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Problem of the Week
Problem A
Crafty Construction

Sam is making square picture frames using popsicle sticks. He has one box of \(50\) popsicle sticks and wants to make \(13\) frames.

  1. Sam plans to make individual frames using four popsicle sticks as shown.

    Two sticks are placed vertically and spaced about one stick length apart. Two more sticks are placed horizontally on top to form a square shape.

    Will he have enough popsicle sticks to make \(13\) frames? Justify your answer.

  2. Sam changes his mind and instead of individual frames, he decides to connect the frames in a row. He starts by making a frame using four popsicle sticks, and then uses three popsicle sticks to create another frame attached to this frame. He then uses three more popsicle sticks to create another frame attached to the first two frames, so he has three connected frames, as shown.

    A shape that looks like three squares placed side by side. Four sticks are placed vertically with space in between them. Three sticks are placed horizontally in a line along the top of the vertical sticks and three sticks are placed in a line along the bottom of the vertical sticks.

    Sam plans to continue this process, using three more popsicle sticks for each frame, until he has \(13\) frames connected in a row. Will he have enough popsicle sticks to make \(13\) frames? Justify your answer.

  3. Can you draw another layout of the \(13\) frames that Sam could have built using at most \(50\) popsicle sticks? How many popsicle sticks does your layout use?

  4. Can you draw a layout of the \(13\) frames that uses fewer than \(35\) popsicle sticks?

Themes: Algebra, Number Sense