Level 4 check

Method. The first column that is different decides which number is greater.

1. Compare the thousands. Look at the first digit on the left.
   8 and 5
2. Compare the thousands. This is the first column that is different.
   8 and 5
3. Write the greater number. The larger digit makes the larger number.
   8475

Check. Check: 8475 > 5663.

Watch out. Do not compare the last digits first.

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 1
2. Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   1 is less than 5
3. Round down. Keep the same tens, and the digits to the right become 0.
   6601 rounds down to 6600
4. Write the answer. This is the nearest multiple.
   6600

Check. Check: 6600 is a multiple of 10, and it is the closest one to 6601.

Watch out. Exactly 5 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 number in parts: thousands, hundreds, then the last two digits.

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

Check. Check: 4000 + 700 + 36 = 4736.

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

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 8
2. Decide: 5 or more. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   8 is at least 5
3. Round up. Add one more ten, and the digits to the right become 0.
   5318 rounds up to 5320
4. Write the answer. This is the nearest multiple.
   5320

Check. Check: 5320 is a multiple of 10, and it is the closest one to 5318.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

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

1. Start at the first number. It is where we begin.
   8656
2. Add 100 each time. Each count moves by the same step.
   8656 + 100 = 8756
3. Add 100 each time. Each count moves by the same step.
   8756 + 100 = 8856
4. Add 100 each time. Each count moves by the same step.
   8856 + 100 = 8956
5. Add 100 each time. Each count moves by the same step.
   8956 + 100 = 9056
6. Add 100 each time. Each count moves by the same step.
   9056 + 100 = 9156
7. Write the answer. This is the last number we reached.
   9156

Check. Count the steps back: 9156 - 500 = 8656.

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

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

1. Start at the first number. It is where we begin.
   9477
2. Take 100 each time. Each count moves by the same step.
   9477 - 100 = 9377
3. Take 100 each time. Each count moves by the same step.
   9377 - 100 = 9277
4. Take 100 each time. Each count moves by the same step.
   9277 - 100 = 9177
5. Write the answer. This is the last number we reached.
   9177

Check. Count the steps back: 9177 + 300 = 9477.

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

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

1. Start at the first number. It is where we begin.
   1792
2. Add 1000 each time. Each count moves by the same step.
   1792 + 1000 = 2792
3. Add 1000 each time. Each count moves by the same step.
   2792 + 1000 = 3792
4. Add 1000 each time. Each count moves by the same step.
   3792 + 1000 = 4792
5. Add 1000 each time. Each count moves by the same step.
   4792 + 1000 = 5792
6. Write the answer. This is the last number we reached.
   5792

Check. Count the steps back: 5792 - 4000 = 1792.

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

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.
   2890
2. Take this from the number to find the missing part. 2895 minus the known parts is the gap.
   2895 - 2890 = 5
3. Write the missing part. It is the value of that column.
   5

Check. Check: 2000 + 800 + 90 + 5 = 2895.

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

Method. Change the thousands digit by one; the other digits stay the same.

1. Look at the thousands digit. Only the thousands digit changes when we add or take away 1000.
   6210 has 6 thousands
2. Add one thousand. The thousands digit goes up or down by 1.
   6 + 1 = 7 thousands
3. Write the answer. The hundreds, tens and ones stay the same.
   7210

Check. Check: 7210 and 6210 differ by exactly 1000.

Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 4
2. Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   4 is less than 5
3. Round down. Keep the same tens, and the digits to the right become 0.
   2224 rounds down to 2220
4. Write the answer. This is the nearest multiple.
   2220

Check. Check: 2220 is a multiple of 10, and it is the closest one to 2224.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

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.
   724
2. Take this from the number to find the missing part. 3724 minus the known parts is the gap.
   3724 - 724 = 3000
3. Write the missing part. It is the value of that column.
   3000

Check. Check: 3000 + 700 + 20 + 4 = 3724.

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

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 992
2. Decide: 500 or more. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.
   992 is at least 500
3. Round up. Add one more thousand, and the digits to the right become 0.
   9992 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 9992.

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. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 3
2. Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   3 is less than 5
3. Round down. Keep the same tens, and the digits to the right become 0.
   4543 rounds down to 4540
4. Write the answer. This is the nearest multiple.
   4540

Check. Check: 4540 is a multiple of 10, and it is the closest one to 4543.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

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.
   2 and 1: 2 is more
2. Write the sign between the numbers. The sign points to the smaller number.
   >

Check. Check: read the sign as words. 2755 is greater than 1479.

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

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 205
2. Decide: less than 500. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.
   205 is less than 500
3. Round down. Keep the same thousands, and the digits to the right become 0.
   6205 rounds down to 6000
4. Write the answer. This is the nearest multiple.
   6000

Check. Check: 6000 is a multiple of 1000, and it is the closest one to 6205.

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. Find the step between the numbers, then count on to fill the gap.

1. Find the step size from two numbers that are next to each other. The step is the same all the way along.
   2600 - 2550 = 50
2. Count from the number before the gap. Add the step to get the missing number.
   2550 + 50 = 2600
3. Write the missing number. It fits the pattern.
   2600

Check. Check: 2600 + 50 is the next number, 2650.

Watch out. Look at the numbers either side of the gap. The step is the same each time.

Method. Change only the column that matches the number you add or take away.

1. Find the thousand digit in 9327. Only the thousand column changes, because 1000 is 1 thousands.
   9327 has 9 thousands
2. Take away 1 thousands. Change that digit only. The other digits stay the same.
   9 - 1 = 8
3. Write the answer. Check that the other digits are the same.
   8327

Check. Check: 8327 + 1000 = 9327.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

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: 0 to 10
4. Subtract the tens column. Take the bottom digit from the top digit.
   10 - 2 = 8
5. Subtract the hundreds column. Take the bottom digit from the top digit.
   9 - 4 = 5
6. Subtract the thousands column. Take the bottom digit from the top digit.
   7 - 3 = 4
7. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   4582

Check. Check: 4582 + 3422 = 8004.

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 9s to find 9 groups of 1. The order of the two numbers does not matter.

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

Check. Check: 1 × 9 is also 9.

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

Method. Division can find how many equal groups fit. Count the groups in steps of the group size.

1. Think of the division: 30 ÷ 3. Each bag holds the same number, so count how many groups of this size there are.
   30 ÷ 3 = ___
2. Count in 3s until you reach 30. Count one bag at a time.
   3, 6, 9, 12, 15, 18, 21, 24, 27, 30
3. Write the answer. This is the number of bags.
   10

Check. Check: 10 bags of 3 is 30.

Watch out. Count the groups, not the number in each group.

Method. Count in 3s to find 3 groups of 1. The order of the two numbers does not matter.

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

Check. Check: 1 × 3 is also 3.

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

Method. Count in 3s to find 3 groups of 8. The order of the two numbers does not matter.

1. Count in 3s, 8 times. Each count adds one more group of 3.
   3, 6, 9, 12, 15, 18, 21, 24
2. The last number we said is the answer. We counted in equal groups.
   3 × 8 = 24
3. Write the answer. The order of the numbers does not change the answer.
   24

Check. Check: 8 × 3 is also 24.

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

Method. Subtract one number from the total. If the check is right, you get the other number.

1. Use the inverse. Subtracting the second number should give back the first.
   8540 - 2332
2. Work out the difference. If the sum is right, this matches the first number.
   8540 - 2332 = 6208
3. Write the check. The check is correct because it gives the first number.
   8540 - 2332 = 6208

Check. Check: 6208 + 2332 = 8540, so the subtraction works both ways.

Watch out. A subtraction can check an addition. Use the inverse operation to check your answer.

Method. Change only the column that matches the number you add or take away.

1. Find the ten digit in 7646. Only the ten column changes, because 40 is 4 tens.
   7646 has 4 tens
2. Add 4 tens. Change that digit only. The other digits stay the same.
   4 + 4 = 8
3. Write the answer. Check that the other digits are the same.
   7686

Check. Check: 7686 - 40 = 7646.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

Method. Grouping: count how many groups of the size you are given can be made from the total.

1. Count in 5s until you reach 35. Each bag takes 5. Count one bag at a time.
   5, 10, 15, 20, 25, 30, 35
2. Count the bags. Each count is one full bag of 5.
   7 bags
3. Write the answer. This is the number of bags.
   7

Check. Check: 7 × 5 = 35.

Watch out. In grouping, you are given the size of each group and you find the number of groups.

Method. Swap the numbers round. The total stays the same.

1. Work out the first fact: 3 × 4. This tells us the total.
   3 × 4 = 12
2. Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.
   4 × 3 = 12
3. Write the missing number. It is the number that moved to the front.
   4

Check. Check: 3 × 4 and 4 × 3 are both 12.

Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.

Method. Grouping: count how many groups of the size you are given can be made from the total.

1. Count in 4s until you reach 32. Each bag takes 4. Count one bag at a time.
   4, 8, 12, 16, 20, 24, 28, 32
2. Count the bags. Each count is one full bag of 4.
   8 bags
3. Write the answer. This is the number of bags.
   8

Check. Check: 8 × 4 = 32.

Watch out. In grouping, you are given the size of each group and you find the number of groups.

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.
   7 + 3 = 10: Write 0 and carry 1 to the next column.
2. Add the tens column. Add the digits, and the carried 1 if there is one.
   2 + 8 + 1 = 11: Write 1 and carry 1 to the next column.
3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
   2 + 2 + 1 = 5: Write 5. There is nothing to carry.
4. Add the thousands column. Add the digits, and the carried 1 if there is one.
   6 + 2 = 8: Write 8. There is nothing to carry.
5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   8510

Check. Check: 8510 - 2283 = 6227.

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.
   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. Use the 9 pattern. The digits of each answer add to 9.

1. Find the tens digit. Take 1 from the number you multiply by 9.
   4 - 1 = 3
2. Find the ones digit. The two digits must add to 9.
   9 - 3 = 6
3. Write the answer. Put the tens digit and the ones digit together.
   36

Check. Check: 3 + 6 = 9, and 36 is 9 × 4.

Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.

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

1. Count in 9s, 9 times. Each count adds one more group of 9.
   9, 18, 27, 36, 45, 54, 63, 72, 81
2. The last number we said is the answer. We counted in equal groups.
   9 × 9 = 81
3. Write the answer. The order of the numbers does not change the answer.
   81

Check. Check: 9 × 9 is also 81.

Watch out. Say the 9 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.
   3 + 5 = 8: Write 8. There is nothing to carry.
2. Add the tens column. Add the digits, and the carried 1 if there is one.
   4 + 6 = 10: Write 0 and carry 1 to the next column.
3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
   2 + 4 + 1 = 7: Write 7. There is nothing to carry.
4. Add the thousands column. Add the digits, and the carried 1 if there is one.
   5 + 1 = 6: Write 6. There is nothing to carry.
5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   6708

Check. Check: 6708 - 1465 = 5243.

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

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

1. Think about the calendar month of August. Months have 28, 30 or 31 days. February is left out here.
   August has 31 days
2. Count the days. Count all the days in the month.
   31 days
3. Write the answer. This is the number of days in the month.
   31

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. 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.
   12:34
2. Add the duration. Add 1 hour 45 minutes to the start time.
   12:34 + 1 hour 45 minutes = 14:19
3. Write the finish time. Use two digits for the hour and minutes.
   14:19

Check. Check: 1 hour 45 minutes before 14:19 is 12:34.

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

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.
   10 equal parts
2. Find the number of parts chosen. These are the parts we count on the top.
   7 parts
3. Write the fraction. Parts chosen over total parts.
   7/10

Check. Check: 7 of the 10 parts is 7/10.

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

Method. Count on from the start time to the end time, in steps: minutes to the next hour, whole hours, then minutes.

1. Count the whole hours up to 08:00. Each full hour is 60 minutes.
   2 hours = 120 minutes
2. Count the minutes from 08:00 to 08:51. Count on the last minutes.
   51 minutes
3. Add the parts. Add the minutes from each part.
   0 + 120 + 51 = 171
4. Write the duration. Give the answer in hours and minutes.
   2 hours 51 minutes

Check. Check: 06:00 plus 2 hours 51 minutes is 08:51.

Watch out. Count the minutes to the next hour first. Do not subtract the hours and the minutes separately.

Method. Equal bars show equal fractions. Count the equal parts in the second bar.

1. Look at the first bar. It has shaded parts out of equal parts.
   1 shaded of 2
2. Look at the second bar. It has twice as many parts, and twice as many shaded.
   2 shaded of 4
3. Write the missing number. The bottom number is the total parts in the second bar.
   4

Check. Check: 2/4 is the same as 1/2.

Watch out. Doubling the top and bottom gives an equal fraction.

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

1. Find the key words. “shared equally” means the same number in each group.
   455 into 5 groups
2. Choose the operation. Sharing into equal groups is division.
   455 ÷ 5
3. Work out the answer. Ask: how many groups of 5 make 455?
   5 × 91 = 455
4. Write the answer. This is the number for each child.
   91

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

1. Find the key words. “sold” and “left” mean some are taken away.
   3008 and 1710
2. Choose the operation. Taking away is subtraction.
   3008 - 1710
3. Work out the answer. Use exchange if a column is too small.
   3008 - 1710 = 1298
4. Write the answer. This is how many are left.
   1298

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. Find one equal part by dividing by the bottom number, then multiply by the top number.

1. Find one equal part: 260 ÷ 10. The bottom number tells how many equal parts.
   260 ÷ 10 = 26
2. Take 6 parts. The top number tells how many parts are blue.
   6 × 26 = 156
3. Write the answer. This is the number of blue ones.
   156

Check. Check: the parts given and the parts left make 260.

Watch out. A fraction of an amount needs the division first, then the multiplication.

Method. A fraction is the number of shaded parts over the number of equal parts.

1. Count the equal parts in the whole. The bottom number is the number of equal parts.
   2 equal parts
2. Count the shaded parts. The top number is the number of shaded parts.
   1 shaded parts
3. Write the fraction. Shaded parts over the total number of parts.
   1/2

Check. Check: 1 + 1 = 2, so the other parts are not shaded.

Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.

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

1. Find the key words. “sold” and “left” mean some are taken away.
   5533 and 4416
2. Choose the operation. Taking away is subtraction.
   5533 - 4416
3. Work out the answer. Use exchange if a column is too small.
   5533 - 4416 = 1117
4. Write the answer. This is how many are left.
   1117

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. 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. Count on from the start time to the end time, in steps: minutes to the next hour, whole hours, then minutes.

1. Count the minutes to the next hour, 12:00. Count on to the next full hour.
   11:52 to 12:00 is 8 minutes
2. Count the whole hours up to 13:00. Each full hour is 60 minutes.
   1 hour = 60 minutes
3. Count the minutes from 13:00 to 13:17. Count on the last minutes.
   17 minutes
4. Add the parts. Add the minutes from each part.
   8 + 60 + 17 = 85
5. Write the duration. Give the answer in hours and minutes.
   1 hour 25 minutes

Check. Check: 11:52 plus 1 hour 25 minutes is 13:17.

Watch out. Count the minutes to the next hour first. Do not subtract the hours and the minutes separately.

Method. Solve in two steps: multiply, then add. Check the first step before the second.

1. Find the first step. The packs have equal groups, so multiply.
   8 × 21 = 168
2. Find the second step. Add the loose ones to the total of the packs.
   168 + 12 = 180
3. Write the answer. This is the total altogether.
   180

Check. Check: work backwards from your answer to see if the story makes sense.

Watch out. In a two-step problem, do the first step, write the answer, then use it in the second step.

Method. A fraction is the number of shaded parts over the number of equal parts.

1. Count the equal parts in the whole. The bottom number is the number of equal parts.
   3 equal parts
2. Count the shaded parts. The top number is the number of shaded parts.
   2 shaded parts
3. Write the fraction. Shaded parts over the total number of parts.
   2/3

Check. Check: 2 + 1 = 3, so the other parts are not shaded.

Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.

Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.

1. Divide 32 into 4 equal parts. The bottom number tells us how many equal parts to make.
   32 ÷ 4 = 8
2. Take 1 of the parts. The top number tells us how many parts to take.
   1 × 8 = 8
3. Write the answer. This is the fraction of the amount.
   8

Check. Check: 3 parts are left and 24 is left over, so 8 + 24 = 32.

Watch out. Divide by the bottom number first, then multiply by the top number.

Method. There are 60 minutes in an hour. Multiply hours by 60 to change to minutes, or divide minutes by 60 to change to hours.

1. Change 5 hours to minutes. There are 60 minutes in 1 hour.
   5 × 60 = 300
2. Add the minutes. Put the extra minutes on the end.
   300 + 30 = 330
3. Write the answer. This is the total number of minutes.
   330

Check. Check: 5 hours is 300 minutes, and 30 more is 330.

Watch out. Do not write 2 hours 135 minutes. Change every 60 minutes into 1 hour.

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.