One whole, equal areas
Name one part of squares, rectangles, an L-shape and a triangle.
Explore this lesson →10 practice questions · Optional read aloud · Thinking pad
Let’s understand the idea.
- The entire outlined shape is one whole. Keep that whole fixed while you divide its area into parts.
- Equal areas can have different outlines. The same number of equal-area tiles gives the same area, even when those tiles are arranged differently.
- Every tile must belong to one part. A part may have pieces in different places; the same letter identifies all of them. No area can be lost or counted twice.
- A unit fraction names one equal-area part of the whole. With four equal parts, each has area 1/4 of the whole.
- To create parts, choose a letter and tap tiles. Change a tile's letter to move its area to another part. Undo reverses your last change. Check every part before naming its fraction.
- Small square tiles within one picture all have the same area. Our triangular tiles are also equal in area: they have matching sizes and shapes after a turn or flip. Compare counts within the same whole and tile size.
Something to notice
Observe physical folding/cutting, ungridded partitions, independent explanations and transfer to unfamiliar wholes. These exact tile tasks accept all complete equal-area assignments, including disconnected pieces with a shared part label; connectedness is not a hidden requirement. Congruent triangular tiles justify equal-area counting without requiring a triangle-area formula. Supported whole/part counts are product bounds, not a Grade 3 Geometry denominator restriction. Correct digital partitions do not establish mastery or retention.
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 3 · 3.G · 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.