Reasoning · Grade 5-2 Dice
Problem
There are 7 hidden faces.
Turning a real tower round in your hands settles which faces are hidden far more reliably than guessing from a flat picture, and counting them first tells you how many pip counts the total has to cover.
K.G.B.4Create A Physical RepresentationSplit the tower into one die at a time.
Breaking a stack into single dice is the natural move when the dice do not affect each other's pip counts — each one can then be answered with a fact about one cube.
K.G.B.4Identify SubproblemsThe top die hides 4.
Filling in a missing addend to reach 7 is first-grade work, and it is the only place in the whole problem where an actual printed number is used.
1.OA.B.4Identify SubproblemsEach of the other three hides 7.
The same situation repeating three times is a pattern worth naming: 'a die stacked between two surfaces always hides 7', which spares a solver from ever guessing an unknown face.
K.G.B.4Look For A PatternEach die below the top hides exactly 7, because its hidden faces are one opposite pair.
The face touching the die above and the face touching the die below are opposite each other, and opposite faces of a die always total 7.
The hidden total for the tower is each die's hidden amount added together, so the four contributions simply add.
Adding them gives 25.
Three equal groups of 7 is a multiplication a third grader can also check by adding 7 + 7 + 7, and then one more addition finishes the problem.
3.OA.D.8Identify SubproblemsTurning the dice leaves the answer unchanged.
Checking which given facts the answer actually leans on is a good habit: here it shows the single printed number is enough, so nothing is missing from the problem.
K.G.B.4Look For A PatternAny die squeezed between two things hides its top and bottom, and those always add to 7 — so you never need to know which numbers are hidden!