Maths for Years 5 and 6

4 Digit + 3 Digit

1.Line up the place values. Ones above ones, hundreds above hundreds etc.
2. Start from ones place value (right side of number).
3. Add these numbers.
4. Write down the ones value.
5. Carry any tens if the value you made was above ten. Put these under the next column.
6. Go onto next place value and add. (Don’t forget to add the carry if you have one)
7. Repeat for the next column until you are finished.

Adding 3 Digit Numbers with 2 Decimal Places

1. Line up the decimal points, including for the answer.
2. Put digits in the correct place value around the decimals.
3. Any blank spaces above other numbers include 0’s if you wish.
4. Add first column on the right (smallest value).
5. Write the value down.
6. Write any carry underneath next place value if needed.
7. Add the next column (including anything carried).
8. Continue for any other digits.

Adding Decimals With Tenths

1. Line up the decimal points, including for the answer.
2. Put digits in the correct position around the decimals.
3. Any blank spaces above other numbers include 0’s if you wish.
4. Add tenths column on the right (smallest value).
5. Write the tenths value down.
6. Write any carry underneath if need.
7. Add the next column (including anything carried).
8. Continue for any other digits.

4 Digit Number - 3 Digit Number

1. Look at the calculation.
2. Write the largest number down.
3. Write the second number down so the places values are in the correct place. E.g. One above ones, tens above tens.
4. Start from the right hand side.
5. Do the top number take away the bottom number.
6. If you cannot do this then exchange.
7. Take a ten from the place value to the left on the top and put this by the number above.
8. Make sure you reduce the place value to the left on the top by one.
9. You may have to exchange more than once.
10. Carry on subtracting to get the answer.

Balanced Missing Number Problem for Addition and Subtraction

1. Look at the complete calculation you have been given on one side.
2. Set this out with accurate place value.
3. Do the calculation remember to exchange if subtracting or carrying when adding.
4. Write down the answer.
5. Look at missing number calculation on the other side.
6. Use the inverse operation and the answer you found from the other side.
7. Do the required calculation.
8. The answer will be the missing number you require

Missing Number Subtraction with 4 Digit Number

1. Look at the calculation.
2. Start from the right hand side.
3. If you have a number in the answer row and another number use the inverse and add the number together.
4. If you have a both numbers in the calculation section then do the subtraction.
5. If you can not do the subtraction then add the one from the exchange. then do the subtraction.
6. In the next column you will need to ensure that you add this exchange back onto this column.
7. If the answer row is larger than the top number then you have also exchanged.

4 Digit x 3 Digit

1. Write numbers in column form with the larger number on top.
2. Multiply the ones place value by the ones of the number below.
3. Record the answer underneath carrying any tens below.
4. Repeat with each digit from right to left always multiplying by the last digit of the second number.
5. Repeat with the next digit on the bottom number, writing this answer under the last. Make sure you put a zero in the ones place value.
6. When this row is done start a new row. Times the hundreds place value. Remember to put two zeros.
Add the two answers together.

Multiplying 2 Decimal Numbers

1. Set out the column multiplication as normal remembering the decimal point and place value.
2. Multiply the tenth first by the numbers above.
3. Remembering the carry and to add them.
3. On a new row add a 0.
4. Multiply the ones place value by the numbers above.
5. Add the two row together.

Multiplying a 3 Digit by a 2 Digit

1. Write numbers in column form with the larger number on top.
2. Multiply the ones place value by the ones of the number below.
3. Record the answer underneath carrying any tens below.
4. Repeat with each digit from right to left always multiplying by the last digit of the second number.
5. Repeat with the next digit on the bottom number, writing this answer under the last. Make sure you put a zero in the ones place value.
6. Add the two answers together.

Whole Number Multiplied by a Decimal Number

1. Set out the numbers in the correct place value. Remember the decimal point.
2. Multiply the tenth by the numbers above.
3. Add the carry when needed.
3. Start a new row and put in a 0.
4. Multiply the one place value by the numbers above.
5. Add the two rows you have made to get the answer.

3 Digit Division (Remainder as Fraction and Decimal)

1. Draw the bus stop.
2. How many of the divisor go into the first digit of the dividend.
3. Write answer above.
4. Any remainders carry onto the next digit of the dividend.
5. Repeat for answer.
Remainder as fraction - put the remainder over the divisor.
Remainder as fraction - at end of answer add a decimal point and then put the remainder next to some zeros under the bus stop. Do this for one more place value.

4 Digit Divided by 1 Digit

1. Draw the bus stop.
2. How many of the divisor go into the first digit of the dividend.
3. Write answer above.
4. Any remainders carry onto the next digit of the dividend.
5. Repeat for answer.
6. If the digit in the dividend is less than the divisor write 0 and carry over everything to the next place value.

4 Digit Division with Missing Number

1. Look at the calculation.
2. See how much of the divisor goes into dividend as normal. Start the problem as normal.
3.If the blank is above the bus stop then see how much the divisor goes into the dividend.
4. Write this number down.
5. If the blank is below the bus stop then times the divisor by the answer above.

Short Division - Remainder as Fraction and Decimal

1. Draw the bus stop.
2. How many of the divisor go into the first digit of the dividend.
3. Write answer above.
4. Any remainders carry onto the next digit of the dividend.
5. Repeat for answer.
Remainder as fraction - put the remainder over the divisor.
Remainder as fraction - at end of answer add a decimal point and then put the remainder next to some zeros under the bus stop. Do this for one more place value.

Long Division - Coin Method

1. Look at the number you are dividing by.
2. To the right hand side write out the coin numbers - 1,2,5,10,20 and 50 if needed.
3. Times the number you are dividing by the coin numbers. Use doubling, halving and multiplying by 10 to help.
4. Draw a grid of 3 columns.
5. Look at the coins to see which number would fit in most and write this down.
6. Do a subtraction to find the remainder.
7. Find which coin fits closest to this number and write this down.
8. Repeat steps 5 & 6.
9. Add the numbers down the left hand side of the grid and remember to include any remainders left.

Adding Fractions - Change Both Denominators

1. Look at both fractions.
2. Times the numerator and denominator of the fraction on the left by the denominator on the right fraction.
3. Times the numerator and denominator of the fraction on the right by the denominator on the left fraction.
4. Add the new numerators.
5. Keep the denominator the same.
6. Simplify if needed.

Adding Fractions - 1 Denominator Change

1. Look for a common multiple of the fractions’ denominators.
2. Multiply one fractions numerator and denominator by the same number so that both fractions have the same denominator.
3. Add the numerators
4. The denominators stay the same.

Adding Mixed Number Fractions

1. Add the wholes.
2. Look at the fractions that are left.
Either... multiply one fraction by a number so both denominators are the same OR... multiply both fractions by the fractions denominator.
3. Add the numerators.
4. Keep the denominators the same.
5. Add this new fraction to the wholes.

Dividing Fractions

1. Swap the denominator and the numerator around the fraction you are dividing by.
2. Multiply the ‘new’ numerators together.
3. Multiply the ‘new’ denominators together.
4. Change from an improper fraction or simplify if needed.

Dividing Fractions by a Whole Number

1. Keep the numerator the same.
2. Times the whole number by the denominator.
3. Simplify if needed.

Multiplying Mixed Number Fractions

1. Multiply the whole numbers together and record this answer.
2. Then change the whole number into a fraction by putting it over one.
3. Multiply the numerators and denominators together.
4. If needed changed this into a mixed number fraction by seeing how many times the denominator goes into the numerator. This is your wholes. Anything left can be put as a fractions.
5. Add this to the answer from when you multiplied the wholes.

Multiplying Fractions

1. Times the numerators together.
2. Times the denominators together.
3. Simplify if needed.

Multiplying Fractions by a Whole Number

1. Change the whole number into a fraction by putting it over one.
2. Multiply the numerators and denominators together.
3. If needed changed this into a mixed number fraction by seeing how many times the denominator goes into the numerator. This is your wholes. Anything left can be put as a fraction.