Full Grade 3 test

Use multiplication to work out a division. Find the number that, multiplied by the divisor, gives the starting number.

For example, 42 ÷ 7 = 6 because 6 × 7 = 42. The divisor is the number after ÷.

A triangle is classified by its greatest angle.

• If one angle is exactly 90°, the triangle is right-angled.
• If one angle is greater than 90°, the triangle is obtuse-angled.
• If all three angles are less than 90°, the triangle is acute-angled.

Find the greatest given angle and use these conditions to select the triangle type.

Find the missing factor by dividing the product by the known factor. This works whether the question mark is before or after the multiplication sign.

For example, for ? × 7 = 42, calculate 42 ÷ 7 = 6. Put the number back and check by multiplying.

Use multiplication to work out a division. Find the number that, multiplied by the divisor, gives the starting number.

For example, 42 ÷ 7 = 6 because 6 × 7 = 42. The divisor is the number after ÷.

Align equal place values. Zeros mark empty places: do not skip them. Add from the right and carry 1 when needed.

Multiplying any number by 0 gives 0. Each group contributes no objects.

For example, 9 × 0 = 0. This differs from multiplying by 1, which leaves the number unchanged.

Compare digits from the left. If they match, move to the next place. The first differing digits determine which number is greater.

The remainder is what is left after an earlier operation. Find that amount first, then divide it into the specified number of equal groups. The starting amount and the remainder are different.

For three segments to form a triangle, the third side must be shorter than the sum of the two given sides and longer than their difference.

1. Add the given side lengths: a + b. The third side must be shorter than this sum.
2. Find the difference between the given side lengths: |a − b|. The third side must be longer than this difference.
3. Choose the listed length that satisfies both conditions.

Rule: if the third side has length c, then |a − b| < c < a + b.

Find the number of faces on one cube and multiply by the number of cubes. Count all faces, not only those visible.

Any non-zero number divided by itself equals 1. The whole amount makes one group of that same size.

For example, 7 ÷ 7 = 1. Check: 1 × 7 = 7. This rule does not apply to 0 ÷ 0 because division by 0 is not possible.

For each starting number, check the condition and calculate the result. Remember that greater than does not include equality. Compare your result with the pair shown.

The ribbon is divided into 10 equal parts. Divide its whole length by 10 to find one part’s length.

Here the length is a multiple of ten: 70 ÷ 10 = 7. The answer is also in centimetres.

Multiplying by 1 leaves the number unchanged. One group of that size has the starting number of objects.

For example, 24 × 1 = 24. Choose the starting number.

The known amount covers as many equal parts as the numerator, the number above the fraction line.

1. Divide the known amount by the numerator to find one part.
2. Multiply one part by the denominator, the number below the line, to find the whole.

For example, if 6 is 2/3 of the whole, one part is 6 ÷ 2 = 3 and the whole is 3 × 3 = 9.

Every album page has the same number of stickers. Multiply the stickers on one page by the number of pages.

Check that you included all the pages stated in the question.

Start at P. Count the horizontal intervals, then the vertical intervals from that new position. Do not count the starting point as a step.

First find the total number of pencils in all the boxes. Then choose the operation that accounts for the pencils removed. Read the arrows from left to right.

Subtract ones from ones, tens from tens, hundreds from hundreds and thousands from thousands. Start at the rightmost column.

Multiply the first two numbers, then multiply that result by the third.

For example, 2 × 4 × 3 = 8 × 3 = 24. Remember to include the third factor.

Both fractions have the same denominator. This means that each whole is divided into parts of the same size.

1. Compare only the numerators written above the fraction bars.
2. The fraction with the greater numerator is greater because it contains more equal parts.
3. Place > or < between the fractions, with the wide side of the sign facing the greater fraction.

Rule: when denominators are equal, the fraction with the greater numerator is greater.

First add the two kinds of pencils in one pack. Multiply this whole amount by the number of packs. The multiplier applies to the entire sum.

The divisor, the number after ÷, is missing. Find it by dividing the starting number by the result shown.

For example, for 48 ÷ ? = 6, the missing divisor is 48 ÷ 6 = 8. Check that 48 ÷ 8 = 6.

The divisor, the number after ÷, is missing. Find it by dividing the starting number by the result shown.

For example, for 48 ÷ ? = 6, the missing divisor is 48 ÷ 6 = 8. Check that 48 ÷ 8 = 6.

It is easiest to work in cents. Add both prices, then subtract the amount you have. Finally write the result in euros and cents.

Add from the right. If a column total is exactly 10, write 0 there and carry 1 to the left. Remember the final carry.

Find the missing factor by dividing the product by the known factor. This works whether the question mark is before or after the multiplication sign.

For example, for ? × 7 = 42, calculate 42 ÷ 7 = 6. Put the number back and check by multiplying.

First subtract the reserved amount, which is not shared. Divide the remainder by the number of children. Brackets express this order: (total − reserve) ÷ number of children.

“More than on day I” gives a difference, not the whole second-day amount. Add the difference to the first day's amount to find the second day's amount. Then add both days.

Align equal place values and subtract from the right. Check by adding the subtracted number to your difference: you should recover the starting number.

The axis lies between the point and its reflection. The distances on each side are equal. Split the full distance into two equal parts.

Compare the opening with a right angle. Also check whether the sides form one straight line. The lengths of the sides do not determine the angle type.

Divide the total number of biscuits by the number placed on each plate. The quotient is the number of plates needed. Check by multiplying the number of plates by the number of biscuits on each plate: this should give the total number of biscuits.

The dividend, the number before ÷, is missing. Find it by multiplying the divisor by the result.

For example, for ? ÷ 7 = 6, the dividend is 7 × 6 = 42. Check by dividing your number by the given divisor.

Both boxes are shared, so add their contents first. Brackets ensure that the whole sum, not just the second box, is divided by the number of groups.

Add ones to ones, tens to tens, hundreds to hundreds and thousands to thousands. No column needs a carry.