Identify equivalent fractions. Simplify fractions.

Follow-up

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

Day 2

Check-up

Compare and order fractions.

Follow-up

Use fraction walls to compare and order fractions.

Day 3

Check-up

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

Follow-up

Use pies to show mixed numbers and improper fractions.

## Unit 12 Fractions 3

### Objectives

Day 1

• Add and subtract fractions with related denominators.

Day 2

• Find fractions of amounts and relate to division.

Day 3

• Revise equivalent fractions for comparing and calculating;
• Revise improper fractions and mixed numbers.

### Teaching and Activities

Day 1

Check-up

Add and subtract fractions with related denominators.

Follow-up

Use fraction walls to write fractions as the same type before adding and subtracting.

Day 2

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.

Day 3

Check-up

Change improper fractions to mixed numbers, simplify fractions and add and subtract fractions with related denominators.

Follow-up

Use bars to identify equivalent fractions to add and subtract fractions with related denominators and visualise mixed numbers and improper fractions.

## Unit 13 Mental Calculations and Money

### Objectives

Day 1

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

Day 2

• Revise adding amounts of money and finding change.

Day 3

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

### Teaching and Activities

Day 1

Check-up

Use inverse operations to check calculations and 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, choosing a strategy.

Follow-up

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