Count, compare and represent collections
Count and compare sets of objects, then show one whole as two parts.
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Count each object once
Put seven small objects in a row. Touch each one as you say one, two, three, four, five, six, seven. The last number tells you how many objects there are: seven.
Move the objects into a circle. There are still seven. Moving an object does not add one or take one away.
If you lose your place, move each counted object into a new group. Start again when you need to. There is no hurry.
Check your understanding 1 Count without losing your place
Count the counters on this mat. Start at one side and touch or point to each counter once. What number do you say last?
Counters on a mat
Each dot is one counter. Work across the mat without missing or counting a dot twice.
View figure data
| Set | Counters |
|---|---|
| Set A | counter; counter; counter; counter; counter; counter; counter |
Show answer
Seven counters. Check by touching each dot once: one, two, three, four, five, six, seven. Do not count the mat or its label as another counter.
For a large collection, move each ten counted objects into its own group. Count the full groups as 10, 20, 30, then count any loose ones. Ten full groups of ten make 100 objects. The groups help you keep your place; they do not change how many objects you have.
Check your understanding 2 A different arrangement
You count six buttons. You spread them out, without adding or removing any. How many buttons are there now?
Show answer
Six. The buttons moved; the amount stayed the same. Touch each button once to check.
Compare by making partners
Put one counter from the first set beside one from the second. Keep making pairs, using every counter once. If only the second set has counters left without partners, the second set has more. The first set has fewer. If every counter has a partner and none are left over, the sets have the same number.
Check your understanding 3 Does more space mean more counters?
Compare Set A with Set B. The counters in Set A are larger and spread farther apart. Does Set A have fewer counters, the same number, or more?
Two sets of counters
Each dot is one counter, whatever its size or spacing. Compare objects, not the length of a row.
View figure data
| Set | Counters |
|---|---|
| Set A | counter; counter; counter; counter |
| Set B | counter; counter; counter; counter; counter; counter |
Show answer
Set A has fewer: four compared with six. Set B has two counters without partners. Bigger counters and wider spaces do not make more objects.
Now try five real counters in each set. Spread one set out. Both sets still have five: every counter can have a partner, with none left over.
One whole can have two parts
Put five objects on your left and three on your right. Count all of them. There are eight altogether.
The whole is eight. The parts are five and three. Each object belongs to one part. We do not count an object in both parts.
Write 5 + 3 = 8. Read it as “five and three make eight”. The sign + means add. The sign = means the amount on the left is the same as the amount on the right.
Now move one object from the first part to the second part. The parts become four and four. The whole stays eight: 4 + 4 = 8.
Try the model. You can change your answer or look at the worked model. This activity has no score.
Check the amounts and how they fit together. Moving a counter inside a box does not change its value. You can also draw on paper and compare with the public answer.
Show solution
First part: 5 counters. Reference whole: 1 counters. Bars use the same scale.
Second part: 3 counters. Reference whole: 1 counters. Bars use the same scale.
You can use real objects or draw dots instead. Make two groups, then draw one loop around both groups to show the whole.
No objects is zero
One part can be empty. Eight objects and no objects still make eight: 8 + 0 = 8.
Check your understanding 4 An empty plate
One plate has no grapes. Another has four grapes. How many grapes are there altogether?
Show answer
Four grapes: 0 + 4 = 4. An empty group is a part with zero objects.
Before you move on
Make seven in two different ways. Say the two parts and the whole each time. Then put the objects away and draw one of your ways from memory. Ask yourself: did I count each object once?
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