Fractions require equal partitioning of the whole
3.NF.A.13.G.A.2
Generated variants — 10
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 32 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 32 equal cells (a 8-by-4 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 32 equal-size cells (8 columns by 4 rows)
- Each cell is the same size, so each cell is 1/32 of the whole
- From the figure, the shaded region covers 7 of the 8 columns across the top 3 of the 4 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 11 of the 32 cells, so the shaded part is 21 of 32, matching the picture.
Change focus to the complement (tool 16): 11 cells are unshaded, so 11/32 is unshaded and the shaded part is 1 - 11/32 = 21/32.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 21/32 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 32 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 24 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 24 equal cells (a 6-by-4 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 24 equal-size cells (6 columns by 4 rows)
- Each cell is the same size, so each cell is 1/24 of the whole
- From the figure, the shaded region covers 5 of the 6 columns across the top 3 of the 4 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 9 of the 24 cells, so the shaded part is 15 of 24, matching the picture.
Change focus to the complement (tool 16): 9 cells are unshaded, so 9/24 is unshaded and the shaded part is 1 - 9/24 = 15/24.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 5/8 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 24 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 8 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 8 equal cells (a 4-by-2 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 8 equal-size cells (4 columns by 2 rows)
- Each cell is the same size, so each cell is 1/8 of the whole
- From the figure, the shaded region covers 3 of the 4 columns across the top 1 of the 2 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 5 of the 8 cells, so the shaded part is 3 of 8, matching the picture.
Change focus to the complement (tool 16): 5 cells are unshaded, so 5/8 is unshaded and the shaded part is 1 - 5/8 = 3/8.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 3/8 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 8 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 12 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 12 equal cells (a 6-by-2 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 12 equal-size cells (6 columns by 2 rows)
- Each cell is the same size, so each cell is 1/12 of the whole
- From the figure, the shaded region covers 5 of the 6 columns across the top 1 of the 2 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 7 of the 12 cells, so the shaded part is 5 of 12, matching the picture.
Change focus to the complement (tool 16): 7 cells are unshaded, so 7/12 is unshaded and the shaded part is 1 - 7/12 = 5/12.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 5/12 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 12 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 18 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 18 equal cells (a 9-by-2 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 18 equal-size cells (9 columns by 2 rows)
- Each cell is the same size, so each cell is 1/18 of the whole
- From the figure, the shaded region covers 7 of the 9 columns across the top 1 of the 2 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 11 of the 18 cells, so the shaded part is 7 of 18, matching the picture.
Change focus to the complement (tool 16): 11 cells are unshaded, so 11/18 is unshaded and the shaded part is 1 - 11/18 = 7/18.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 7/18 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 18 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 50 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 50 equal cells (a 10-by-5 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 50 equal-size cells (10 columns by 5 rows)
- Each cell is the same size, so each cell is 1/50 of the whole
- From the figure, the shaded region covers 7 of the 10 columns across the top 4 of the 5 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 22 of the 50 cells, so the shaded part is 28 of 50, matching the picture.
Change focus to the complement (tool 16): 22 cells are unshaded, so 22/50 is unshaded and the shaded part is 1 - 22/50 = 28/50.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 14/25 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 50 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 24 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 24 equal cells (a 8-by-3 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 24 equal-size cells (8 columns by 3 rows)
- Each cell is the same size, so each cell is 1/24 of the whole
- From the figure, the shaded region covers 5 of the 8 columns across the top 2 of the 3 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 14 of the 24 cells, so the shaded part is 10 of 24, matching the picture.
Change focus to the complement (tool 16): 14 cells are unshaded, so 14/24 is unshaded and the shaded part is 1 - 14/24 = 10/24.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 5/12 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 24 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 16 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 16 equal cells (a 4-by-4 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 16 equal-size cells (4 columns by 4 rows)
- Each cell is the same size, so each cell is 1/16 of the whole
- From the figure, the shaded region covers 3 of the 4 columns across the top 3 of the 4 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 7 of the 16 cells, so the shaded part is 9 of 16, matching the picture.
Change focus to the complement (tool 16): 7 cells are unshaded, so 7/16 is unshaded and the shaded part is 1 - 7/16 = 9/16.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 9/16 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 16 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 15 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 15 equal cells (a 5-by-3 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 15 equal-size cells (5 columns by 3 rows)
- Each cell is the same size, so each cell is 1/15 of the whole
- From the figure, the shaded region covers 2 of the 5 columns across the top 2 of the 3 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 11 of the 15 cells, so the shaded part is 4 of 15, matching the picture.
Change focus to the complement (tool 16): 11 cells are unshaded, so 11/15 is unshaded and the shaded part is 1 - 11/15 = 4/15.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 4/15 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 15 cells as equal parts of the rectangle
Write a fraction that tells what part of the whole is shaded.
(Figure) A rectangle has tick marks along each side that divide the whole rectangle into 9 equal-size cells. A portion of the rectangle is shaded.
Show solution
Understand
A rectangle is partitioned by tick marks into 9 equal cells (a 3-by-3 grid). Part of it is shaded. Write, as a fraction, what part of the whole rectangle is shaded.
- The whole rectangle is divided into 9 equal-size cells (3 columns by 3 rows)
- Each cell is the same size, so each cell is 1/9 of the whole
- From the figure, the shaded region covers 2 of the 3 columns across the top 1 of the 3 rows
- The fraction of the whole rectangle that is shaded
- The whole must be divided into equal parts to name a fraction
- The fraction is shaded cells over total cells, written in simplest form
Plan
#1 Draw a Diagram · also uses: #7 Identify Subproblems
The grid is already a diagram of equal parts, so we count shaded cells against the total. Breaking the count into rows and columns (a subproblem) makes the shaded count quick and reliable.
Execute
Review
The unshaded region is 7 of the 9 cells, so the shaded part is 2 of 9, matching the picture.
Change focus to the complement (tool 16): 7 cells are unshaded, so 7/9 is unshaded and the shaded part is 1 - 7/9 = 2/9.
Standards · min grade 3
3.NF.A.1Understand a fraction as quantity formed by parts of a whole — Naming the shaded amount as 2/9 of the whole3.G.A.2Partition shapes into equal parts with equal areas — Recognizing the 9 cells as equal parts of the rectangle