Problem
See which edges are hidden
The dashed edges are the three hiding behind the box: one unknown, one 4 cm and one 7 cm.
A fifth grader can hold a box and notice that the three edges meeting at the far back corner are exactly the ones you cannot see.
5.MD.C.3Visualize Spatial RelationshipsWrite the total of the hidden edges
Add up the three hidden edge lengths and set the sum equal to the given 16 cm.
Putting the three hidden lengths into one addition sentence turns the picture into a number sentence we can finish.
5.OA.A.1Draw A DiagramCombine the known parts
The two known hidden edges are 4 cm and 7 cm, which total 11 cm.
Adding the parts we do know shrinks the problem to a single missing piece.
5.OA.A.1Work BackwardsWork backwards to find the unknown edge
Since the three hidden edges total 16 cm and the two known ones total 11 cm, the remaining edge ○ is 16 − 11.
Subtracting the part we know from the whole hands back the missing length — the heart of working backwards.
5.OA.A.1Work BackwardsThe unknown hidden edge is 16 cm less the 11 cm the two known hidden edges take up.
Why?
The three hidden edges together make up the whole 16 cm, so the unknown one is exactly what is left once the two known ones are set aside.
Why?
Taking the known part off the total undoes the adding that put it into the total in the first place.
The dashed edges are the ones hiding behind the box; add the lengths you know, then subtract from the total to uncover the missing one.
- See which edges are hidden
- Write the total of the hidden edges
- Combine the known parts
- Work backwards to find the unknown edge