Idaho Grade 3 Math

Can two rectangles use the same border but cover different areas?

Model two rectangular paper panels: Panel A is 3 units by 5 units; Panel B is 2 units by 6 units. Compare how much unit-length border each needs and how many unit squares cover its face. Keep the linear unit the same for both panels. This is a classroom model with stated dimensions, not a measurement of a real room or plot.

Follow the reasoning

Each rectangle has two sides of each stated length. Adding all four sides gives sixteen units for either perimeter. Covering A with unit squares makes three rows of five, or fifteen square units. Covering B makes two rows of six, or twelve square units. The equal boundary lengths do not make the covered areas equal. Ask the student to trace the edges for perimeter and point to the square units inside for area, then explain why the answers use different units.

Check the explanation

Adding only 3 + 5 counts half of A’s boundary. Multiplying 3 × 5 answers the coverage question, not the border question. A claim that the longer-looking rectangle must have greater area also needs checking: B has the longer side but the smaller area in this pair. Both comparisons depend on the stated dimensions and shared unit. An illustration’s display size alone cannot establish either measurement.

Choose the next comparison

Make a 1-by-7 rectangle on unit-grid paper. Its perimeter is also sixteen units, while its area is seven square units. Compare all three and explain which quantity remains fixed. Next draw two rectangles with area twelve square units, such as 2 by 6 and 3 by 4, and compare their perimeters: sixteen and fourteen units. Discuss how this second pair reverses the fixed quantity. Use the models to explain the relationship rather than memorize a claim that equal area always means equal perimeter or that equal perimeter always means equal area.

Selected references from Idaho’s adopted mathematics document

The Idaho mathematics standards directory links the adopted January 2022 document. These selected references identify the worked activity’s focus. Idaho’s essential-standards guidance helps schools prioritize teaching without revising or removing adopted requirements. Read the full document and confirm the school’s current instructional sequence.

Sources checked October 6, 2026. Read complete requirements, clarifications, limitations, and mathematical practices alongside the school’s sequence. This selected activity is an entry point for instruction.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; open each activity’s directions to understand its timer, tools, question count, and scoring.

Grade 3 is within Idaho’s ISAT mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Read Idaho’s assessment overview.

Keep one example of the student’s reasoning with the practice result. Choose a smaller model, a related question, or a new context according to the difficulty revealed in the worked activity.