B77 — Mystery Numbers: Part/Whole and Equations

Problem Strings for Fluency and Beyond · Mystery Numbers: Part/Whole and Equations

Teacher notes

This string is like B75.

Notice the numbers chosen and the placement of the unknowns. This string is crafted to generate discussion on partial products and/or partial quotients. This will be the case throughout this string for finding unknowns. The strategies that evolve here are partial products, 28 = 7 x 4 = (7 x 2) + (7 x 4), and /or partial quotients, 28 ÷ 4 = (20 ÷ 4) + (8 ÷ 4).

The string

28 = ( 7 x 2) + (? X 2)
28 ÷ ? = (20 ÷ 4) + (8 ÷ 4)
24 ÷ 6 = ?
? x 4 = 24
? ÷ 4 = (28 ÷ 4) – (4 ÷ 4)
? = (2 x 9) + (2 x 9)
36 ÷ ? = (20 ÷ 4) + (16 ÷ 4)
48 ÷ 8 = (40 ÷ ?) + (8 ÷ 8)
56 ÷ 8 = (? ÷ 8) + (16 ÷ 8)
? ÷ 9 = (90 ÷ 9) – (18 ÷ 9)