## SUPPOSITION CONCEPT

###### DIRECT SUPPOSITION
The Supposition concept can be a challenging one for students. At Model Math, we first introduce this idea in Primary 2 and gradually build upon it through repetition and more complex problems. This video example demonstrates the basics of the Supposition concept.
###### SUPPOSITION WITH PENALTY
The Supposition concept can be a challenging one for students. At Model Math, we first introduce this idea in Primary 2 and gradually build upon it through repetition and more complex problems. In Primary 4, we introduce Supposition with Penalty, which is a higher-level problem-solving technique that utilises the Supposition concept. It is common for students to need more than one lesson to fully grasp this concept, so we will be revisiting it in future lessons.

## PROBLEM SUMS WITH EXTERNAL TRANSFER

###### EXTERNAL TRANSFER, GIVEN DIFFERENCE
Peter had 20 more stickers than John at first. John then lost 169 stickers in a game. Peter now had four times as many stickers as John. How many stickers did John have at first?
###### EXTERNAL TRANSFER, UNCHANGED DIFFERENCE
Shop A and Shop B had 75 kg and 54 kg of flour, respectively. After both shops sold the same amount of flour, Shop A had four times as much flour as Shop B. How much flour did each shop sell?
###### EXTERNAL TRANSFER, GIVEN UNITS
In a container, the number of sweets was five times the number of chocolates. After John took out 26 sweets, there were 30 more sweets than chocolates. How many sweets were there at first?

## PROBLEM SUMS WITH INTERNAL TRANSFER

###### INTERNAL TRANSFER, GIVEN UNITS
Bottle A contained four times as much water as Bottle B at first. After 12 L of water was transferred from Bottle A to Bottle B, there was an equal amount of water in both bottles. How much water was there altogether?
###### INTERNAL TRANSFER, TOTAL UNCHANGED
Peter had \$52 and Yenni had \$26. After Peter gave some money to Yenni, Yenni had \$10 more than Peter. How much did Peter give to Yenni?
###### APPROXIMATION & ESTIMATION
1. An even number is 500 when rounded off to the nearest hundred. What is the greatest possible value of the even number?
2. Which is the best estimate for 55 x 42?

## MULTIPLICATIONS AND GROUPING

###### TOTAL CONCEPT, REGROUPING
Amber received \$12 for every belt she sold. She also received a bonus of \$50 for every 8 belts she sold. She sold 84 belts. How much money did she receive altogether?
###### TOTAL CONCEPT, REGROUPING
Amber is selling frying pans. For every frying pan she sells, she will earn \$6. She will also earn an additional \$15 for every 7 pans she sells. If she sells 23 pans, how much will she earn in all?

## COMPARISON MODEL PROBLEM SUMS

###### STACKING MODEL
In Primary 3, students learned about the Comparison Model for comparing the values of two different items, such as “a jar has 3 more cookies than a can.” Now, we would like to introduce a new method called the Stacking Model. This technique is used when comparing multiple items of the same type, for instance “3 jars have 5 more cookies than 3 cans.” The Stacking Model provides a visual representation and makes it easier to understand and compare multiple items.
###### COMPARISON OF QUANTITY AND UNITS
Peter had three times as many stickers as Yenni. John had 63 fewer stickers than Peter. The three children had 119 stickers altogether. How many more stickers did Yenni have than John?

## SHORTAGE AND SURPLUS PROBLEM SUMS

###### LISTING FOR HIGHEST COMMON FACTORS

Peter wants to lay his floor with square carpet tiles. The rectangular shaped floor measures 160 cm by 90 cm.

a) Find the largest possible length of the side of each carpet tile.

b) Find the number of tiles that are needed to cover the floor.

###### SHORTAGE AND SURPLUS, LISTING METHOD WITH NO FIXED GROUPS
There are between 10 to 20 beads in a container. Amber wants to put the beads in packets. If she puts 3 in each packet, there will be 2 beads left. If she puts 4 in each packet, there will be 1 bead left. How many beads are there in the container?
###### SHORTAGE AND SURPLUS, UNITS METHOD
Yenni had some money. She wanted to buy 16 markers but was short of \$9. In the end, she bought 9 markers and had \$5 left. How much money did Yenni have at first?
###### SHORTAGE AND SURPLUS, LISTING METHOD FIXED NUMBER OF GROUPS
Yenni had some gummies. She shared the gummies equally amongst some friends. If she gave each friend 4 gummies, she would have 1 gummy left. If she gave each friend 5 gummies, she would be short of 4 gummies. How many gummies did she have?

## COMMON FRACTIONS PROBLEM SUMS

###### FRACTIONS AS PART OF REMAINDER WITH CHANGING DENOMINATOR
1/4 of the people in the school are teachers and the rest are children. 1/3 of the children are girls. There are 10 boys. How people are there in the school?
###### FRACTIONS AS PART OF REMAINDER WITH REDRAWING REMAINDER
Yenni had some money. She wanted to buy 16 markePeter had some beads. He used 1/5 of the beads and gave 1/3 of the remainder to Yenni. Peter had 8 beads left. How many beads did Peter have at first?
###### TOTAL CONCEPT, DIRECT APPLICATION
1 m of ribbon cost \$8. How much does 3 3/4 m of ribbon cost?
###### EXTERNAL TRANSFER WITH 1 GROUP UNCHANGED
There are 30 markers in the box. 3 are yellow and the rest are black. After John used some black markers, 1/4 of the markers are yellow. How many black markers are used?
###### EXTERNAL TRANSFER WITH 1 GROUP UNCHANGED.
The number of apples is 2/5 the number of pears in a basket. 6 more pears are added to the basket and the number of apples is 2/7 the number of pears. How many apples and pears were in the basket at first?
###### INTERNAL PROPORTION TRANSFER
John had 183 stickers. After he gave 1/3 of it to Yenni, he had 95 stickers fewer than Yenni. How many stickers did Yenni have at first?

## COMMON DECIMALS PROBLEM SUMS

###### DECIMALS, ESTIMATION AND APPROXIMATION

a) A ribbon is 2.33 m when rounded off to 2 decimal places. What is the smallest possible length of the ribbon?

b) Yenni’s mass is 47.6 kg when rounded off to the nearest tenth. What is her largest possible mass? Leave your answer in 2 decimal places.

###### EXTERNAL TRANSFER
Class A had an equal number of boys and girls. After 26 boys and 8 girls were transferred to another class, there were thrice as many girls as boys. How much boys were there in Class A at first?
###### EXTERNAL TRANSFER
Bag A had thrice as many coins as Bag B. After \$18.60 of coins and \$3.40 of coins were removed from Bag A and B respectively, both bags had an equal amount of money. How much coins did Bag A have at first?
###### INTERNAL TRANSFERS
John and Peter had an equal amount of money at first. After John received \$46.30 from his father and Peter spent \$20.10, John had thrice as much money as Peter. How much money did John have at first?
###### BEFORE CHANGE AFTER, FIND CHANGE.
Yenni had \$84.50 and Amber had \$42.00. After Amber spent some money and Yenni spent \$21.50, Yenni had thrice as much money as Amber. How much money did Amber spend?
###### DECIMALS AND GROUPING
Yenni bought twice as many muffins as cupcakes for her birthday party. Each muffin cost \$1.75 and each cupcake cost \$2.50. How many muffins did she buy if she paid a total of \$48?

## AREA AND PERIMETER

###### AREA AND PERIMETER IGNORE REMAINDER
Peter has a rectangular cardboard measuring 15 cm by 9 cm. He wants to cut out smaller squares of side 2 cm from it. What is the maximum number of squares that can be cut out from the cardboard?
###### AREA AND PERIMETER – COMPARISON BY UNITS
The figure below is made up of 3 identical rectangles. The perimeter of the whole figure is 100 cm. What is the area of the whole figure?