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Geometry and Measurement 6-8 / Week 01 / Build Day
6/6
Week 01 · Area by Cutting and Composing

Build Day

Build Day: The real floor
// Cut a shape apart, slide it together, count the squares
⏱ about 20 min

Build Day: The Real Floor

Saturday morning the whole family stands at the garage door with the tape measure.

"Build Day," Raven says. "We find a real floor shape, measure it, and work out its area in square meters."

"The garage is a rectangle," Rocket says. "Too easy. The porch has that slanted end. Trapezoid!"

"What do you notice about where to measure the height?" Raven asks.

"Straight across, not along the slanted edge," Rocket says. "I learned that on Monday."

Nova hovers above the porch, her light making a straight line from one parallel side to the other. "Measure twice," she says.

Rocket's cousin holds the end of the tape. "Then we draw it on grid paper and count squares to check." Nova hums. "Good plan."

  1. Area is the number of unit squares a shape covers, in square units.
  2. A parallelogram slides into a rectangle: area = base × height. The height is the straight-across distance.
  3. A triangle is half of a parallelogram: area = ½ × base × height.
  4. A trapezoid is two triangles with the same height: area = ½ × (top + bottom) × height.
  5. Any polygon decomposes into rectangles and triangles. Find each piece, then add.
◇ MEASURE A REAL FLOOR
Choose a floor, rug or garden bed with straight sides. Sketch its shape in the Blueprint Book.
Cut the sketch into rectangles and triangles. Decide where the base and height of each piece are.
Measure each base and height with the tape measure, in centimeters or meters. Measure twice.
Work out each piece's area and add them. Then draw the shape on grid paper to scale and count squares.
Compare the two answers. If they differ, find the slip together.
For a grown-up
This week your student learned to find areas by cutting shapes into rectangles and triangles.
Ask them why a triangle's area has a half in it. The answer should mention two triangles making a parallelogram.
Hold the tape measure end and keep it off walkways. Let it roll back slowly so it does not snap.
Safety first
A grown-up holds the tape measure. Let it rewind slowly, and keep fingers clear of the end.
Shoes on in the garage. Measure around furniture, never by climbing on it.
BUILD DAY CHECK
  • Read the question.
  • Tap your answer.
A trapezoid with base 3 m, top 2 m and height 2 mThe porch is a trapezoid: top 2 m, bottom 3 m, height 2 m. What is its area in square meters?
A parallelogram with base 4 m and height 3 mA rug is a parallelogram with base 4 m and height 3 m. What is its area in square meters?
A triangle with base 6 m and height 4 mA garden bed is a triangle with base 6 m and height 4 m. What is its area in square meters?
A garage floor is a 6 by 5 rectangle with a 2 by 3 rectangle added on. What is its area in square meters?
Build Day checkTrue or false?
The height of a trapezoid is measured straight across between the parallel sides.?
Counting squares on a scale drawing can check a computed area.?
A rectangle's area is half of base × height.?
WHY THIS EXERCISEMeasuring a real floor shows that the paper shapes stand for real cardboard, real rooms and real tape.
Draw the floor shape your family measured, with its cut lines, bases and heights labeled.

Great measuring, crew. Next week: a taped grid on the floor, string walls, and polygons from their coordinates.

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