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← 3-2 · Rectangle sides are multiples of the diameter · Radius and Diameter Relationships

Rectangle sides are multiples of the diameter · 10 practice problems

3.OA.C.73.G.A.1

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 25

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the square of side length 10 cm10\ \text{cm} on the right, without any of them overlapping. How many circles can you draw at most?

10 cm 10 cm
Show solution

Understand

Inside a 10 cm by 10 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 10 cm wide and 10 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 10 cm fits 10 / 2 = 5 cells, and down 10 cm fits 10 / 2 = 5 rows of cells.
10÷2=5, 10÷2=510 \div 2 = 5,\ 10 \div 2 = 5
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 5 by 5 grid of cells holds one circle per cell.
5×5=255 \times 5 = 25
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 25

Review

25 circles is a whole number, as it must be for counting objects. The 5 columns times 5 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 5 x 5 = 25 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 2 answer: 6

You want to draw as many circles with radius 2 cm2\ \text{cm} as possible inside the 12 cm12\ \text{cm} by 8 cm8\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

12 cm 8 cm
Show solution

Understand

Inside a 12 cm by 8 cm rectangle, we want to draw as many circles of radius 2 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 12 cm wide and 8 cm tall.
  • Each circle has radius 2 cm, so each circle has diameter 4 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-2 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 4 cm needs a 4 cm by 4 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 2 cm has diameter 2 + 2 = 4 cm, so it fits inside a small 4 cm by 4 cm square cell.
2+2=42 + 2 = 4
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 12 cm fits 12 / 4 = 3 cells, and down 8 cm fits 8 / 4 = 2 rows of cells.
12÷4=3, 8÷4=212 \div 4 = 3,\ 8 \div 4 = 2
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 3 by 2 grid of cells holds one circle per cell.
3×2=63 \times 2 = 6
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 6

Review

6 circles is a whole number, as it must be for counting objects. The 3 columns times 2 rows of 4 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-2 circle spans a 4 cm diameter and needs a 4 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 3 x 2 = 6 total.
💡 Each circle needs a 4 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 3 answer: 12

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the 9 cm9\ \text{cm} by 6 cm6\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

9 cm 6 cm
Show solution

Understand

Inside a 9 cm by 6 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 9 cm wide and 6 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 9 cm fits 9 / 2 = 4 cells, and down 6 cm fits 6 / 2 = 3 rows of cells.
9÷2=4, 6÷2=39 \div 2 = 4,\ 6 \div 2 = 3
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 4 by 3 grid of cells holds one circle per cell.
4×3=124 \times 3 = 12
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 12

Review

12 circles is a whole number, as it must be for counting objects. The 4 columns times 3 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 4 x 3 = 12 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 4 answer: 6

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the 6 cm6\ \text{cm} by 4 cm4\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

6 cm 4 cm
Show solution

Understand

Inside a 6 cm by 4 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 6 cm wide and 4 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 6 cm fits 6 / 2 = 3 cells, and down 4 cm fits 4 / 2 = 2 rows of cells.
6÷2=3, 4÷2=26 \div 2 = 3,\ 4 \div 2 = 2
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 3 by 2 grid of cells holds one circle per cell.
3×2=63 \times 2 = 6
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 6

Review

6 circles is a whole number, as it must be for counting objects. The 3 columns times 2 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 3 x 2 = 6 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 5 answer: 21

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the 14 cm14\ \text{cm} by 6 cm6\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

14 cm 6 cm
Show solution

Understand

Inside a 14 cm by 6 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 14 cm wide and 6 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 14 cm fits 14 / 2 = 7 cells, and down 6 cm fits 6 / 2 = 3 rows of cells.
14÷2=7, 6÷2=314 \div 2 = 7,\ 6 \div 2 = 3
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 7 by 3 grid of cells holds one circle per cell.
7×3=217 \times 3 = 21
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 21

Review

21 circles is a whole number, as it must be for counting objects. The 7 columns times 3 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 7 x 3 = 21 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 6 answer: 4

You want to draw as many circles with radius 2 cm2\ \text{cm} as possible inside the square of side length 8 cm8\ \text{cm} on the right, without any of them overlapping. How many circles can you draw at most?

8 cm 8 cm
Show solution

Understand

Inside a 8 cm by 8 cm rectangle, we want to draw as many circles of radius 2 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 8 cm wide and 8 cm tall.
  • Each circle has radius 2 cm, so each circle has diameter 4 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-2 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 4 cm needs a 4 cm by 4 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 2 cm has diameter 2 + 2 = 4 cm, so it fits inside a small 4 cm by 4 cm square cell.
2+2=42 + 2 = 4
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 8 cm fits 8 / 4 = 2 cells, and down 8 cm fits 8 / 4 = 2 rows of cells.
8÷4=2, 8÷4=28 \div 4 = 2,\ 8 \div 4 = 2
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 2 by 2 grid of cells holds one circle per cell.
2×2=42 \times 2 = 4
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 4

Review

4 circles is a whole number, as it must be for counting objects. The 2 columns times 2 rows of 4 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-2 circle spans a 4 cm diameter and needs a 4 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 2 x 2 = 4 total.
💡 Each circle needs a 4 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 7 answer: 10

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the 10 cm10\ \text{cm} by 4 cm4\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

10 cm 4 cm
Show solution

Understand

Inside a 10 cm by 4 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 10 cm wide and 4 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 10 cm fits 10 / 2 = 5 cells, and down 4 cm fits 4 / 2 = 2 rows of cells.
10÷2=5, 4÷2=210 \div 2 = 5,\ 4 \div 2 = 2
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 5 by 2 grid of cells holds one circle per cell.
5×2=105 \times 2 = 10
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 10

Review

10 circles is a whole number, as it must be for counting objects. The 5 columns times 2 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 5 x 2 = 10 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 8 answer: 9

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the square of side length 6 cm6\ \text{cm} on the right, without any of them overlapping. How many circles can you draw at most?

6 cm 6 cm
Show solution

Understand

Inside a 6 cm by 6 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 6 cm wide and 6 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 6 cm fits 6 / 2 = 3 cells, and down 6 cm fits 6 / 2 = 3 rows of cells.
6÷2=3, 6÷2=36 \div 2 = 3,\ 6 \div 2 = 3
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 3 by 3 grid of cells holds one circle per cell.
3×3=93 \times 3 = 9
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 9

Review

9 circles is a whole number, as it must be for counting objects. The 3 columns times 3 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 3 x 3 = 9 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 9 answer: 2

You want to draw as many circles with radius 5 cm5\ \text{cm} as possible inside the 20 cm20\ \text{cm} by 10 cm10\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

20 cm 10 cm
Show solution

Understand

Inside a 20 cm by 10 cm rectangle, we want to draw as many circles of radius 5 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 20 cm wide and 10 cm tall.
  • Each circle has radius 5 cm, so each circle has diameter 10 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-5 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 10 cm needs a 10 cm by 10 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 5 cm has diameter 5 + 5 = 10 cm, so it fits inside a small 10 cm by 10 cm square cell.
5+5=105 + 5 = 10
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 20 cm fits 20 / 10 = 2 cells, and down 10 cm fits 10 / 10 = 1 rows of cells.
20÷10=2, 10÷10=120 \div 10 = 2,\ 10 \div 10 = 1
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 2 by 1 grid of cells holds one circle per cell.
2×1=22 \times 1 = 2
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 2

Review

2 circles is a whole number, as it must be for counting objects. The 2 columns times 1 rows of 10 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-5 circle spans a 10 cm diameter and needs a 10 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 2 x 1 = 2 total.
💡 Each circle needs a 10 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!
Variant 10 answer: 12

You want to draw as many circles with radius 1 cm1\ \text{cm} as possible inside the 8 cm8\ \text{cm} by 6 cm6\ \text{cm} rectangle on the right, without any of them overlapping. How many circles can you draw at most?

8 cm 6 cm
Show solution

Understand

Inside a 8 cm by 6 cm rectangle, we want to draw as many circles of radius 1 cm as possible without any overlapping. We must find the largest number of circles that fit.

Givens
  • The rectangle is 8 cm wide and 6 cm tall.
  • Each circle has radius 1 cm, so each circle has diameter 2 cm.
  • No two circles may overlap.
Unknowns
  • The greatest number of non-overlapping radius-1 cm circles that fit in the rectangle.
Constraints
  • Each circle of diameter 2 cm needs a 2 cm by 2 cm space.
  • Circles must stay inside the rectangle and may touch but not overlap.

Plan

#1 Draw a Diagram · also uses: #10 Create a Physical Representation#5 Look for a Pattern

Each circle sits neatly in a square cell as wide as its diameter. Drawing the rectangle as a grid of these cells shows how many fit across and down, and the rows-times-columns pattern gives the total.

Execute

#1 Draw a Diagram 3.G.A.1
A circle of radius 1 cm has diameter 1 + 1 = 2 cm, so it fits inside a small 2 cm by 2 cm square cell.
1+1=21 + 1 = 2
The widest part of a circle is its diameter, which equals twice the radius.
#5 Look for a Pattern 3.OA.C.7
Across 8 cm fits 8 / 2 = 4 cells, and down 6 cm fits 6 / 2 = 3 rows of cells.
8÷2=4, 6÷2=38 \div 2 = 4,\ 6 \div 2 = 3
Splitting a length into equal pieces is division within 100.
#10 Create a Physical Representation 3.OA.C.7
A 4 by 3 grid of cells holds one circle per cell.
4×3=124 \times 3 = 12
Equal rows and columns of objects are counted by multiplication, an array model from Grade 3.
Answer: 12

Review

12 circles is a whole number, as it must be for counting objects. The 4 columns times 3 rows of 2 cm cells agree with the grid drawn in the figure.

Lay the circles out physically in a simple grid and count them directly (Tool 10, Create a Physical Representation).

Standards · min grade 3

  • 3.G.A.1 Understand that shapes in different categories share attributes — Knowing each radius-1 circle spans a 2 cm diameter and needs a 2 cm cell.
  • 3.OA.C.7 Fluently multiply and divide within 100 — Computing cells per side and 4 x 3 = 12 total.
💡 Each circle needs a 2 cm box -- count the boxes across and down, then multiply, just like a Grade 3 array!