Year 6 Maths reasoning (SATs): Paper B

Method. Write each part in its column.

1. Millions. Eight million is 8,000,000.
   8,000,000
2. Thousands. Sixty thousand is 60,000.
   60,000
3. Units. Three hundred and four is 304.
   304
4. Write the answer.
   8,060,304

Check. 8,000,000 + 60,000 + 304 = 8,060,304. ✓

Method. Look at the tens digit.

1. Tens digit. The tens digit is 5, so round up.
   5
2. Round. 4,600 + 100 = 4,700.
   4,700
3. Write the answer.
   4,700

Check. 4,700 is the nearest hundred. ✓

Method. Subtracting a negative is adding.

1. Rewrite. -12 + 20 + 5.
   -12 + 20 + 5
2. Work out. -12 + 20 = 8, then 8 + 5 = 13.
   13
3. Write the answer.
   13

Check. 13 - 5 = 8, and 8 + 12 = 20. ✓

Method. Brackets first, then divide and multiply, then add.

1. Brackets. 9 + 3 = 12.
   12
2. Divide and multiply. 12 / 4 = 3 and 2 x 5 = 10.
   3 and 10
3. Add. 3 + 10 = 13.
   13
4. Write the answer.
   13

Check. 3 + 10 = 13. ✓

Method. List the pairs that multiply to 36.

1. Pairs. 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6.
   4 x 9
2. Check the sum. 4 + 9 = 13.
   4 and 9
3. Write the answer.
   4 and 9

Check. 4 x 9 = 36 and 4 + 9 = 13. ✓

Method. The 5 is in the tenths place, so the decimal is 5 tenths.

1. Write as tenths. 2.5 = 2 and 5 tenths.
   2 5/10
2. Simplify. 5/10 = 1/2.
   2 1/2
3. Write the answer.
   2 1/2

Check. 2 1/2 = 2.5. ✓

Method. Add the whole numbers, then the fractions.

1. Whole numbers. 2 + 1 = 3.
   3
2. Fractions. 1/3 + 5/6 = 2/6 + 5/6 = 7/6 = 1 1/6.
   1 1/6
3. Total. 3 + 1 1/6 = 4 1/6.
   4 1/6
4. Write the answer.
   4 1/6

Check. 4 1/6 = 25/6. ✓

Method. Multiply the top by 5.

1. Multiply the top. 5 x 2 = 10, so 10/3.
   10/3
2. Mixed number. 10 / 3 = 3 remainder 1, so 3 1/3.
   3 1/3
3. Write the answer.
   3 1/3

Check. 3 x 3 + 1 = 10. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. 3/8 = 0.375 and 0.3750 is the same, and 37.5% is 0.375 as a percentage.
   0.375, 0.3750, 37.5%
3. Leave the others unticked. These do not match.
   0.38, 3.8% are not ticked
4. Write the answer.
   0.375, 0.3750, 37.5%

Check. Each ticked option is true. ✓

Watch out. 0.38 and 3.8% are not equal to 3/8.

Method. Find one part from the pears, then multiply.

1. One part. 40 / 8 = 5.
   5
2. Apples. 5 x 5 = 25.
   25
3. Write the answer.
   25

Check. 25 : 40 = 5 : 8. ✓

Method. Divide the new length by the original length.

1. Divide. 30 / 12 = 2.5.
   2.5
2. Write the answer.
   2.5

Check. 12 x 2.5 = 30. ✓

Method. Find the total parts, then one part.

1. Total parts. 3 + 4 + 7 = 14 parts.
   14
2. One part. 280 / 14 = 20 sweets.
   20
3. Largest share. 7 x 20 = 140 sweets.
   140
4. Write the answer.
   140

Check. 60 + 80 + 140 = 280. ✓

Method. Find the price of one pen, then multiply by 4.

1. One pen. 8.40 / 6 = 1.40 pounds.
   1.40
2. Four pens. 1.40 x 4 = 5.60 pounds.
   5.60
3. Write the answer.
   5.60

Check. 5.60 / 4 = 1.40. ✓

Method. Change the hours to minutes, then add.

1. Hours. 2 x 60 = 120.
   120
2. Add. 120 + 45 = 165.
   165
3. Write the answer.
   165

Check. 165 / 60 = 2.75. ✓

Method. Work out how many lots of 5 miles there are.

1. Lots of 5 miles. 25 / 5 = 5 lots.
   5
2. Kilometres. 5 x 8 = 40 km.
   40 km
3. Write the answer.
   40

Check. 5 x 8 = 40. ✓

Method. Area = base x perpendicular height.

1. Multiply. 14 x 6 = 84.
   84 cm²
2. Write the answer.
   84

Check. 84 / 6 = 14. ✓

Method. Work out each perimeter.

1. First. 2 x (3 + 8) = 22 cm.
   22
2. Second. 2 x (4 + 6) = 20 cm.
   20
3. Compare. 20 is smaller than 22, so 4 by 6 is smaller.
   4 cm by 6 cm
4. Write the answer.
   4 cm by 6 cm

Check. 20 < 22. ✓

Method. Angles in a quadrilateral add up to 360 degrees.

1. Add. 110 + 75 + 90 = 275.
   275
2. Subtract. 360 - 275 = 85.
   85
3. Write the answer.
   85

Check. 275 + 85 = 360. ✓

Method. Find the total parts, then one part.

1. Total parts. 1 + 2 + 3 = 6 parts.
   6
2. One part. 180 / 6 = 30 degrees.
   30
3. Largest. 3 x 30 = 90 degrees.
   90
4. Write the answer.
   90

Check. 30 + 60 + 90 = 180. ✓

Method. Test each choice against the question.

1. Read what the question asks. Decide what the answer must do or show.
2. Test the choice. A rectangle does not have to have four equal sides, so it is not always a square.
   no fits
3. Reject the other choices. Only a rectangle with equal sides is a square.
   yes do not fit
4. Write the answer.
   no

Check. no is the one that fits. ✓

Method. Divide 360 by the number of sides.

1. Divide. 360 / 10 = 36.
   36
2. Write the answer.
   36

Check. 36 x 10 = 360. ✓

Method. Halve the sums of the coordinates.

1. x. (-3 + 5) / 2 = 1.
   1
2. y. (1 + (-3)) / 2 = -1.
   -1
3. Write the answer.
   (1, -1)

Check. (1, -1) is halfway between the corners. ✓

Method. Use x becomes 2 x 2 - x, and y stays the same.

1. (1, 2). 2 x 2 - 1 = 3, so (3, 2).
   (3, 2)
2. (4, 2). 4 - 4 = 0, so (0, 2).
   (0, 2)
3. (4, 5). So (0, 5).
   (0, 5)
4. Write the answer.
   (3, 2), (0, 2), (0, 5)

Check. Each point is the same distance from x = 2. ✓

Method. Anticlockwise goes back one place each quarter turn.

1. Order. Clockwise: North, East, South, West.
   South is 2
2. Three quarter turns back. South -> East -> North -> West.
   West
3. Write the answer.
   West

Check. Three steps back from South is West. ✓

Method. Check whether 102 - 2 is a multiple of 5.

1. Subtract 2. 102 - 2 = 100.
   100
2. Divide. 100 / 5 = 20, a whole number, so n = 20.
   n = 20
3. Write the answer.
   yes

Check. 5 x 20 + 2 = 102. ✓

Method. Divide both sides by 3 first.

1. Divide by 3. x + 4 = 27 / 3 = 9.
   x + 4 = 9
2. Subtract 4. x = 9 - 4 = 5.
   5
3. Write the answer.
   5

Check. 3 x (5 + 4) = 27. ✓

Method. Substitute n = 7, then multiply before you subtract.

1. Substitute. 5 x 7 - 3.
   35 - 3
2. Work out. 35 - 3 = 32.
   32
3. Write the answer.
   32

Check. 35 - 3 = 32. ✓

Method. List the pairs in order, starting with a = 1.

1. List. 1 + 14, 2 + 13, 3 + 12, 4 + 11, 5 + 10, 6 + 9, 7 + 8.
   7 pairs
2. Count. There are 7 pairs.
   7
3. Write the answer.
   7

Check. Each pair adds to 15. ✓

Method. The total is 5 x 9 = 45.

1. Total. 5 x 9 = 45.
   45
2. Subtract the four known values. 7 + 10 + 12 + 8 = 37, so the fifth is 45 - 37 = 8.
   8
3. Write the answer.
   8

Check. 37 + 8 = 45. ✓

Method. Order the values first; with six values, take halfway between the middle two.

1. Order. 2, 4, 5, 7, 9, 12.
   2, 4, 5, 7, 9, 12
2. Middle two. The middle two are 5 and 7, so the median is (5 + 7) / 2 = 6.
   6
3. Write the answer.
   6

Check. 5 and 7 average to 6. ✓

Method. Change = later reading - earlier reading.

1. Subtract. 9 - 14 = -5.
   -5
2. Write the answer.
   -5

Check. 14 + (-5) = 9. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. February 18 is more than January 12, and February is the largest value. The other statements are not shown by the chart.
   Sales were higher in February than January, The most sales were in February
3. Leave the others unticked. These do not match.
   Sales were higher in March than February, Sales will rise next month are not ticked
4. Write the answer.
   Sales were higher in February than January, The most sales were in February

Check. Each ticked option is true. ✓

Watch out. March 15 is less than February 18, and the chart does not show what happens next month.

Method. Work out the cost first, then take it away.

1. Cost. 4 x 4.75 = 19 pounds.
   19
2. Left. 30 - 19 = 11 pounds.
   11
3. Write the answer.
   11

Check. 19 + 11 = 30. ✓

Method. Change 2 hours to minutes first.

1. Minutes. 2 hours = 120 minutes.
   120
2. Fraction. 120 / 5 = 24, then 24 x 3 = 72 minutes.
   72
3. Write the answer.
   72

Check. 72 / 120 = 3/5. ✓

Method. Work out each amount, then compare.

1. 3/4 of 20. 20 / 4 = 5, then 5 x 3 = 15.
   15
2. 60% of 20. 20 / 100 = 0.2, then 0.2 x 60 = 12.
   12
3. Compare. 15 is more than 12.
   3/4 is more
4. Write the answer.
   3/4 of 20 is 15 pounds, and 60% of 20 is 12 pounds, so 3/4 is more.

Check. 15 > 12. ✓

Method. Test each choice against the question.

1. Read what the question asks. Decide what the answer must do or show.
2. Test the choice. A square has all sides equal and all angles equal, so it is regular.
   a square fits
3. Reject the other choices. A rectangle and a rhombus do not have all their angles equal (or all sides equal, for the rectangle).
   a rectangle and a rhombus do not fit
4. Write the answer.
   a square

Check. a square is the one that fits. ✓

Method. Take the apex from 180, then halve.

1. Total of base angles. 180 - 40 = 140.
   140
2. Each. 140 / 2 = 70.
   70
3. Write the answer.
   70

Check. 40 + 70 + 70 = 180. ✓

Method. Do one step at a time.

1. Reflect. The reflection in the x-axis changes the sign of y: (3, 2).
   (3, 2)
2. Translate. Add 1 to x: (4, 2).
   (4, 2)
3. Write the answer.
   (4, 2)

Check. (3 + 1, 2) = (4, 2). ✓

Method. Multiply by 100.

1. Multiply. 2.25 x 100 = 225.
   225 cm
2. Write the answer.
   225 cm

Check. 225 / 100 = 2.25. ✓

Method. Write 0.4 as tenths, then simplify.

1. Tenths. 0.4 = 4/10.
   4/10
2. Simplify. Divide the top and bottom by 2: 2/5.
   2/5
3. Write the answer.
   2/5

Check. 2/5 = 0.4. ✓