Primary 5 Heuristic Concepts

DIFFERENCE CONCEPT

John can bake 3 cupcakes in an hour. Peter can bake 5 cupcakes in an hour. John has 8 more cupcakes than Peter. If they start baking at the same time, how many hours later will Peter have 8 more cupcakes than John?

SHORTAGE AND SURPLUS

John wanted to pack an equal number of stamps in 32 packets but was short of 157 stamps. He packs the same number of stamps into 24 packets and has 11 stamps left. How many stamps did John have at first?

QUANTITY INTERNAL TRANSFER

John has $64 more than Yenni. After John gives Yenni $9, John has thrice as much money as Yenni. How much does John have at first?

QUANTITY VALUE WITH EXTRA QUANTITY REVISION

101 cards were shared with some boys and girls. There were 4 more boys than girls. Each boy received 5 cards and each girl received 4 cards. How many boys are there?

DISTRIBUTION OF DIFFERENCE

Ten boys were tasked to paint the chairs in an auditorium. One of them fell sick and the rest had to paint 6 more chairs each. How many chairs did they have to paint altogether?

UNCHANGED DIFFERENCE

At first, there were 410 more men than women at an exhibition. At lunch time, a total of 250 men and women left the exhibition. There were as many men as women who left the exhibition. In the end, there were 3 times as many men as women who remained behind. How many men were at the exhibition at first?

QUANTITY AND VALUE INVOLVING TOTAL DIFFERENCE

There are 3/5 as many boys as girls at a party. Each boy is given 4 balloons and each girl is given 2 balloons. The total number of balloons received by the boys is 200 more than the girls. How many boys were at the party?

QUANTITY AND VALUE INVOLVING EXTRA QUANTITY AND TOTAL DIFF IN VALUE (EXAMPLE 1)

John bought 4 more books than files. A book cost $13 and a file cost $5. If he paid $116 more for the books than the files, how many books did John buy?

QUANTITY AND VALUE INVOLVING EXTRA QUANTITY AND TOTAL DIFF IN VALUE (EXAMPLE 2)

Peter bought 6 more chairs than tables. A table cost $36 and a chair cost $18. If he paid $396 more for the tables than the chairs, how many chairs are there?

HOW TO SOLVE SIMULTANEOUS STATEMENTS?

Simultaneous statements were first introduced in Primary 4. This example is a Primary 5 simultaneous question. “Simultaneous concept” is arithmetic math. It is solving 2 unknowns with 2 number statements. This is a useful skill to acquire early in the year as it can be applied to solve subsequent problem sums.

QUANTITY EXTERNAL TRANSFER USING MODEL (EXAMPLE 1)

John and Peter had some stamps. Peter had 23 more stamps than John. After Peter gave away 57 stamps, John had thrice as many stamps as Peter. Find the number of stamps Peter had in the end.

QUANTITY EXTERNAL TRANSFER USING MODEL (EXAMPLE 2)

John and Peter had an equal number of stickers at first. John gave away 28 of his stickers and Peter bought another 14 stickers. In the end, Peter had thrice as many stickers as John. How many stickers did John have at first?

QUANTITY INTERNAL TRANSFER USING MODEL

John had 16 more beads than Peter at first. After John gave Peter 20 beads, Peter had 4 times as many beads as John. How many beads did John have at first?

QUANTITY INTERNAL TRANSFER WITH SCENARIOS

John and Peter had some sticks. If John gave Peter 30 sticks, they would have an equal number of sticks. If Peter gave John 30 sticks, John would have 4 times as many sticks as Peter. How many sticks did John have?

VOLUME INVOLVE WORKING FORWARD/BACKWARDS

A rectangular tank measuring 30 cm by 12 cm by 16 cm contained some water. A cubical container with side measuring 12 cm is completely filled with water. All of the water from the cubical container is poured into the rectangular tank and as a result the rectangular tank became 2/3 full. What was the amount of water in the rectangular tank at first?

DIFFERENCE UNCHANGED CONCEPT

John gets $8 more allowance than Yenni each week. Every week, each of them spends $36 on food and saves the rest. When John saves $108 Yenni saves $60.

a) How many weeks does John take to save $108?

b) How much allowance does John get each week?

EXCHANGE WITH INCREASE IN TOTAL

Peter had a total of 40 pens and highlighters at first. He then decided to exchange all his pens for highlighters. He exchanged each pen for 5 highlighters and had a total of 88 highlighters in the end. How many pens did he have at first?

SIMULTANEOUS CONCEPT

A sum of money can be used to buy either 8 identical wallets or 20 identical key chains. Each wallet cost $14.40 more than each key chain. How much did each key chain cost?

MULTIPLICATION OF FRACTIONS

Multiplying fractions is a crucial skill for students in solving math problems in exams. Multiplying fractions accurately is essential for working with more complex math problems involving ratios, proportions, and fractions in their simplest form. To help students master this skill, this video will provide a simple step-by-step guide on how to multiply fractions, breaking down the process into easy-to-follow steps that students can apply to various exam questions.

DIVISION OF FRACTIONS

Learning to divide fractions is important for P5, particularly when solving math problems in exams. Students must understand how to divide fractions into smaller parts to work with them accurately in various mathematical operations. This skill enables students to handle complex problems in exams, including ratios, proportions, and fractions in their simplest form. This video will provide students with a simple step-by-step guide to learning the mechanics of dividing fractions, breaking down the process into easy-to-understand steps.

MULTIPLICATION OF MIXED NUMBER WITH A FRACTION

Learning the arithmetic mechanics of multiplication of mixed numbers with a fraction is crucial for students when it comes to solving math problems in exams. Being able to perform this operation accurately is essential when working with more complex math problems that involve fractions, ratios, and proportions. To help students, this video will provide a simple step-by-step guide on how to multiply mixed numbers with a fraction, breaking down the process into easy-to-follow steps.

FRACTION AS UNITS VS AS MEASUREMENT

The difference between fractions as a unit of measure and fractions as a proportion is whether the fraction is being used to indicate a specific quantity or a proportion of a whole.

REASONING FRACTIONS

I am thinking of a fraction. The difference between the numerator and the denominator is 23. When 5 is added to the denominator, the fraction becomes 1/5. What is the fraction?

REMAINDER CONCEPT WITH + VALUES

Yenni ate 2/7 of her jellybeans on Monday. She ate 2 more jellybeans on Tuesday than on Monday. If she still had 25 jellybeans, how many jellybeans did she have at first?

REMAINDER CONCEPT WITH +/– VALUES AND 2 BRANCHES

Yenni used 300 g more than 1/3 of the flour to bake a cake. She then used 50 g more than 1/4 of the remainder to bake tarts. If she has 700 g of flour left, how much flour did she have at first?

REMAINDER CONCEPT WITH UNKNOWN REMAINDER 1

Peter has some savings at first. He spent $211 on a game console and 1/3 of the remainder on birthday gifts. If he had $28 in the end, how much savings did he have at first?

REMAINDER CONCEPT WITH UNKNOWN REMAINDER 2

Yenni went shopping and spent $60 on a table. She used 3/4 of her remaining money to buy a chair. She was then left with 1/5 of her initial amount of money. How much money did she have at first?

REMAINDER CONCEPT WITH UNKNOWN REMAINDER 3

Yenni spent $18 on food and 1/3 of the remainder on books. She saved the rest of her money, which was 4/9 of her money at first. How much did she have at first?

PROPORTION EXTERNAL TRANSFER WITH REMAINDER THEORY

Peter spent 1/6 of his money on a pair of shoes and 1/2 of the remainder on a pair of headphones. After that, his mother gave him $1292. Now Peter has twice of his original amount of money. How much money did he have at first?

REMAINDER THEORY

Peter spent 1/4 of his money to buy a bag. He spent 2/5 of the remainder on 4 shirts and saved the rest.

a) What fraction of Peter’s money did he spend on the 4 shirts?

b) The bag cost $168 more than one shirt. Given that the price of each shirt was the same, how much did Peter save?

AREA OF TRIANGLE APPLICATION

AREA OF COMPOSITE FIGURES

AREA OF TRIANGLES INVOLVING FOLDED FIGURES

TRIANGLES IN SQUARE GRIDS

RATIO INVOLVING PART AND WHOLE

There were 480 children in a school. 240 of them were girls. What was the ratio of the number of girls to the number of boys? In the fish tank, there are 18 fishes. 12 of them are guppies and the rest are mollies. Find the ratio of the number of guppies to the number of mollies.

RATIO AND FRACTION RELATIONSHIP

John had 3/4 as many pencils as Yenni. Find the ratio of the number of pencils John had to the number of pencils Yenni had. The ratio of John’s salary to Peter’s salary is 3 : 7. What fraction of the total salary is John’s salary?

RATIO, IDENTIFY COMMON BASE. GROUP AS COMMON BASE

The ratio of Peter’s money to John’s money is in the ratio 3 : 4. The ratio of John’s money to Amber’s money is 2 : 3. If they have $1014 altogether, how much money does Peter have?

RATIO, IDENTIFY COMMON BASE. TOTAL AS COMMON BASE

There are an equal number of boys and girls in a school. 3/4 of the boys and half the girls wear glasses. Find the ratio of the number of boys to girls who do not wear glasses.

RATIO, EQUIVALENT PROPORTION

1/3 of Yenni’s money is equal to 2/5 of John’s money. The difference in the amount of money they had is $21. What is the total amount of money that Yenni and John have?

RATIO INVOLVING UNCHANGED TOTAL

How many more squares must be shaded so that the ratio of the number of unshaded squares to the number of shaded squares becomes 1 : 5?

RATIO INVOLVING UNCHANGED DIFFERENCE

There were 144 children and three times as many adults at a school football match. An equal number of children and adults left in the middle of the match. At the end of the match, there were 7 times as many adults as children. How many children were there at the end of the match?

PROPORTION EXTERNAL TRANSFER

Peter had twice as much money as Amber at first. Peter spent 1/3 of his money and Amber spent 2/3 of her money. In the end, Peter had $75 more than Amber. How much money did Peter have at first?

PROPORTION EXTERNAL TRANSFER

John and Peter had $1000 altogether at first. John spent 1/5 of his money and Peter spent 1/4 of his money. They had a total of $787.50 in the end. How much money did John have at first?

PERCENTAGE DIFFERENCE

John had $2000 and Peter had $3000. John spent 30% of his money and Peter spent 60% of his money. Who had more money left and how many percent more?

PERCENTAGE CHANGE

Amber saved $300 last month. She saved $500 this month. What was the percentage increase in her savings for this month?

COMPARING PERCENTAGE USING RATIO

Yenni had 70% as many beads as Amber and 40% more beads than Peter. Yenni had 56 more beads than Peter. How many beads did the three children have altogether?

PERCENTAGE AND REMAINDER THEORY

Amber had a sum of money. The original price of a refrigerator was $7100, and she bought it at a discount of 30%. She then spent 2/5 of the remainder on a vacuum cleaner. She then had 1/4 of her money left. How much money did she have at first?

GST ON DISCOUNTED PRICE

A hairdryer which originally costs $260 has a discount of 15% during a sale. What is the final price of the hairdryer including 8% GST?

PERCENTAGE OF A PERCENTAGE

Peter spent 80% of his allowance and saved the rest. With the same amount of allowance, if he increased his spending by 20%, find the percentage decrease in his savings.