Daily 5 Math Practice: 30 Oct Worked Solutions

A wrong answer is not the end of a question. It is often the most useful part, because it shows where the thinking slipped. The trouble is that a final answer on its own cannot say where. Was a place value misread, a unit forgotten, or a step skipped? You only find out by looking at the working, line by line. That is what this post is for. Each grade below has the five questions from its Daily 5 video, and every one comes with its hints and steps written out in full, so you and your child can find the exact line where a slip happened and put it right together.

Start with your child's grade and watch the video in that section. Then have your child work all five questions on paper. Open a solution only after an answer is written down, and compare the working one line at a time. The hints and steps match the video exactly.

Primary 3 (P3) Math: Whole Numbers, Measurement, Area and Perimeter

This P3 set covers the value of a digit in a four-digit number, changing litres and millilitres into millilitres, taking away hundreds mentally, the perimeter of a square, and a harder money problem with two kinds of notes. For the perimeter question, check that every side has been counted. In the notes problem, a sensible first guess that is then adjusted is a good place to start.

Primary 3 (P3) Daily 5 video for 30 Oct. Watch it, then try the five questions below before opening any solution.

Question 1 · Numbers up to 10,000 · easy

What is the value of the digit

7

7863

Show the worked solution

Hint 1

Split

7863

into its thousands, hundreds, tens, and ones parts.

Hint 2

Add the other place-value parts:

800 + 60 + 3 = 863

→ $863$ .

Final step

The number is

7863

, so the digit's thousands value is

7863 - 863 = 7000

→ 7000

Answer: 7000

Question 2 · Measurement · easy

Express

6\ell\ 512\text{ ml}

in millilitres.

Show the worked solution

Hint 1

1\ell = 1000\text{ ml}

Hint 2

Convert the whole litres first:

6 \times 1000 = 6000

→ 6000 ml.

Final step

Add

512\text{ ml}

6000 + 512 = 6512

→ 6512

Answer: 6512

Question 3 · Mental Math · medium

What is

300

less than

5434

Show the worked solution

Hint 1

Subtracting

300

only changes the digit in the hundreds place. What is the hundreds digit of

5434

→ $4$

Hint 2

Subtract

3

from the hundreds digit (

4 - 3 = 1

) and keep the other digits the same

Answer: 5134

Question 4 · Area and Perimeter · medium

A square has a side of

5\text{ cm}

. Find its perimeter.

Show the worked solution

Hint 1

Pair two sides of the square first.

Hint 2

The pair is

5 + 5 = 10

→ 10 cm.

Final step

Add all the side lengths:

5 + 5 + 5 + 5 = 20

→ 20

Answer: 20

Question 5 · Guess-and-Check with Money · hard

The total amount of

18

$2

notes and

$5

notes is

$60

. How many

$5

notes are there?

Show the worked solution

Hint 1

Suppose all

18

notes were

$2

notes. What would the total be? Compare it with the real total.

Hint 2

Each swap adds

5 - 2 = 3

dollars

→ $3$ dollars per swap. Compare the total with the all- $2$ total.

Final step

All-

2

total:

2 \times 18 = 36

. Shortfall:

60 - 36 = 24

. Each swap adds

5 - 2 = 3

. The number of

$5

notes is

24 \div 3 = 8

→ 8

Answer: 8

Primary 4 (P4) Math: Whole Numbers, Area and Perimeter, Decimals

The P4 questions practise rounding a whole number to the nearest hundred and a decimal to two decimal places, finding the perimeter of a square when only its area is given, a fraction of a set, and a harder problem about two repeating schedules. In the fraction question, read carefully whether it asks for the part given away or the part kept.

Primary 4 (P4) Daily 5 video for 30 Oct. Watch it, then try the five questions below before opening any solution.

Question 1 · Rounding and Estimation · easy

Round

53,400

to the nearest hundred.

Show the worked solution

Hint 1

Look at the digit in the tens place

→ 0.

Hint 2

If it is 5 or more, round up. Otherwise, round down

Answer: 53400

Question 2 · Area and Perimeter · medium

What is the perimeter of a square with an area of

25\text{ cm}^2

Show the worked solution

Hint 1

A square has four equal sides.

Hint 2

Find the side: it is the number that multiplies by itself to give the area.

Final step

The side is

5\text{ cm}

because

5 \times 5 = 25

. Perimeter

= 4 \times 5 = 20\text{ cm}

→ 20

Answer: 20

Question 3 · Rounding · medium

Round

7.251

2

decimal places.

Show the worked solution

Hint 1

Find the digit one place to the right of the rounding place.

Hint 2

The deciding digit is

1

, which is less than five

→ $1$ .

Final step

Round down:

7.251 \to 7.25

→ 7.25

Answer: 7.25

Question 4 · Fraction of a Set · medium

Mrs. Lee had

25

stamps. She gave

\frac{4}{5}

of them to her brother. How many stamps did she have left?

Show the worked solution

Hint 1

Find the part given away by splitting this question's total into

5

equal groups and taking

4

of them.

Hint 2

After taking

4

of the

5

equal groups, find the value of the groups left using this question's total.

Final step

Given away:

25 \div 5 \times 4 = 20

. Left:

25 - 20 = 5

→ 5

Answer: 5

Question 5 · Factors and Multiples · hard

Ali exercises every

3

days and Bala exercises every

5

days. Both exercised today. After how many days will they both exercise on the same day again?

Show the worked solution

Hint 1

Compare the repeating cycles to find when both events happen together again.

Hint 2

The first two multiples of 3 are

3 \times 1 = 3

and

3 \times 2 = 6

→ 6 days.

Final step

Multiples of

3

are 3, 6, 9, 12, 15. Multiples of

5

are 5, 10, 15. The first common time is 15 days

→ 15

Answer: 15

Primary 5 (P5) Math: Percentage, Volume, Area of Triangle

This P5 set covers a percentage of a quantity, counting the unit cubes in a solid, a missing edge of a box from its volume, and two hard problems: a shaded area where two rectangles overlap, and a ratio that changes when one group grows. For the cubes, keep track of the ones already counted. In the ratio problem, ask which group does not change.

Primary 5 (P5) Daily 5 video for 30 Oct. Watch it, then try the five questions below before opening any solution.

Question 1 · Finding a Percentage Part of a Whole · easy

A shop had

180

kettles. It sold

35\%

of them. How many kettles did it sell?

Show the worked solution

Hint 1

For the kettles, find 10% of the total first.

Hint 2

One tenth of the kettles is

180 \div 10 = 18

→ 18 kettles.

Final step

Scale that 10% amount to 35%:

18 \times 35 \div 10 = 63

→ 63

Answer: 63

Question 2 · Volume of Cube and Cuboid · medium

How many unit cubes form this solid?

Show the worked solution

Hint 1

Count the cubes in each layer starting from the bottom.

Hint 2

Bottom layer: ...

Final step

Top layer: ..

→ 10

Answer: 10

Question 3 · Basic Volume · medium

A rectangular box has a volume of

900\text{ cm}^3

. Its length is

9\text{ cm}

and its height is

10\text{ cm}

. Find its width.

Show the worked solution

Hint 1

Volume

= L \times W \times H

. So the missing dimension

= Volume \div (\text{product of other two dimensions})

Hint 2

Product of given sides:

... \times ... = ...

Final step

900 \div ...

→ 10

Answer: 10

Question 4 · Composite Area · hard

Two identical rectangles, each

14\text{ cm}

7\text{ cm}

, overlap so that the overlapping part forms a square in the middle (this square is not shaded). The distance from the edge of the overlap square to the far end of a rectangle, measured along its

14\text{ cm}

side, is

11\text{ cm}

. Find the total shaded area.

Show the worked solution

Hint 1

The overlap square's side is the rectangle's length minus the given distance:

14 - 11 = 3\text{ cm}

Hint 2

Find the area of one rectangle:

14 \times 7 = 98\text{ cm}^2

Final step

The unshaded overlap square (area

3 \times 3 = 9\text{ cm}^2

) is counted in both rectangles, so subtract it twice:

2 \times 98 - 2 \times 9

→ 178

Answer: 178

Question 5 · Ratio Word Problems · hard

The ratio of the number of adults to children was

3 : 4

. After

15

adults were added, the ratio became

2 : 1

. How many children were there?

Show the worked solution

Hint 1

The number of children is unchanged, so name that shared quantity before scaling the ending ratio.

Hint 2

Scale the ending ratio by 4:

2 \times 4 = 8

and

1 \times 4 = 4

→ 8 : 4 scaled units.

Final step

Reuse the starting units for children:

4 \times 3 = 12

→ 12

Answer: 12

Primary 6 (P6) Math: Algebra, Ratio, Fractions

The P6 questions start with substituting a value into an algebraic expression and a direct ratio problem, then move to three hard ones: two rails compared with an offset bar model, a fraction taken from what remains, and a price with a discount followed by GST. In the last two, notice that the second change works on a new amount, not the original one.

Primary 6 (P6) Daily 5 video for 30 Oct. Watch it, then try the five questions below before opening any solution.

Question 1 · Algebraic Expressions · easy

Evaluate the expression

3a + 8

when

a = 6

Show the worked solution

Hint 1

Substitute

a = 6

into the expression:

3(6) + 8

Hint 2

Multiply first:

3 \times 6 = 18

Final step

Add

8

→ 26

Answer: 26

Question 2 · Word Problems · medium

The ratio of the number of boys to the number of girls is

2:6

. If there are

14

boys, how many girls are there?

Show the worked solution

Hint 1

2

units represents

14

boys. Find 1 unit (

14 \div 2

)

→ $7$ .

Hint 2

Multiply the unit value by girls's units (

6 \times 7

)

Answer: 42

Question 3 · Ratio with Offset Bar Models · hard

The figure shows two rails drawn between the same two dashed lines. The ratio of the length of rail R to the length of rail S is

5 : 3

. Find the length of rail S in metres.

Show the worked solution

Hint 1

Both rails span the same two dashed lines. Their labels show

4.5

m and

2.1

m; subtract these gaps.

Hint 2

The ratio counts differ by

5 - 3 = 2

units. Divide the length difference by this count to find one unit.

Final step

Labels differ by

4.5 - 2.1 = 2.4

m. One unit is

2.4 \div 2 = 1.2

m. Rail S has 3 units:

3 \times 1.2 = 3.6

→ 3.6

Answer: 3.6

Question 4 · Fraction Word Problems · hard

Mary had

180

marbles. She gave away

\frac{1}{3}

of them. Then she lost

\frac{1}{4}

of the remainder. How many marbles did she have left?

Show the worked solution

Hint 1

Find how many were gave:

180 \times \frac{1}{3} = 60

. Remainder:

180 - 60 = 120

Hint 2

Find how many were lost:

120 \times \frac{1}{4} = 30

. Left:

120 - 30

Answer: 90

Question 5 · Percentage - Combined Charges · hard

A laptop costs

$1000

. A member gets a

10\%

discount.

9\%

GST is charged on the discounted price. How much does the member pay in total?

Show the worked solution

Hint 1

After the discount, the laptop's price has

100 - 10 = 90

percent left.

Hint 2

The discounted price of the laptop is

1000 \times 90 \div 100 = 900

Final step

Its GST is

900 \times 9 \div 100 = 81

. Add the GST:

900 + 81 = 981

→ 981

Answer: 981

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Daily 5 Math Practice: 30 Oct Worked Solutions

Try what you just learned

Primary 3 (P3) Math: Whole Numbers, Measurement, Area and Perimeter

Primary 4 (P4) Math: Whole Numbers, Area and Perimeter, Decimals

Primary 5 (P5) Math: Percentage, Volume, Area of Triangle

Primary 6 (P6) Math: Algebra, Ratio, Fractions

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