Primary 2 Method and Model Drawing

Systematic listing

A systematic list helps us find every possible result without missing one or counting one twice. Keep the first choice fixed, pair it with every allowed second choice, then move to the next first choice.

1. Choose one first digit or item.
2. List every allowed second digit or item in a steady order.
3. Change the first choice and repeat.
4. Check the rule, then count the results you listed.

Use the digits 1, 5 and 8. Use each digit at most once in each number. How many different two-digit numbers can you make?

Check: Each number uses two different digits. The digits may be used again in a different number. The complete list is 15, 18, 51, 58, 81, 85: 6 numbers.

A child orders one drink and one treat. The drinks are orange juice and apple juice. The treats are chocolate cake and a muffin. How many different combinations can the child make?

Check: Every combination has exactly one drink and one treat. There are 4 different combinations.

Ask: “Which first choice are we holding fixed? Have we paired it with every allowed second choice?”

Common mistake: Including 11, 55 or 88 in the first example repeats a digit in one number. In the food example, choosing both cake and muffin makes two treats, so it does not follow the rule.

Model drawing: Part-whole model

The whole is known, but one part is missing. Draw the known parts next to the missing part, and label the total across the full bar.

At a school book fair, 125 books were sold. 38 were picture books and 47 were storybooks. The rest were information books. How many information books were sold?

Common mistake: Adding 38 and 47 and giving that as the answer. Those are the known books. Subtract their sum from 125 to find the remaining books.

Model drawing: Comparison model

Align the bars at the left. The extra part of the longer bar shows the difference. Find the shorter amount, then add both amounts for the total.

Maya has 64 stickers. Sam has 28 fewer stickers than Maya. How many stickers do they have altogether?

Common mistake: Stopping after finding Sam's stickers. The question asks for both children altogether, so add Sam's amount to Maya's 64.

Method: Before and after

When one person gives some objects to another person, draw the amounts before and after the transfer. The objects given are taken away from one person and added to the other. After the transfer, both people have the same amount.

Maya has 8 more stickers than Sam. Maya gives some stickers to Sam. After that, they have an equal number of stickers. How many stickers did Maya give to Sam?

Common mistake: Giving all 8 extra stickers to Sam would make Sam have 8 more instead. Maya gives half of the difference so the two amounts become equal.

Method: Working backwards

Use working backwards when the final result is given and you need to find the value at first. Start from the final result and reverse each change, beginning with the last move. In this lift example, reverse “up” by going down and “down” by going up.

A delivery worker got into a lift. It went up 3 floors, then down 5 floors, and then up 4 floors. It stopped at Level 7. Which level did the delivery worker start on?

Common mistake: Reversing the moves in the order they were read, or going up again to reverse “up”. Start at Level 7, reverse the last move first, and use the opposite direction.

Method: Grouping Method

When the same number of two items is bought, make a group with one of each. Find the cost of one group, then work out how many groups the total money buys.

One pen costs $1. One book costs $2. Maya buys the same number of pens and books. She spends $9 altogether. How many pens and books does she buy?

Common mistake: Dividing $9 by only the pen price or only the book price forgets that Maya bought the same number of each. First find the $3 cost of one pen-and-book group.