# Let’s differentiate!

You know how some classes have a range of student understanding? Oh that would be all classes!

So we’ll need to differentiate. That’s easy at A Learning Place A Teaching Place, because the Concept Sequences and Grade Scope and Sequences were created to allow for differentiation. Your teacher judgement is both respected and necessary!

**Scroll to the Grade you are interested in!**

Kindergarten/Prep/Reception: The sample weekly plan for Weeks 3 – 4 looks like this:

Students will be at different levels in their capacity to say the forward and backward number sequence, write numerals, recognise numerals, and count items. To differentiate, you could prepare colour-coded resources for each student.

Count forwards – identify which number each student can count forwards to. 5 times a day, ask them to count forwards to the next number to a friend. For example, I can count to 5. I am told to count to 6 to a friend. When I can count to 6, I am told to count to 7. If I lose 6, I just count to 6 again until I have 6, then I count to 7 – activities in Investigation ECG 1 could be used.

Count backwards – identify which number each student can count backwards from. 5 times a day, ask them to count backwards from the next number to a friend. For example, I can count backwards from 5. I am told to count backwards from 6 to a friend. When I can count backwards from 6, I am told to count backwards from 7. If I lose 6, I just count backwards from 6 again until I have 6, then I count backwards from 7 – activities in Investigation ECG 1 could be used.

Write numerals – prepare a bag for each student containing the numbers they can write, plus the next number – printed in red. For example, I can write numerals 1, 4 and 10. My red bag will contain the numerals 1 and 2 only. My job is to learn to write the number 2. When I can write the number 2, I will be given 3. When I can write 1, 2 and 3, I will be given 4 – which I can already write. If I lose 2 or 3, 4 is removed again until I can write 2 and 3. After I can write 1, 2, 3 and 4, I am given 5 as well. Every time I am given my red bag, my activity is to write each numeral – activities in Investigation ECG 2 could be used.

Recognise numerals – prepare a bag for each student containing the numbers they do recognise, plus the next number – printed in blue. For example, I recognise numerals 1, 2, 4 and 6. My blue bag will contain the numerals 1, 2 and 3 only. My job is to learn to recognise the number 3. When I recognise the number 3, I will be given 4 – which I can already recognise. If I lose 3, 4 is removed again until I can recognise 3. After I can recognise 1, 2, 3 and 4, I am given 5 as well. Every time I am given my blue bag, my activity is to place the numerals in order, name each numeral; place the numerals in random order, name each numeral – activities in Investigation ECG 3 could be used.

Count items with one-to-one correspondence – prepare a container for each student containing the number of items they can count, plus one more. For example, I can count up to 3 items. My container has 4 items (counters). My job is to learn to count 4 items. When I can count 4 items, I will be given another item – 5. If I lose counting 4 items, 1 item is removed again until I can count 4. After I can count 5 items, I am given another item – 6. Every time I am given my container, my activity is to place place out the items (counters), count them aloud while moving each item, explain how many there are, draw each item, count each item I have drawn – activities in Investigation ECG 5 could be used.

Year 1 – The sample weekly plan for Weeks 8 – 10 looks like this:

Students will be at different levels in their capacities and understandings.

Some students may not yet be able to to say the forward and backward number sequence, write numerals, recognise numerals, and count items (ECG concepts). To differentiate for students who are still developing these capacities and understanding, you could prepare colour-coded resources for each student – see Kindergarten/Prep/Reception above. These students could engage in the Explicit Teaching segment of the lesson with the class, then in the Investigation segment, be given their colour-coded resources – the colour of the resource prompts them to investigate independently – no need to sit with an adult!

Some students may be adding and subtracting using counters, while others are adding and subtracting on a number line. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, adding with counters, subtracting with counters, adding on a number line, subtracting on a number line. In the Investigation segment, students then use either number cards, or playing cards, to generate the numbers they are ready to add or subtract. They add or subtract using their current understanding – either using counters or recording on a number line – activities in Investigation AS 3 and 4 could be used.

Some students may be investigating place value of teen numbers with blocks, while others are investigating place value of teen numbers without blocks. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, investigating place value of teen numbers with blocks, and investigating place value of teen numbers without blocks. In the Investigation segment, students then use either number cards, or playing cards, to generate the numbers they are ready to investigate place value of teen numbers. They investigate place value of teen numbers using their current understanding – either with blocks or without – activities in Investigation PV 7 could be used.

Some students may be partitioning with blocks, while others are partitioning without blocks. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, partitioning with blocks, and partitioning without blocks. In the Investigation segment, students then use either number cards, or playing cards, to generate the numbers they are ready to partition. They partition using their current understanding – either with blocks or without – activities in Investigation PV 8 could be used.

Naming two-dimensional shapes and measuring using informal units is self-differentiating as students select their own shapes, and their own length and units.

Year 2 – The sample weekly plan for Weeks 1 – 2 looks like this:

Students will be at different levels in their capacities and understandings.

Some students may not yet be able to to count forwards and backwards by ones, write numerals, recognise numerals, and count items (ECG concepts). To differentiate for students who are still developing these capacities and understanding, you could prepare colour-coded resources for each student – see Kindergarten/Prep/Reception above. These students could engage in the Explicit Teaching segment of the lesson with the class, then in the Investigation segment, be given their colour-coded resources – the colour of the resource prompts them to investigate independently – no need to sit with an adult!

Some students may be counting forwards and backwards by 10s on the decade, while others are counting forwards and backwards by 10s off the decade. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, counting forwards and backwards by 10s on the decade, and counting forwards and backwards by 10s off the decade. In the Investigation segment, students then use playing cards, to generate the numbers – either a tens number or a number with tens and ones – that they are ready to count forwards or backwards by 10s from (students who cannot yet count forwards and backwards by 1s could count by 1s instead). They count forwards or backwards by 10s using their current understanding – activities in Investigation PV 10, PA 11 could be used.

Some students may still be adding and subtracting single-digit numbers using counters, while others are still adding and subtracting single-digit numbers on a number line while others are ready to add and subtract 10s numbers. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, adding and subtracting single-digit numbers using counters, adding and subtracting single-digit numbers on a number line, and adding and subtracting 10s numbers – you may also need to bring in some place value concepts (see the ‘Year 2 Scope and Sequence – Differentiated’ in ‘Teaching Resources’, ‘Year 2’ for more information). In the Investigation segment, students then use playing cards, to generate the numbers they are ready to add or subtract. They add or subtract using their current understanding – adding or subtracting single-digit numbers using counters, adding or subtracting single-digit numbers on a number line, or adding or subtracting 10s numbers – activities in Investigation AS 13 could be used (the same activities can be used for adding and subtracting any-sized numbers!). Some students may be investigating a place value concept of friends of 10, partitioning, or place value of teen or two-digit numbers to allow them to progress in their addition and subtraction levels. (see the ‘Year 2 Scope and Sequence – Differentiated’ in ‘Teaching Resources’, ‘Year 2’ for more information)

Making a tape measure using informal units is self-differentiating as students select their own units.

Year 3 – The sample weekly plan for Weeks 1 – 2 looks like this:

Students will be at different levels in their capacities and understandings.

Some students may be counting forwards and backwards by 1000s, some by 100s, some by 10s and some by 1s. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, counting forwards and backwards by 1000s, by 100s, by 10s and by 1s. In the Investigation segment, students then use playing cards, to generate the numbers that they are ready to count forwards or backwards by 1000s, by 100s, by 10s and by 1s from. They count forwards or backwards by 1000s, by 100s, by 10s and by 1s using their current understanding – activities in Investigation PV 17, PA 16 could be used.

Some students may be investigating place value of four-digit numbers, some three-digit numbers, some two-digit numbers, and some teen numbers. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, place value of four-digit numbers, three-digit numbers, two-digit numbers, and teen numbers. In the Investigation segment, students then use playing cards, to generate the numbers that they are ready to investigate place value of – four-digit numbers, three-digit numbers, two-digit numbers, and teen numbers. They investigate place value of four-digit numbers, three-digit numbers, two-digit numbers, or teen numbers using their current understanding – activities in Investigation PV 17, PA 16 could be used.

Some students may still be adding and subtracting single-digit numbers, others 10s numbers, others two-digit numbers, and others three-digit numbers, and others four-digit numbers. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, adding and subtracting single-digit numbers, 10s numbers, two-digit numbers, and three-digit numbers, and four-digit numbers – you may also need to bring in some place value concepts (see the ‘Year 3 Scope and Sequence – Differentiated’ in ‘Teaching Resources’, ‘Year 3’ for more information). In the Investigation segment, students then use playing cards, to generate the numbers they are ready to add or subtract. They add or subtract using their current understanding – adding and subtracting single-digit numbers, 10s numbers, two-digit numbers, three-digit numbers, or four-digit numbers – activities in Investigation AS 21 could be used (the same activities can be used for adding and subtracting any-sized numbers!). Some students may be investigating a place value concept of friends of 10, partitioning, or place value of two- or three-digit numbers to allow them to progress in their addition and subtraction levels. (see the ‘Year 3 Scope and Sequence – Differentiated’ in ‘Teaching Resources’, ‘Year 3’ for more information)

Data and Chance is self-differentiating as students develop their capacity to record and interpret data.

For differentiating measuring length – see Year 4 below.

Year 4 – The sample weekly plan for Weeks 5 – 6 looks like this:

Students will be at different levels in their capacities and understandings.

Some students may be counting forwards and backwards by 1000s, some by 100s, some by 10s and some by 1s. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, counting forwards and backwards by 1000s, by 100s, by 10s and by 1s. In the Investigation segment, students then use playing cards, to generate the numbers that they are ready to count forwards or backwards by 1000s, by 100s, by 10s and by 1s from. They count forwards or backwards by 1000s, by 100s, by 10s and by 1s using their current understanding – activities in Investigation PV 19, PA 20 could be used.

Some students may be investigating place value of five-digit numbers, four-digit numbers, some three-digit numbers, some two-digit numbers, and some teen numbers. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, place value of five-digit numbers, four-digit numbers, three-digit numbers, two-digit numbers, and teen numbers. In the Investigation segment, students then use playing cards, to generate the numbers that they are ready to investigate place value of – five-digit numbers, four-digit numbers, three-digit numbers, two-digit numbers, and teen numbers. They investigate place value of four-digit numbers, three-digit numbers, two-digit numbers, or teen numbers using their current understanding – activities in Investigation PV 19, PA 20 could be used.

Some students may still be adding and subtracting single-digit numbers, others 10s numbers, others two-digit numbers, and others three-digit numbers, others four-digit numbers, and others five-digit numbers. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, adding and subtracting single-digit numbers, 10s numbers, two-digit numbers, and three-digit numbers, four-digit numbers, and five-digit numbers – you may also need to bring in some place value concepts (see the ‘Year 4 Scope and Sequence – Differentiated’ in ‘Teaching Resources’, ‘Year 4’ for more information). In the Investigation segment, students then use playing cards, to generate the numbers they are ready to add or subtract. They add or subtract using their current understanding – adding and subtracting single-digit numbers, 10s numbers, two-digit numbers, three-digit numbers, or four-digit numbers – activities in Investigation AS 24 could be used (the same activities can be used for adding and subtracting any-sized numbers!). Some students may be investigating a place value concept of friends of 10, partitioning, or place value of two- or three-digit numbers to allow them to progress in their addition and subtraction levels. (see the ‘Year 4 Scope and Sequence – Differentiated’ in ‘Teaching Resources’, ‘Year 4’ for more information)

Some students may be ready to investigate multiplicative place value of whole numbers, some to tenths, and some to hundredths. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, multiplicative place value of whole numbers, to tenths, and to hundredths. In the Investigation segment, students then use playing cards, to generate the numbers they are ready to investigate multiplicative place value of – whole numbers, to tenths, or to hundredths – activities in Investigation PV 20, 21, FD 11, 12 could be used (the same activities can be used for multiplicative place value of any-sized numbers!)

Some students may be ready to measure in millimetres, and some in combinations of centimetres and millimetres, some in centimetres and fraction of a centimetre, and some in centimetres and a decimal fraction of a centimetre. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, measuring in millimetres, in combinations of centimetres and millimetres, in centimetres and fraction of a centimetre, and in centimetres and a decimal fraction of a centimetre. In the Investigation segment, students measure lengths that they are ready to – in millimetres, in combinations of centimetres and millimetres, in centimetres and fraction of a centimetre, and in centimetres and a decimal fraction of a centimetre – activities in Investigation MG 39 could be used. NB: The same differentiation applies to measuring in metres and centimetres where some students may be ready to measure in centimetres, and some in combinations of metres and centimetres, some in metres and fraction of a metre, and some in metres and a decimal fraction of a metre.

Some students may be ready to investigate time in ‘am’ and ‘pm’ while some may be investigating telling time to the minute, the quarter hour, and the half hour on analog and digital clocks. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, telling the time to the minute, the quarter hour, the half hour, and in ‘am’ and ‘pm’. In the Investigation segment, students use clocks with hands that move in sync to make times they are ready to investigate – time to the minute, the quarter hour, the half hour, and in ‘am’ and ‘pm’ – activities in Investigation T 6, 10, 11, 13 could be used.

Year 5 – The sample weekly plan for Weeks 5 – 7 looks like this:

Some students may be investigating place value of five-digit numbers, four-digit numbers, some three-digit numbers, some two-digit numbers, and some teen numbers. Students add and subtract weekly to ensure they continue to develop their understanding and capacity. For differentiation, see Year 4 above.

Some students may be investigating multiplying and dividing by 2, 4, 3, 5, 9, 6, 8, or 7. Students multiply and divide weekly to ensure they continue to develop their understanding and capacity. Students select cards to make numbers they are ready to investigate multiplying or dividing.

Some students may be ready to investigate constructing and measuring angles with a protractor, some angle and side properties of triangles, some quadrilaterals, some other shapes with sides. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, constructing and measuring angles with a protractor, angle and side properties of triangles, and quadrilaterals. In the Investigation segment, students measure and construct angles and shapes that they are ready to – activities in Investigation MG 48, 49 could be used.

Some students may be ready to investigate the meaning of the denominator, some the numerator and some the vinculum. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, the meaning of the denominator, the numerator and the vinculum. In the Investigation segment, students investigate the meaning of the denominator, the numerator and the vinculum – activities in Investigation FD 7, 9, 19 could be used.

Some students may be ready to investigate multiplicative place value multiplying and dividing by 10, 100 and 100 of whole numbers, some to tenths, and some to hundredths. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, multiplicative place value multiplying and dividing by 10, 100 and 100 of whole numbers, to tenths, and to hundredths. In the Investigation segment, students then use playing cards, to generate the numbers they are ready to investigate multiplicative place value multiplying and dividing by 10, 100 and 100 of – whole numbers, to tenths, or to hundredths – activities in Investigation PV 24, FD 18 could be used (the same activities can be used for multiplicative place value of any-sized numbers!)

Some students may be ready to measure and convert between millimetres and centimetres, some between metres and centimetres, and some between metres and kilometres. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, measuring and converting between millimetres and centimetres, between metres and centimetres, and between metres and kilometres. In the Investigation segment, students measure and convert between units of measurement that they are ready to – between millimetres and centimetres, between metres and centimetres, and between metres and kilometres – activities in Investigation MG 39, 51 could be used.

Year 6 – The sample weekly plan for Weeks 6 – 10 looks like this:

Some students may be investigating place value of five-digit numbers, four-digit numbers, some three-digit numbers, some two-digit numbers, and some teen numbers. Students add and subtract weekly to ensure they continue to develop their understanding and capacity. For differentiation, see Year 4 above.

Some students may be investigating multiplying and dividing by 2, 4, 3, 5, 9, 6, 8, or 7, or multiplying two-digit numbers, or multiplying and dividing decimals. Students multiply and divide weekly to ensure they continue to develop their understanding and capacity. Students select cards to make numbers they are ready to investigate multiplying or dividing.

Some students may be ready to investigate division as multiplication by a fraction while others are still developing their understanding that division means we finding a fraction ‘of’ a number. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, dividing by finding a fraction ‘of’ the number, dividing by finding a fraction ‘times’ the number. In the Investigation segment, students then use playing cards, to generate the numbers they are ready to investigate dividing, either by finding a fraction ‘of’ the number, or by multiplying the number by a fraction – activities in Investigation MD 10 – 17, MD 27, FD 27 could be used.

Some students may be ready to investigate fractions in their simplest form through calculation, while others are developing their understanding of equivalent fractions using material and the relationship between the numerator and the denominator. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, equivalent fractions using material and the relationship between the numerator and the denominator, and fractions in their simplest form through calculation. In the Investigation segment, students then use playing cards, to generate the fractions they are ready to create equivalent fractions of, or to create fractions in their simplest form – activities in Investigation FD 13, 28 could be used.

Some students may be ready to measure and convert between millimetres and centimetres, some between metres and centimetres, and some between metres and kilometres, and some between all units of measurement. In the Explicit Teaching segment of the lesson, use questioning to work through the levels of understanding demonstrated in the class, for example, measuring and converting between millimetres and centimetres, between metres and centimetres, and between metres and kilometres. In the Investigation segment, students measure and convert between units of measurement that they are ready to – between millimetres and centimetres, between metres and centimetres, between metres and kilometres, and between all units of measurement – activities in Investigation MG 39, 51, 59 could be used.

Diagonals on shapes is self-differentiating as students select their own shapes.