How to estimate the quotients

Learners estimate a quotient by swapping the dividend for a nearby multiple of the divisor.

• Find the closest multiple: 86 is close to 90, and 9 divides 90
• Go beyond rounding to tens: 5,087 becomes 5,088 because 24 × 212 = 5,088
• Pick the nearer multiple: 32 is 2 away from 30 and 3 away from 35
• Divide the compatible numbers with long division

Estimating to judge an answer is part of 4.OA.A.3; dividing four- and five-digit numbers by two-digit divisors is 5.NBT.B.6.

Print page one and go through the orange example together, line by line.

• Write the dividend, an arrow, and the compatible number in the left box.
• Set out the long division on the grid, one digit per square.
• Finish with "The estimated quotient is …" as in the example.

The second page repeats this layout for every exercise, with each subtraction step shown in green, so your child can find exactly where a calculation went off track.

• Rounding to the nearest ten out of habit: 24,551 rounds to 24,550, which 14 does not divide; the compatible number is 24,556.
• Choosing the farther multiple: for 32 ÷ 5, 30 is closer than 35.
• Treating the estimate as exact: 5,087 ÷ 24 is really about 211.96.

Note: in question 3 the key writes "24,551 ÷ 14" on its last line; the division shown is 24,556 ÷ 14 = 1,754. Next, compare each estimate with the exact quotient.