Step-by-step Maths Level 4 Level 4 check: check-up and practice test questions

Method. Write the parts chosen on top, and the total number of equal parts on the bottom.

1. Find the number of equal parts in the whole. The whole is split into this many equal parts.
   2 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   1 parts
3. Write the fraction. Parts chosen over total parts.
   1/2

Check. Check: 1 of the 2 parts is 1/2.

Watch out. The top number is never bigger than the bottom number for a fraction of one whole.

Method. Use the facts: 60 minutes in an hour, 24 hours in a day, and the number of days in each month.

1. Remember how many hours there are in 1 day. There are 24 hours in 1 day.
   1 day = 24 hours
2. Multiply by 7. There are 7 days.
   7 × 24 = 168
3. Write the answer. This is the total number of hours.
   168

Check. Check the fact: 60 minutes, 24 hours, or the days in the month.

Watch out. Learn the months with 30 days: April, June, September and November. All the others have 31 days, except February.

Method. Count in 8s to find 8 groups of 5. The order of the two numbers does not matter.

1. Count in 8s, 5 times. Each count adds one more group of 8.
   8, 16, 24, 32, 40
2. The last number we said is the answer. We counted in equal groups.
   8 × 5 = 40
3. Write the answer. The order of the numbers does not change the answer.
   40

Check. Check: 5 × 8 is also 40.

Watch out. Say the 8 times table in order until you reach the fact you need.

Method. Count in steps of the same size, one step at a time.

1. Start at the first number. It is where we begin.
   8750
2. Add 50 each time. Each count moves by the same step.
   8750 + 50 = 8800
3. Add 50 each time. Each count moves by the same step.
   8800 + 50 = 8850
4. Add 50 each time. Each count moves by the same step.
   8850 + 50 = 8900
5. Write the answer. This is the last number we reached.
   8900

Check. Count the steps back: 8900 - 150 = 8750.

Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.

Method. Equivalent fractions: multiply or divide the top and bottom by the same number.

1. Multiply the top number by 3. Do the same to the top and the bottom.
   1 × 3 = 3
2. Multiply the bottom number by 3. The fraction keeps the same value.
   4 × 3 = 12
3. Write the missing number. This is the bottom number of the equal fraction.
   12

Check. Check: 1/4 and 3/12 are equal, both are the same part of a whole.

Watch out. Do the same to the top and the bottom. Never change one and not the other.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

1. Subtract the ones column. Take the bottom digit from the top digit.
   4 - 2 = 2
2. Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.
   thousands: 8 to 7; hundreds: 0 to 10
3. Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.
   hundreds: 10 to 9; tens: 6 to 16
4. Subtract the tens column. Take the bottom digit from the top digit.
   16 - 9 = 7
5. Subtract the hundreds column. Take the bottom digit from the top digit.
   9 - 6 = 3
6. Subtract the thousands column. Take the bottom digit from the top digit.
   7 - 1 = 6
7. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   6372

Check. Check: 6372 + 1692 = 8064.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Method. An array shows equal groups. Divide the total by the number of rows to find the number in each row.

1. Read the array. The dots are in equal rows.
   4 rows, 28 dots
2. Share the dots into the rows. Each row has the same number of dots.
   28 ÷ 4 = 7
3. Check with multiplication. Rows × dots in each row gives the total.
   4 × 7 = 28
4. Write the answer. This is the number in each row.
   7

Check. Check: 4 rows of 7 make 28.

Watch out. The number of rows is the divisor. Each row is one equal group.

Method. Find the parts we know, then subtract them from the whole.

1. Add the parts we know. These are the parts written in the sum.
   7403
2. Take this from the number to find the missing part. 7453 minus the known parts is the gap.
   7453 - 7403 = 50
3. Write the missing part. It is the value of that column.
   50

Check. Check: 7000 + 400 + 50 + 3 = 7453.

Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.

Method. Read the number in parts: thousands, hundreds, then the last two digits.

1. Say the thousands. Read the thousands digit first.
   eight thousand
2. Say the hundreds. Then read the hundreds.
   one hundred
3. Say the tens and ones. Put the last two digits together. Use and before them.
   twenty-seven
4. Write the answer in words. Join the parts together.
   eight thousand one hundred and twenty-seven

Check. Check: 8000 + 100 + 27 = 8127.

Watch out. Put and before the tens and ones when there are hundreds, as in four hundred and six.

Method. Sharing: put the same number into each group. Divide the total by the number of groups.

1. Count the friends. Each friend gets the same number.
   2 friends
2. Share the items one at a time. Put one in each group, then start again until none are left.
   10 shared into 2 groups
3. Count the items in one group. Each group has the same number.
   10 ÷ 2 = 5
4. Write the answer. This is how many each friend gets.
   5

Check. Check: 5 × 2 = 10.

Watch out. The number of friends is the number of groups, not the number in each group.

Method. Add the length of the activity to the start time. Carry extra minutes into the hours.

1. Write the start time. It is where we begin.
   17:34
2. Add the duration. Add 50 minutes to the start time.
   17:34 + 50 minutes = 18:24
3. Write the finish time. Use two digits for the hour and minutes.
   18:24

Check. Check: 50 minutes before 18:24 is 17:34.

Watch out. When the minutes go past 60, add one hour and take away 60 minutes.

Method. Compare the numbers column by column, starting with the thousands.

1. Look at the thousands. Numbers with fewer thousands are smaller.
   6600: 6, 1937: 1, 9401: 9, 3600: 3
2. Look at the hundreds for numbers with the same thousands. Compare the next column only when the first is the same.
   Put them in groups by thousands first
3. Order the numbers. Put them smallest to largest.
   1937, 3600, 6600, 9401
4. Write the answer in order. Write each number once.
   1937, 3600, 6600, 9401

Check. Check: each number is less than the next one in the list.

Watch out. Compare the thousands first, then the hundreds, then the tens, then the ones.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

1. Subtract the ones column. Take the bottom digit from the top digit.
   4 - 3 = 1
2. Subtract the tens column. Take the bottom digit from the top digit.
   3 - 2 = 1
3. Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.
   thousands: 8 to 7; hundreds: 0 to 10
4. Subtract the hundreds column. Take the bottom digit from the top digit.
   10 - 2 = 8
5. Subtract the thousands column. Take the bottom digit from the top digit.
   7 - 4 = 3
6. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   3811

Check. Check: 3811 + 4223 = 8034.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Method. Equivalent fractions: multiply or divide the top and bottom by the same number.

1. Divide the top number by 2. Divide the top and the bottom by the same number.
   2 ÷ 2 = 1
2. Divide the bottom number by 2. The fraction keeps the same value.
   8 ÷ 2 = 4
3. Write the missing number. This is the top number of the simpler fraction.
   1

Check. Check: 2/8 and 1/4 are equal.

Watch out. Do the same to the top and the bottom. Never change one and not the other.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

1. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
   tens: 6 to 5; ones: 3 to 13
2. Subtract the ones column. Take the bottom digit from the top digit.
   13 - 6 = 7
3. Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.
   thousands: 7 to 6; hundreds: 0 to 10
4. Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.
   hundreds: 10 to 9; tens: 5 to 15
5. Subtract the tens column. Take the bottom digit from the top digit.
   15 - 9 = 6
6. Subtract the hundreds column. Take the bottom digit from the top digit.
   9 - 4 = 5
7. Subtract the thousands column. Take the bottom digit from the top digit.
   6 - 6 = 0
8. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   567

Check. Check: 567 + 6496 = 7063.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Method. Count in 6s to find 6 groups of 8. The order of the two numbers does not matter.

1. Count in 6s, 8 times. Each count adds one more group of 6.
   6, 12, 18, 24, 30, 36, 42, 48
2. The last number we said is the answer. We counted in equal groups.
   6 × 8 = 48
3. Write the answer. The order of the numbers does not change the answer.
   48

Check. Check: 8 × 6 is also 48.

Watch out. Say the 6 times table in order until you reach the fact you need.

Method. Compare the thousands first, then the hundreds, then the tens, then the ones.

1. Compare the thousands. The first column that is different decides the order.
   8 and 3: 8 is more
2. Write the sign between the numbers. The sign points to the smaller number.
   >

Check. Check: read the sign as words. 8479 is greater than 3831.

Watch out. The arrow always points to the smaller number. Compare the thousands first, not the last digits.

Method. Work backwards: undo each step in the reverse order, then check forwards.

1. Undo the doubling. Halve the result first.
   3344 ÷ 2 = 1672
2. Undo the take away. Add back the number that was taken away.
   1672 + 90 = 1762
3. Write the answer. This was the number I started with.
   1762

Check. Check: follow the steps forwards from your answer to get the result in the question.

Watch out. Undo the last step first. Addition is undone by subtraction, and multiplication by division.

Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.

1. Think of the multiplication: 4 × ___ = 44. Division asks how many groups.
   4 × ___ = 44
2. Count in 4s until you reach 44. Count the steps as you go.
   4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
3. Write the answer. This is the number of groups.
   11

Check. Check: 4 × 11 = 44.

Watch out. The times table of 4 is the key. Division is the opposite of multiplication.

Method. Count in 9s to find 9 groups of 5. The order of the two numbers does not matter.

1. Count in 9s, 5 times. Each count adds one more group of 9.
   9, 18, 27, 36, 45
2. The last number we said is the answer. We counted in equal groups.
   9 × 5 = 45
3. Write the answer. The order of the numbers does not change the answer.
   45

Check. Check: 5 × 9 is also 45.

Watch out. Say the 9 times table in order until you reach the fact you need.

Method. Count in 3s to find 3 groups of 12. The order of the two numbers does not matter.

1. Count in 3s, 12 times. Each count adds one more group of 3.
   3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
2. The last number we said is the answer. We counted in equal groups.
   3 × 12 = 36
3. Write the answer. The order of the numbers does not change the answer.
   36

Check. Check: 12 × 3 is also 36.

Watch out. Say the 3 times table in order until you reach the fact you need.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

1. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
   tens: 9 to 8; ones: 2 to 12
2. Subtract the ones column. Take the bottom digit from the top digit.
   12 - 8 = 4
3. Subtract the tens column. Take the bottom digit from the top digit.
   8 - 3 = 5
4. Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.
   thousands: 6 to 5; hundreds: 0 to 10
5. Subtract the hundreds column. Take the bottom digit from the top digit.
   10 - 2 = 8
6. Subtract the thousands column. Take the bottom digit from the top digit.
   5 - 5 = 0
7. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   854

Check. Check: 854 + 5238 = 6092.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Method. Find one equal part, then multiply it by the top number.

1. Share 40 into 2 equal groups. Each group is one equal part of the set.
   40 ÷ 2 = 20
2. Count 1 of the groups. The shaded part is the top number of groups.
   1 × 20 = 20
3. Write the answer. This is how many are shaded.
   20

Check. Check: 20 of the 40 are shaded.

Watch out. The shaded part is always a fraction of the total set, not of the bottom number.

Method. Find the key words, choose the operation (addition), then work out the answer.

1. Find the key words. “altogether” means put the two amounts together.
   2419 and 986
2. Choose the operation. Putting amounts together is addition.
   2419 + 986
3. Work out the answer. Add the thousands, hundreds, tens and ones.
   2419 + 986 = 3405
4. Write the answer. Give the total with the thing it counts.
   3405

Check. Check the answer with the opposite operation to make sure it fits the story.

Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.

Method. Count in 8s to find 8 groups of 8. The order of the two numbers does not matter.

1. Count in 8s, 8 times. Each count adds one more group of 8.
   8, 16, 24, 32, 40, 48, 56, 64
2. The last number we said is the answer. We counted in equal groups.
   8 × 8 = 64
3. Write the answer. The order of the numbers does not change the answer.
   64

Check. Check: 8 × 8 is also 64.

Watch out. Say the 8 times table in order until you reach the fact you need.

Method. Add column by column, starting with the ones. Carry any ten to the next column on the left.

1. Add the ones column. Add the digits, and the carried 1 if there is one.
   4 + 2 = 6: Write 6. There is nothing to carry.
2. Add the tens column. Add the digits, and the carried 1 if there is one.
   3 + 2 = 5: Write 5. There is nothing to carry.
3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
   2 + 0 = 2: Write 2. There is nothing to carry.
4. Add the thousands column. Add the digits, and the carried 1 if there is one.
   3 + 6 = 9: Write 9. There is nothing to carry.
5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   9256

Check. Check: 9256 - 6022 = 3234.

Watch out. Do not forget the carried 1 in the next column. Write the carried 1 small above the column.

Method. An array shows equal groups. Divide the total by the number of rows to find the number in each row.

1. Read the array. The dots are in equal rows.
   6 rows, 54 dots
2. Share the dots into the rows. Each row has the same number of dots.
   54 ÷ 6 = 9
3. Check with multiplication. Rows × dots in each row gives the total.
   6 × 9 = 54
4. Write the answer. This is the number in each row.
   9

Check. Check: 6 rows of 9 make 54.

Watch out. The number of rows is the divisor. Each row is one equal group.

Method. Round to the nearest 1000: look at the digits to the right of the thousand place.

1. Look at the hundreds, tens and ones together. The digits on the right tell us which way to go.
   the last three digits are 522
2. Decide: 500 or more. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.
   522 is at least 500
3. Round up. Add one more thousand, and the digits to the right become 0.
   9522 rounds up to 10000
4. Write the answer. This is the nearest multiple.
   10000

Check. Check: 10000 is a multiple of 1000, and it is the closest one to 9522.

Watch out. Exactly 500 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Read the minutes from the long hand, then the hour from the short hand.

1. Read the minute hand, the long hand. Each number on the clock face is 5 minutes.
   5 fives = 25 minutes
2. Count the small marks past that number. Each small mark is 1 minute.
   25 + 3 = 28 minutes
3. Read the hour hand, the short hand. It shows the hour that has passed, so read the hour before it.
   the hour is 9
4. Write the time. Write the hour, then a colon, then two digits for the minutes.
   9:28

Check. Check: the hour is 9, and the long hand shows 28 minutes.

Watch out. The short hand must be near the hour, and the long hand counts the minutes. Use two digits for minutes, like 7:05.

Method. Count in 9s to find 9 groups of 8. The order of the two numbers does not matter.

1. Count in 9s, 8 times. Each count adds one more group of 9.
   9, 18, 27, 36, 45, 54, 63, 72
2. The last number we said is the answer. We counted in equal groups.
   9 × 8 = 72
3. Write the answer. The order of the numbers does not change the answer.
   72

Check. Check: 8 × 9 is also 72.

Watch out. Say the 9 times table in order until you reach the fact you need.