Kentucky Grade 3 Math

How many square units cover the whole figure?

This original drawn figure consists of a 9-by-4 rectangle and a 5-by-3 rectangle attached below its left part. They share an edge but have no overlapping area. Every small grid square represents one square unit. Find the area of the L-shaped figure and explain why multiplying 9 by 7 would count too much.

Build the calculation from the model

The upper part has four rows of nine unit squares, so its area is 9 × 4 = 36 square units. The lower part has three rows of five unit squares, giving 5 × 3 = 15 square units. Because the parts do not overlap, add their areas: 36 + 15 = 51 square units. The shared boundary is an edge, not another row of squares. A supported explanation identifies the parts, connects each product to its rows and columns, and gives the total with square units. Multiplication counts an array efficiently; addition combines the two separate covered regions.

Check an answer that covers the wrong shape

The figure’s full width is nine units and its full height is seven units, but it does not fill that entire rectangle. The upper right edge stops at the step. Multiplying 9 × 7 gives 63 square units and includes the missing 4-by-3 corner. That corner contains twelve square units, so the bounding rectangle has twelve more squares than the actual figure. Students can check the error on the grid instead of simply hearing that the answer is wrong. The difference is about which region has been counted, not a mistake in multiplying nine by seven.

Explain the units and the partition

Area measures the covered surface. The numbers four and three are lengths used to locate rows; the products describe numbers of unit squares. Giving the answer as fifty-one units would lose that distinction. Drawing another valid partition can produce the same area, provided every part belongs to the figure and no part is counted twice. Before adding products, point to each counted region. A line through the shape changes its partition, not the amount of surface it covers. If a drawing lacks equal square units, do not count its marks as though each represents the same area.

Try a related change

Keep the upper rectangle but make the lower attachment four units wide and three units high. Draw the changed outline before calculating: the new lower part has twelve square units, so the total becomes forty-eight. Compare it with the original fifty-one and explain the three-square-unit difference. This transfer checks whether the student connects the dimensions and the covered region. Kentucky’s selected expectation continues onto the next PDF page, where part d addresses adding areas of non-overlapping rectangles. Read the complete standard, its practices, and the local sequence when selecting further area work.

Selected references from Kentucky mathematics standards

The Kentucky mathematics standards directory links the current mathematics document, whose cover identifies adoption in 2019. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. 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 Kentucky’s general summative KSA 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 Kentucky’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.