Division patterns with zeroes

Students spot that the basic fact stays the same while the zeros move along.

• Extend a fact: 16 ÷ 8 = 2, so 160,000 ÷ 8 = 20,000
• Count the zeros the dividend gains: one more zero in, one more zero out
• Find a missing dividend: ? ÷ 3 = 30,000 gives 90,000
• Find a missing divisor: 84,000,000 ÷ ? = 21,000,000 gives 4

Dividing with place-value strategies is 4.NBT.B.6; explaining the pattern in the number of zeros is 5.NBT.A.2.

Print page one. Start with the top half: say the basic fact out loud, then copy the zeros from the dividend to the answer.

• In the bottom half, read each line as a sentence before filling the blank.
• When the quotient is given, multiply back: 300 × 3 = 900, so the divisor is 3.
• Compare each line with the one above it; the pattern is the shortcut.

Page two holds every missing number in red.

• Dropping a zero: 350,000 ÷ 5 is 70,000, not 7,000. Have your child count zeros on both sides.
• Adding a zero to the divisor too: in 900 ÷ ? = 300 the divisor is still 3.
• Mixing up dividend and quotient in the missing-number lines.

Note: line 4 of the right-hand column leaves both blanks empty on page one; the key follows the pattern with 84,000 ÷ 4 = 21,000. Next, try patterns where the divisor ends in zeros, such as 4,800 ÷ 60.