Number Multiplication and Division

Assessment Task 10

Number – Multiplication and division

National Curriculum attainment target

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

Prerequisite checklist

Can the pupil:

solve problems that involve combining groups of 2, 5 or 10?
solve problems that involve sharing into equal groups?
solve problems involving doubling and halving?

Success criteria

Understand multiplication using arrays
Solve problems that involve combining groups of 2, 5 or 10 using concrete objects and pictorial representations
Understand division as ‘sharing’
Understand division as ‘grouping’
Solve problems that involve sharing objects into equal groups using concrete objects and pictorial representations

Resources

Resource 14: Array cards

two copies of Resource 15: Combining groups of 2, 5 or 10

two copies of Resource 16: Sharing into equal groups: sheep (alternatively, if available use plastic farm animals)

two copies of Resource 17: Sharing into equal groups: fields (enlarged to A3) several sheets of A4 paper counters

NOTE

Prior to the Assessment Task:

Cut out the array cards from Resource 14. Place them in a pile.

Cut out the picture cards from Resource 15. Place each of the different types of fruit into separate piles.

Place the 70 sheep from Resource 16 into a pile.

.Assessment Task

Success criterion A:Add a one-digit number (including zero) to a two-digit number to 20

What to do / What to say / What to look out for
Place one of the array cards from Resource 14 in front of the pupil, e.g.

Ask questions similar to the ones shown here: / How many dots are there in each row?
How many rows are there?
How many dots are there altogether?
How can you work it out without counting all the dots? / Can the pupil use an array to describe multiplication?
Repeat above using other array cards until the pupil has sufficiently demonstrated their understanding of multiplication using arrays.

Success criterion B:Solve problems that involve combining groups of 2, 5 or 10 using concrete objects and pictorial representations

What to do / What to say / What to look out for
Place several picture cards of the same type from Resource 15 in front of the pupil, i. e. / There are five bananas in each ‘hand’. How many bananas are there altogether? / Can the pupil combine groups of2, 5 or 10 and find out how manythere are altogether?
Repeat above using the other picture cards from Resource 15, asking questions similar to the ones shown here: / There are ten grapes in each bunch. How many grapes are there altogether in these four bunches?
How many cherries are there altogether in eight bunches? Use the cherries to show me.
Occasionally ask the pupil to explain how they worked out the answer. / How did you work that out?
How did you get that answer?
How did you know that there are that many grapes?
How can you work it out without counting them all?
Continue until the pupil has sufficiently demonstrated that they can solve problems that involve combining groups of 2, 5 or 10.

Success criterion C:Understand division as ‘sharing’

What to do / What to say / What to look out for
Draw three rings on one of the sheets of A4 paper and place 12 counters near the paper, i.e.
/ How many counters are there? I want you to share these 12 counters equally between three groups. / Can the pupil share out equally a quantity into a given number of groups?
So, how many counters are there in each group?
Repeat above drawing a different number of rings and using a different number of counters until the pupil has sufficiently demonstrated their understanding of division as ‘sharing’.

Success criterion D: Understand division as ‘grouping’

What to do / What to say / What to look out for
Place 15 counters on the table infront of the pupil. / How many counters are there? I want you to arrange these counters into groups of five. / Can the pupil work out how many equal groups there are for a given quantity?
So, how many groups of five counters are there in 15?
Repeat above using a different number of counters and asking the pupil to arrange them into groups of a different size until the pupil has sufficiently demonstrated their understanding of division as ‘grouping’.

Success criterion E: Solve problems that involve sharing objects into equal groups using concrete objects and pictorial representations

What to do / What to say / What to look out for
Fold one of the sheets of 5 fields from Resource 17, so that only two fields are visible. Place 8 sheep beside the 2 fields, e.g. / How many sheep are there?
How many fields are there?
I want you to share these eight sheep equally between these two fields. / Can the pupil share out equally a quantity into a given number of groups?
So, how many sheep are there in each field?
Repeat above asking the pupil to share one or more of the following:
a multiple of 2 sheep between 2 fields;
a multiple of 3 sheep between 3 fields;
a multiple of 4 sheep between 4 fields;
a multiple of 5 sheep between 5 fields;
a multiple of 10 sheep between 10 fields.
Continue until the pupil has sufficiently demonstrated that they can solve practical problems that involve sharing objects into equal groups.

What to do for those pupils working below or above expectations

Refer to the ‘Tracking back and forward through the Mathematics National Curriculum attainment targets’ charts on pages 193–200.