Maths Mastery with Greater Depth - Year 1 Maths Mastery with Greater Depth

Number - Number and place value

National Curriculum objective, Year 1, Number and place value • count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

Counting Challenge 1:

Challenge 1 Answer Dan is not correct. There are 23 counters.

Dan has these counters.

Assessment During the task, notice if pupils work systematically, e.g. counting across or down or crossing off counters as they count them. If they don’t, counting systematically is probably something they need to focus on.

I think there are 22 counters.

Assess their confidence in counting out loud to their friend to explain how they got their answer. Is their counting fluent? Are they pronouncing numbers properly? Do they miss any out? If they get a different number when counting a second time, assess their reasoning by asking if this affects their answer to the question ‘Is Dan correct?’. If they repeatedly get different numbers, suggest a strategy such as crossing off the counters as they count to help them reach the correct answer.

Counting objects accurately most of the time indicates mastery – even if pupils occasionally make an error by missing out one counter, or counting one twice.

You could repeat the activity with a handful of real counters to count.

Challenge 2:

Is Dan correct? Explain to a friend.

Note

Amy is counting:

‘Read a number in numerals’ is a separate National Curriculum objective. You may also wish to check that the pupil can read ‘22’, but if they cannot, read them the question so you can assess their counting.

95, 96, 97 …

Counting pictures of objects is a higher level skill than counting manipulative objects, particularly where there are a large number. If pupils find counting the pictures systematically difficult, give them real counters, so they can move each counter to one side as they count it.

Carry on counting out loud until you get to 115.

Challenge 3:

Lola wants to launch her toy rocket.

Challenge 2 Answer Pupil correctly counts 98, 99, 100, 101, … to 115

Challenge 4:

Start at 29 and count down to zero for her launch.

Assessment

Marek is counting down from 108:

During the task, assess their confidence in counting out loud. Is their counting fluent? Are they pronouncing numbers properly? Do they miss any out?

108, 107, 106 …

You could repeat the activity with a different starting number to check that the pupil understands the pattern of counting up across any tens boundary, as well as the hundred boundary. Doing this independently and accurately would indicate depth of mastery.

You could ask the pupil: When you were counting, did you say the number 88? Why not? Assess their confidence in explaining. If they say that 88 is less than, or before 98, this assesses the objective ‘use the language of less than’.

Carry on counting out loud until you get to 90.

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Note ‘Read a number in numerals’ is a separate National Curriculum objective. You may also wish to check that the pupil can read ’95, 96, 97 and 115’, but if they cannot, read them the question so you can assess their counting.

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National Curriculum objective, Year 1, Number and place value

Number - Number and place value

• count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

Challenge 5:

34, 35, 36

Challenge 3 Answer

Read Dan’s numbers out loud.

Pupil correctly counts down from 29, 28, 27, … and so on to zero.

Write down the next ten numbers Dan will say.

Assessment During the task, assess their confidence in counting out loud. Is their counting down fluent? Are they pronouncing numbers properly? Do they miss any out?

Dan started counting at 1.

Challenge 6:

Amy has these digit cards:

1

4

6

To check the pupil’s fluency you could repeat the activity with a different starting number, e.g. 12, or you could count down from 10 to zero, missing out e.g. 6, and ask: What number did I miss out?

She uses two of the cards to make this number: 41

Note

What number is this?

‘Read a number in numerals’ is a separate National Curriculum objective. You may also wish to check that the pupil can read ‘10, 9, 8’ but if they cannot, read them the question so you can assess their fluency in counting down.

Write down all the numbers you can make using these digit cards. Read out the numbers you have made to a friend.

Challenge 4 Answer Pupil correctly counts down from 106, 105, 104, … and so on to 90.

Assessment

How do you know you have them all? Explain to a friend.

Challenge 7:

Lola arranges these cubes in twos:

During the task, assess their confidence in counting out loud. Is their counting down fluent? Are they pronouncing numbers properly? Do they miss any out?

You could repeat the activity with a different starting number, to check that the pupil understands the pattern of counting down across a tens boundary, as well as the hundred boundary. Doing this independently and accurately would indicate depth of mastery.

How many cubes does Lola have? Count up in twos.

You could ask the pupil: When you were counting, did you say the number 110? Why not? Assess their confidence in explaining. If they say that 110 is more than, or after 108, this assesses the objective ‘use the language of more than’.

These are Ellie’s cubes.

Note ‘Read a number in numerals’ is a separate National Curriculum objective. You may also wish to check that the pupil can read ’108, 107, 106’ though this is not required for Year 1, where they should be taught to read numbers to 100.

If they cannot, read them the question so you can assess their fluency in counting down.

How many cubes does Ellie have? Count up in twos.

Is it quicker to count up the cubes in twos, or by counting 1, 2, 3, …? Explain to a friend.

Challenge 8:

Marek has these 10p pieces:

I have 55p.

Is Marek correct? Explain to a friend.

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National Curriculum objective, Year 1, Number and place value • count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

National Curriculum objective, Year 1, Number and place value • count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

Challenge 5 Answer

Challenge 7 Answer

37, 38, 39, 40, 41, 42, 43, 44, 45, 46

Pupil counts 2, 4, 6, 8, 10 for Lola’s cubes and 2, 4, 6, 8, 10, 12, 14, 16 for Ellie’s cubes.

Assessment

It is quicker to count in twos, as you don’t have to say so many numbers.

During the task, first check that pupils can read the numbers 34, 35, 36. Then assess their confidence in counting if they are counting out loud. As the pupil writes the numbers down, check that they are forming numerals correctly, and that they combine two numerals to make the number they want.

Assess how the pupil decides when they have written enough numbers down, e.g. by counting the number they have written.

You could repeat the activity with a different starting number to check that the pupil understands the pattern of writing numbers across any tens boundary. Doing this independently and accurately would indicate depth of mastery.

Challenge 6 Answer Pupil reads the number 41.

1, 4, 7, 14, 41, 16, 61, 46, 64, 146, 164, 614, 641, 416, 461

Assessment Pupils may find it easier to have ‘real’ digit cards for 1, 4 and 6, so they can move them physically to make the different numbers. During the task, notice if pupils work systematically. If they do not, this is something they could work on.

Assessment During the task, assess pupils’ confidence in counting out loud in twos. Are they pronouncing numbers properly? Do they miss any out?

Notice if pupils work systematically, counting the given pairs for Lola’s cubes, and following the same approach for Ellie’s cubes. If they don’t, counting systematically is probably something they need to focus on. Some pupils may wish to draw rings round the pairs of Ellie’s cubes, as in Lola’s cubes, before counting.

For comparing counting in twos, with counting 1, 2, 3, … assess how well they can explain their reasoning to a friend.

You could ask the pupil to count all the cubes for both girls in twos, to check that they understand the pattern of counting in twos up to 24. Or you could give them an even number of cubes to count in twos. Doing this independently and accurately would indicate depth of mastery.

Note Counting pictures of objects is a higher level skill than counting manipulative objects, particularly where there are a large number. If pupils find counting the pictures systematically difficult, give them real cubes to arrange in pairs, so they can move each pair to one side as they count it.

As the pupil writes the numbers down, check that they are forming numerals correctly. As they read them to a friend, assess their pronunciation and accuracy. Look out for confusion between –teen and –ty when saying numbers.

Support pupils to correct errors by focussing on ‘teen’ meaning ‘one ten’ and ‘ty’ meaning ‘tens’.

Challenge 8 Answer

Once they have read out all the numbers they have written down, assess their confidence in explaining to a friend how they knew they had found all the possible numbers.

Assessment

You could repeat this activity with different number cards.

Note Pupils may only make the two-digit numbers, following the pattern of the example given. Making and reading threedigit numbers is a Year 2 objective, so you do not need to prompt pupils to find the three-digit numbers if they do not do it independently.

Marek is not correct, he has 60p.

During the task, assess pupils’ confidence in counting out loud in tens (if the pupil solves the problem this way). Are they pronouncing numbers properly? Do they miss any out?

Assess how well they can explain their reasoning to a friend. They could count that Marek has 60p and this is not the same as 55p. Or they may realise that when counting from 0 in tens all the numbers have a zero in the ones place, so 55 cannot be made from 10p pieces (recognising multiples of 10 like this is a Year 2 objective).

You could ask the pupils to count the value of different numbers of 10p coins, up to 100p.

You could give pupils 10p coins and ask how many 10p coins they need to make 30p or 70p.

Note Counting pictures of objects is a higher level skill than counting manipulative objects, particularly where there are a large number. If pupils find counting the pictures difficult, give them 10p coins to count, so they can move each pair to one side as they count it.

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