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 ÷.

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.

Equal likelihood requires equal counts of the two letters. Find how many tokens the smaller count needs to reach the larger count.

Subtract from the right. If a place does not have enough units, borrow from the left. Use the reduced digit in the next step and borrow again if needed.

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

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

Ten identical boxes contain ten times as many pencils as one box. Multiply the amount in one box by 10.

To multiply a positive whole number by 10, append a 0. For example, 6 × 10 = 60.

You know the total number of balls and how many fit in one box. Divide the total by the amount in one box to find the number of boxes.

Check: number of boxes × balls in one box = all the balls.

Start with the ones. If their sum is at least 10, write the ones digit and carry 1 to the tens column. Include that carried ten.

Calculate the complete set price separately for each shop: multiply the notebook price by the quantity and add the pencil price. Find the difference and write it 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.

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.

First read the operation sign and the second number.

• Multiplying by 0 gives 0.
• Multiplying or dividing by 1 leaves the number unchanged.
• To multiply a positive whole number by 10, append a 0.
• To divide a multiple of 10 by 10, remove its final 0.
• A non-zero number divided by itself gives 1.
• Division by 0 is not possible. For that case, choose the answer saying the operation is invalid.

Sharing the cards equally gives every child the same amount. Divide the total number of cards by the number of children.

Multiplying one child’s amount by the number of children must give all the cards again.

Subtract the known addend from the sum. Put the result in place of the question mark and check the addition.

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

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.

Think about which position makes the greatest difference to a number’s value when its digit changes.

Multiplication adds equal groups. For example, 6 × 7 means six groups of seven.

Use the times table or count 7, 14, 21, 28, 35, 42. You can swap the factors: 6 × 7 = 7 × 6.

Earlier tosses do not change the coin. Compare the two sides in one new toss of a fair coin.

Compare the lengths of all three sides.

• If all three sides are equal, choose equilateral.
• If exactly two sides are equal, choose isosceles.
• If all three sides are different, choose scalene.

The question is about sides, so you do not need to calculate angles.

Look at the centre of the marked dot, not its letter. A point on the circle must lie exactly on the circular line.

To borrow across zeros, find the nearest nonzero digit on the left and reduce it by 1. Intervening zeros become 9 and the place being borrowed into receives 10 units.

Add the subtracted number to the difference to find the starting number. Check by carrying out the subtraction.