Recognize Equal Area in Differently Shaped Shares
Use identical square grids so tile counts can show area.
About 15 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: A four-by-four square contains sixteen unit tiles.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Equal shares need equal area, but their outlines do not always need the same shape. A square cut vertically into halves gives two rectangles; cut diagonally, it gives two triangles. Each construction gives halves because the paired pieces have equal area and cover the original whole.
Use identical square grids so tile counts can show area. Compare stated piece counts and check that the pieces cover one whole with no overlap. Decide equality from covered area, not only the outside appearance.
Use equal tile counts to compare covered area. Different outlines do not automatically mean different amounts of a whole. Draw or label each piece’s count of equal unit tiles.
- Draw or label each piece’s count of equal unit tiles.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Use identical square grids so tile counts can show area.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
A four-by-four square contains sixteen unit tiles. One share covers eight tiles as a rectangle; another same-size square can be split along its diagonal into equal triangular halves. Both types of half cover half the whole, despite different boundary shapes. Use equal tile counts to compare covered area. Different outlines do not automatically mean different amounts of a whole. Draw or label each piece’s count of equal unit tiles.
Check your reasoning
Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.
Helpful tips
- Use equal tile counts to compare covered area.
- Different outlines do not automatically mean different amounts of a whole.
See the answer and explanation
Yes, their areas are equal
Each piece covers 4 of the 8 equal tiles, so both have half the area.
Take it further
A 12-tile whole has pieces of 4,4,4 tiles with different outlines. Expected: three equal-area thirds.
Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.
More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
Your choices are temporary. Feedback appears after you check all the answers.
Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.
Check the subject sources
These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.