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Primary Maths · Year 4Chapter 3 · Times tables to 12 × 12
Year 4 · Times Tables · Lesson 3.7

Year 4: Using known facts, word problems and the times table check

Part of the Year 4 times tables chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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3.7

Using known facts, word problems and the times table check

Year 4
Known and derived facts, Multiplication and division problems, Times tables check practice

Use a fact you know to work out new facts. Suppose you know 6 × 7 = 42. Then 60 is 6 tens, so 60 × 7 is 6 tens × 7 = 42 tens = 420. In the same way, 6 × 70 = 420 (6 groups of 7 tens) and 600 × 7 = 4,200 (42 hundreds). The digits stay the same and the zeros move along. Division works the same way: 420 ÷ 7 = 60 and 4,200 ÷ 7 = 600.

6 groups of 7 tens: 6 × 7 tens = 42 tens = 420. Each green rod is one ten.

You can also get a new fact from a nearby fact. Add or take away one group: 7 × 7 is 6 × 7 plus one more 7, which is 42 + 7 = 49. Double: 12 × 7 is double 6 × 7, so double 42 is 84. Halve: 3 × 7 is half of 6 × 7, so half of 42 is 21.

5 × 7 and 1 × 7
6 × 7 = 5 × 7 + 1 × 7
6 × 7 and 1 × 7
7 × 7 = 6 × 7 + 1 × 7
Blue dots are the fact you know. Orange dots are the extra group. Each extra row of 7 dots adds 7.

Word problems. Read the problem twice. Draw a bar model. If you know the size of each group and the number of groups, multiply to find the total. If you know the total and want to share it equally, or find how many groups, divide. Write the unit (like £, cm or “pens”) in your answer.

9999?
Multiply: 4 bags of 9. Total?
????36
Divide: 36 shared by 4. Each?
In a bar model, equal bars mean equal groups. The bracket shows the total.

The times tables check. In Year 4 you take a short check on the computer. There are 25 questions like 7 × 8 = ?, and you get 6 seconds for each one. The best preparation is a little practice every day. Make sure you know the ten tricky facts where both numbers are from 6 to 9 (shaded below), and use the tricks in this chapter to build any fact in a flash. The practice sets in this section use the same style: 25 questions, 6 seconds each. Cover the answers and see how many you can do in time!

×123456789101112112345678910111222468101214161820222433691215182124273033364481216202428323640444855101520253035404550556066121824303642485460667277142128354249566370778488162432404856647280889699182736455463728190991081010203040506070809010011012011112233445566778899110121132121224364860728496108120132144
The 16 shaded boxes are the trickiest. Because 7 × 8 = 8 × 7, there are only 10 different facts to learn.

Key words. A known fact is a fact you can recall. A derived fact is a new fact that you work out from a known fact.

Key ideas

  • Use a known fact and place value: 6 × 7 = 42, so 60 × 7 = 420, 6 × 70 = 420 and 600 × 7 = 4,200.
  • Division too: 42 ÷ 7 = 6, so 420 ÷ 7 = 60.
  • Nearby facts: add or take away one group. Double or halve the number of groups.
  • Equal groups with a total to find: multiply. A total to share or split into groups: divide.
  • Times tables check: 25 questions, 6 seconds each.
Worked example 3.7.1
Use the fact 6 × 7 = 42 to work out 60 × 7.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 6 × 7 = 42, and place value. 60 is 6 tens, so the answer is 42 tens.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    6 × 7 = 42
  2. Say the bigger number in tens. 60 is 6 tens.
    60 = 6 tens
  3. Multiply, using the known fact. 6 tens × 7 = 42 tens, because 6 × 7 = 42.
    6 × 7 = 42, so 6 tens × 7 = 42 tens
  4. Change 42 tens back to a number. 1 ten is 10, so 42 tens is 42 × 10.
    42 tens = 420
  5. Write the answer.
    60 × 7 = 420

Check. Divide back: 420 ÷ 7 = 60. ✓

Watch out. The answer is 42 tens, which has 1 zero on the end. Count the zeros carefully.

Worked example 3.7.2
Use the fact 4 × 8 = 32 to work out 4 × 80.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 4 × 8 = 32, and place value. 80 is 8 tens, so the answer is 32 tens.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    4 × 8 = 32
  2. Say the bigger number in tens. 80 is 8 tens.
    80 = 8 tens
  3. Multiply, using the known fact. 8 tens × 4 = 32 tens, because 8 × 4 = 32.
    8 × 4 = 32, so 8 tens × 4 = 32 tens
  4. Change 32 tens back to a number. 1 ten is 10, so 32 tens is 32 × 10.
    32 tens = 320
  5. Write the answer.
    4 × 80 = 320

Check. Divide back: 320 ÷ 80 = 4. ✓

Watch out. The answer is 32 tens, which has 1 zero on the end. Count the zeros carefully.

Worked example 3.7.3
Use the fact 9 × 5 = 45 to work out 900 × 5.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 9 × 5 = 45, and place value. 900 is 9 hundreds, so the answer is 45 hundreds.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    9 × 5 = 45
  2. Say the bigger number in hundreds. 900 is 9 hundreds.
    900 = 9 hundreds
  3. Multiply, using the known fact. 9 hundreds × 5 = 45 hundreds, because 9 × 5 = 45.
    9 × 5 = 45, so 9 hundreds × 5 = 45 hundreds
  4. Change 45 hundreds back to a number. 1 hundred is 100, so 45 hundreds is 45 × 100.
    45 hundreds = 4,500
  5. Write the answer.
    900 × 5 = 4,500

Check. Divide back: 4,500 ÷ 5 = 900. ✓

Watch out. The answer is 45 hundreds, which has 2 zeros on the end. Count the zeros carefully.

Worked example 3.7.4
Use the fact 56 ÷ 8 = 7 to work out 560 ÷ 8.

Key words. A known fact is a fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 56 ÷ 8 = 7, and place value. 560 is 56 tens, so the answer is 7 tens.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    56 ÷ 8 = 7
  2. Say the big number in tens. 560 is 56 tens.
    560 = 56 tens
  3. Divide, using the known fact. 56 tens ÷ 8 = 7 tens, because 56 ÷ 8 = 7.
    56 ÷ 8 = 7, so 56 tens ÷ 8 = 7 tens
  4. Change 7 tens back to a number. Put the zeros back.
    7 tens = 70
  5. Write the answer.
    560 ÷ 8 = 70

Check. Multiply back: 70 × 8 = 560. ✓

Watch out. Keep the zeros. 420 ÷ 7 is 60, not 6.

Worked example 3.7.5
Use the fact 36 ÷ 9 = 4 to work out 3,600 ÷ 9.

Key words. A known fact is a fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 36 ÷ 9 = 4, and place value. 3,600 is 36 hundreds, so the answer is 4 hundreds.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    36 ÷ 9 = 4
  2. Say the big number in hundreds. 3,600 is 36 hundreds.
    3,600 = 36 hundreds
  3. Divide, using the known fact. 36 hundreds ÷ 9 = 4 hundreds, because 36 ÷ 9 = 4.
    36 ÷ 9 = 4, so 36 hundreds ÷ 9 = 4 hundreds
  4. Change 4 hundreds back to a number. Put the zeros back.
    4 hundreds = 400
  5. Write the answer.
    3,600 ÷ 9 = 400

Check. Multiply back: 400 × 9 = 3,600. ✓

Watch out. Keep the zeros. 420 ÷ 7 is 60, not 6.

Worked example 3.7.6
You know that 6 × 8 = 48. Use this fact to work out 7 × 8.

Key words. A derived fact is a new fact you work out from a fact you already know.

Method. 7 is one more than 6, so add one more group of 8 to the answer to 6 × 8.

  1. Write the fact you know. We start from the fact we know.
    6 × 8 = 48
  2. Compare 7 with 6. 7 is one more than 6, so we need one more group of 8.
    7 = 6 + 1
  3. Add one more group. One group is 8.
    48 + 8 = 56
  4. Write the answer.
    7 × 8 = 56

Check. Check by dividing: 56 ÷ 8 = 7. ✓

Watch out. Add 8, the size of one group, not 7 or 1.

Worked example 3.7.7
You know that 6 × 7 = 42. Use this fact to work out 12 × 7.

Key words. A derived fact is a new fact you work out from a fact you already know.

Method. 12 is double 6, so double the answer to 6 × 7.

  1. Write the fact you know. We start from the fact we know.
    6 × 7 = 42
  2. Compare 12 with 6. 12 is double 6, so 12 groups of 7 are double 6 groups of 7.
    12 = 2 × 6
  3. Double the known answer.
    double 40 = 80, double 2 = 4, so 80 + 4 = 84
  4. Write the answer.
    12 × 7 = 84

Check. Check by dividing: 84 ÷ 7 = 12. ✓

Watch out. Doubling the number of groups doubles the total. Do not double the other number as well.

Worked example 3.7.8
Leo buys 6 packs of pencils. Each pack has 12 pencils. He gives 15 pencils to his friends. How many pencils does Leo have left?

Method. Two steps. First find how many pencils Leo buys by multiplying. Then take away the pencils he gives away.

  1. Draw a bar model for step 1. 6 equal packs of 12. We want the total.
    121212121212?
  2. Step 1: multiply. Equal groups, so multiply.
    10 × 6 = 60
    6 + 6 = 12
    60 + 12 = 72
    6 × 12 = 72
  3. Step 2: take away. Leo gives 15 pencils away. Take 10 first, then 5.
    72 − 10 = 62, then 62 − 5 = 57
  4. Write the answer.
    57 pencils

Check. Add back: 57 + 15 = 72 and 72 ÷ 6 = 12. ✓

Watch out. The answer to step 1 (72) is not the final answer. Check what the question asks for.

Worked example 3.7.9
72 apples are shared equally between 8 bags. How many apples are in each bag?

Method. Dividing is the opposite of multiplying. Use the times table to find how many times the number fits.

  1. Draw a bar model. The whole is 72. It is split into 8 equal parts. We want the size of one part.
    ????????72
  2. Choose the operation. Sharing equally means dividing.
    72 ÷ 8
  3. Use the times tables. Think: what do we multiply 8 by to get 72?
    9 × 8 = 72, so 72 ÷ 8 = 9
  4. Write the answer. Include the unit.
    9 apples

Check. Multiply back: 9 × 8 = 72. ✓

Watch out. Read the question carefully. Does it ask for the size of each group, or for how many groups?

Watch out

Keep the zeros! 60 × 7 is 420, not 42. Write the known fact first, then say how many tens or hundreds you have. In word problems, do not choose multiply or divide because of one word in the question. Draw a bar model and decide if you know the total or the size of each group.

Exercise 3G  Using known facts

Non-calculator
1
FUse the fact 6 × 4 = 24 to work out each answer.
(a)60 × 4
(b)6 × 40
(c)600 × 4
(d)240 ÷ 4
(e)2,400 ÷ 4
(f)240 ÷ 6
2
FUse the fact 8 × 7 = 56 to work out each answer.
(a)80 × 7
(b)8 × 70
(c)800 × 7
(d)560 ÷ 7
(e)560 ÷ 8
(f)5,600 ÷ 8
3
FQuick-fire! Use a times table fact and place value.
(a)30 × 8
(b)7 × 50
(c)90 × 6
(d)4 × 700
(e)110 × 3
(f)8 × 90
4
FDivide. Use a times table fact and place value.
(a)360 ÷ 6
(b)480 ÷ 8
(c)2,100 ÷ 7
(d)5,400 ÷ 9
(e)880 ÷ 11
(f)1,200 ÷ 12
5
FYou know that 5 × 8 = 40. Use this fact to work out each answer.
(a)6 × 8
(b)4 × 8
(c)10 × 8
6
FDouble or halve a fact you know.
(a)6 × 9.   You know 3 × 9 = 27.
(b)6 × 5.   You know 12 × 5 = 60.
(c)8 × 7.   You know 4 × 7 = 28.
(d)6 × 6.   You know 12 × 6 = 72.
7
PSA stamp costs 60p. Hana buys 8 stamps. How much do the stamps cost altogether?
60p60p60p60p60p60p60p60p?
8
PSA bus holds 70 passengers. There are 6 full buses. How many passengers is that altogether?
707070707070?
9
PSA school orders 540 pencils. They are packed in boxes of 9. How many boxes does the school get?
10
RZoe says, “6 × 7 = 42, so 60 × 7 = 42 too.” What mistake did Zoe make? What is 60 × 7?
11
RWhich one is the odd one out?   A  6 × 70    B  60 × 7    C  42 × 10    D  600 × 7
12
RAlways, sometimes or never?   When you multiply a whole number by a multiple of 10, the answer ends in 0.
13
RUse the fact 7 × 8 = 56 to write down four more facts about 5,600.

Exercise 3H  Multiplication and division problems

Non-calculator
1
FThere are 12 months in one year. How many months are there in 7 years?
12121212121212?
2
FSam has 60 stickers. He shares them equally between 5 friends. How many stickers does each friend get?
?????60
3
FA book costs £8. A school buys 12 books. How much do the books cost altogether?
£8£8£8£8£8£8£8£8£8£8£8£8?
4
FA teacher has 99 pencils. She puts 9 pencils in each pot. How many pots does she fill?
9999999999
5
PSAisha buys 4 packs of stickers. There are 12 stickers in each pack. She gives 15 stickers to her cousin. How many stickers does Aisha have left?
6
PSCakes cost £6 each. Leo buys 7 cakes. He pays with a £50 note. How much change does he get?
£6£6£6£6£6£6£6?
7
PSMr Khan buys 5 boxes of 8 markers and 3 boxes of 12 markers. How many markers does he buy altogether?
8
PSMei reads 7 pages every day for 12 days. Ben reads 9 pages every day for 9 days. Who reads more pages? How many more?
9
PSThe table shows the price of a pack of cards.
CardsPrice of one pack
Football£4
Animals£7

Sam buys 8 packs of football cards and 6 packs of animal cards. How much does he spend?
10
RThere are 9 rows of seats in a hall, with 7 seats in each row. Which bar model, A or B, matches this? Do the two bar models give the same total? Explain why.
A
777777777?
B
9999999?
11
RAnil says, “8 packs of 6 buns is the same number of buns as 6 packs of 8 buns.” Is Anil right? Prove it.
8 rows of 6
6 rows of 8
12
RWhich two of these problems need division? Tick two boxes. You do not need to work out the answers.
A   6 bags have 9 apples in each bag. How many apples are there?
B   42 pens are shared equally between 6 children. How many pens does each child get?
C   A rope 56 m long is cut into pieces that are each 7 m long. How many pieces are there?
D   A train has 8 carriages with 12 seats in each carriage. How many seats are there?
13
RA farmer has 10 animals. Some are chickens and some are cows. There are 28 legs altogether. A chicken has 2 legs and a cow has 4 legs. How many chickens and how many cows are there?

Exercise 3I  Times tables check practice: 25 questions, 6 seconds each

Non-calculator
1
FSet A (25 questions): a warm-up with the easier tables. Give yourself 6 seconds for each question (2 minutes 30 seconds in total). Cover the answers and write your answers on paper.
(a)9 × 2 =
(b)5 × 4 =
(c)3 × 3 =
(d)4 × 11 =
(e)11 × 2 =
(f)3 × 5 =
(g)10 × 5 =
(h)3 × 10 =
(i)7 × 5 =
(j)8 × 4 =
(k)5 × 11 =
(l)10 × 11 =
(m)4 × 2 =
(n)3 × 4 =
(o)2 × 5 =
(p)10 × 9 =
(q)3 × 7 =
(r)9 × 3 =
(s)6 × 4 =
(t)5 × 9 =
(u)11 × 3 =
(v)4 × 4 =
(w)12 × 10 =
(x)8 × 11 =
(y)4 × 12 =
2
FSet B (25 questions): a mix of all the tables. Give yourself 6 seconds for each question (2 minutes 30 seconds in total). Cover the answers and write your answers on paper.
(a)3 × 7 =
(b)11 × 9 =
(c)8 × 10 =
(d)2 × 8 =
(e)2 × 3 =
(f)10 × 9 =
(g)11 × 7 =
(h)5 × 10 =
(i)5 × 9 =
(j)7 × 7 =
(k)10 × 11 =
(l)2 × 5 =
(m)11 × 8 =
(n)6 × 3 =
(o)7 × 5 =
(p)3 × 8 =
(q)12 × 6 =
(r)6 × 7 =
(s)9 × 2 =
(t)8 × 6 =
(u)11 × 3 =
(v)8 × 5 =
(w)9 × 4 =
(x)4 × 10 =
(y)3 × 3 =
3
FSet C (25 questions): the tricky tables 6, 7, 8, 9 and 12. Give yourself 6 seconds for each question (2 minutes 30 seconds in total). Cover the answers and write your answers on paper.
(a)7 × 3 =
(b)2 × 9 =
(c)8 × 2 =
(d)9 × 6 =
(e)12 × 6 =
(f)12 × 7 =
(g)7 × 10 =
(h)6 × 7 =
(i)6 × 8 =
(j)12 × 11 =
(k)12 × 12 =
(l)11 × 8 =
(m)8 × 10 =
(n)12 × 4 =
(o)12 × 8 =
(p)7 × 8 =
(q)7 × 9 =
(r)9 × 5 =
(s)2 × 12 =
(t)12 × 9 =
(u)6 × 5 =
(v)4 × 9 =
(w)6 × 6 =
(x)9 × 3 =
(y)5 × 7 =
4
FSet D (20 questions): division facts and missing numbers. Try to answer each one in 10 seconds.
(a)56 ÷ 7 =
(b)6 × ? = 36
(c)? × 6 = 24
(d)? ÷ 7 = 10
(e)132 ÷ ? = 12
(f)30 ÷ 6 =
(g)11 × ? = 121
(h)? × 3 = 21
(i)? ÷ 3 = 10
(j)30 ÷ ? = 6
(k)99 ÷ 11 =
(l)5 × ? = 40
(m)? × 8 = 32
(n)? ÷ 4 = 11
(o)77 ÷ ? = 11
(p)60 ÷ 10 =
(q)6 × ? = 36
(r)? × 4 = 16
(s)? ÷ 6 = 11
(t)120 ÷ ? = 12
5
PSIn the times tables check there are 25 questions and you have 6 seconds for each. How many seconds is that altogether? Write your answer in minutes and seconds too.
6
RShow two different ways to work out 7 × 8.
7
RDev says, “There are 16 tricky facts to learn, because the grid below has 16 boxes.” Explain why Dev only needs to learn 10 facts.
×6789636424854742495663848566472954637281

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