Area & Perimeter
Find the perimeter of a rectangle with length 5 units and width 3 units.
Perimeter = 2(5+3)=16 units.
Show or name where 1/4 goes on a number line between 0 and 1.
1/4 one-quarter of the way from 0 to 1.
What is 6X7?
42
There are 4 bags with 6 apples each. How many apples total?
24 apples.
How many square unit tiles cover a rectangle 4 units by 2 units? What is its area?
8 square units.
A rectangle has a perimeter 20 units. If one side is 6 units, what is the length of the opposite side?
Perimeter 20 so sum of two adjacent sides = 10. If one side is 6, the other side = 4.
Mark and label the point for ¾ on a number line divided into fourths. How many fourths make the whole?
3/4 is at the third mark when dividing 0–1 into 4 equal parts; 4 fourths = 1.
Find the unknown: 8X___= 56.
A ribbon is 90 cm long. It is cut into 9 equal pieces. How long is each piece?
10 cm each.
Use multiplication to find the area of a rectangle 6 units by 3 units.
18 square units.
Draw or describe two different rectangles that each have perimeter 16 units but different areas. (Give side lengths.)
Examples: 1×7 and 2×6 give perimeter 16 (1+7=8→2×8=16; 2+6=8→2×8=16) Areas 7 and 12.
Which fraction is larger: 2/3 or 3/4? Explain by reasoning about size or using a number line.
3/4 is larger because 3/4=0.75 and ⅔ approx0.666... or by comparing distances on number line.
A student knows 9X6= 54. Use that to find 54 /9 and explain the relationship.
Decompose a 6 by 5 rectangle into two smaller rectangles and show how adding their areas gives the whole area.
Two students share 24 counters equally. How many does each get? Show division as an unknown-factor problem.
Each gets 12 counters.
Decompose a 6 by 5 rectangle into two smaller rectangles and show how adding their areas gives the whole area.
Example: split 6×5 into 6×2 and 6×3 → areas 12 and 18 → total 30.
A student makes a rectilinear shape by joining two rectangles: one 3 by 4 and one 3 by 2. What is the total area and the perimeter of the combined shape?
Areas: 3×4=12 and 3×2=6 so total area 18 square units.
Draw a number line from 0 to 2 and show the position of 5/4 and explain why it appears where it does.
5/4 is 1 1/4, so place one whole and one quarter past 1.
Multiply: 7X 80. (Use place-value thinking.)
7 x 80 = 560 (7×8 then add zero).
A classroom used 3 rows of desks with 7 desks in each row. Each desk holds 2 students. How many students can the rows hold total?
3×7=21 desks ×2 students = 42 students.
Explain with a diagram how area models show the distributive property for 3 x (4 + 5).
3x(4+5)=3x9=27 and distributive: 3x4 + 3x5 =12+15=27 (use area model).
A rectangle has length 12 units and area 36 square units. What is the width? Show how area and multiplication explain your answer.
Area = 36 so width = 36/12 = 3 units
Explain why 1/2 equals 2/4 using a number line or a visual fraction model.
Visual: two fourths equal one-half; on number line both mark the same points.
Find a pair of whole numbers between 1 and 12 whose product is 84. Show how you know.
7×12 =84 (or 12×7). Pairs: (7,12), (6,14 not in 1–12), valid within 1–12: 7 and 12.
A baker needs to make 72 muffins placed equally into pans holding 8 muffins each. How many pans are needed? Show your reasoning and check using multiplication.
2 ÷ 8 = 9 pans.
A rectilinear figure is made of three non-overlapping rectangles: 2×3, 2×4, and 3×3. Find its total area and explain your decomposition.
Areas: 2×3=6, 2×4=8, 3×3=9 → total 23 square units.