Find every rectangle
Find all factor pairs while keeping every tile.
Explore this lesson →8 practice questions · Optional read aloud · Thinking pad
Let’s understand the idea.
- Keep the total fixed and arrange every object into equal rows. A factor pair gives the two positive whole-number dimensions of a complete rectangle.
- Try row widths in order. Record each exact pair once: rotating a rectangle repeats a pair, and a square pair appears once.
- If a × b = n, a and b are factors of n, and n is a multiple of each. A number is its own factor; one is a factor of every positive whole number.
- A number is an exact multiple of a positive group size when complete groups leave nothing over. Never count a partial group as another complete group.
- A prime number has exactly two distinct positive factors: 1 and itself. A composite number has more than two. One has only one distinct factor, so it is neither.
Something to notice
These tasks assess complete positive unordered factor-pair inventories, factor/multiple direction, one-digit multiple decisions with exact groups and leftovers, and prime/composite classification justified by a complete pair list. The proof lesson deliberately reuses the pair-construction targets as a scaffold; fresh unaided classification transfer remains separate work. The unassessed fixed-total rectangle experiment supports targets and row widths through 100. Rotations are equivalent; duplicate pairs are invalid. These calculations do not establish unaided oral proof, retained fluency, generalization to unrestricted integers or educational effectiveness. Greatest common factors and least common multiples are not required here.
Try it. Change it. Explain it.
Open the lesson to use its pictures and controls. In How it works, connect the picture to the idea. In Play & discover, change the quantities and notice what stays the same. In Your turn, answer questions and use the explanation to check your reasoning.
You can ask for help, draw on the thinking pad, or listen to the question and answer options. Progress distinguishes independent work from work completed with help.
Let’s try it →Curriculum connection
Grade 4 · 4.OA · US Common Core
This lesson is mapped to these standards. A completed activity is practice evidence, not a claim of mastery. Content is checked against the linked official standards and its mathematical models are tested.