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← 3-1 · Count segments between points on a line · Systematically Count Shapes in a Figure

Count segments between points on a line · 5 practice problems

4.G.A.13.OA.D.9

Generated variants — 5

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

Variant 1 answer: 12 line segments

How many line segments are there in the figure below?

The figure is a closed shape made entirely of straight lines. It is a large rectangle whose bottom edge is interrupted by an inward battlement-shaped notch (a crown-like cutout), so the outline runs through a sequence of horizontal and vertical segments. Count every line segment (a straight stretch joining one corner point to the next) along the outline of the figure.

Show solution

Understand

The figure is a rectangle whose bottom edge is cut by an inward battlement notch with 1 raised tab(s). I must count how many straight line segments make up the whole outline.

Givens
  • The figure is a single closed shape made only of straight horizontal and vertical lines.
  • It is a large rectangle with an inward battlement notch cut into the bottom middle.
  • The notch profile contains 1 upward tab(s).
Unknowns
  • The number of straight line segments along the outline.
Constraints
  • A line segment is one straight stretch between two neighboring corner points.
  • Each corner is where the outline changes direction.

Plan

#1 Draw a Diagram · also uses: #2 Make a Systematic List

Trace the outline like a pencil walk and mark every corner where the direction changes; for a closed rectilinear shape the number of segments equals the number of corners.

Execute

#1 Draw a Diagram 4.G.A.1
Start at the top-left corner and walk clockwise. The top edge is one segment and the right edge down is one segment.
22
Each straight side counts as one line segment, the Grade 4 idea of identifying line segments in a figure.
#2 Make a Systematic List 4.G.A.1
Continuing clockwise across the crenellated bottom, each horizontal ledge and vertical tab wall is one segment. The bottom profile uses 9 segments in all.
2+8=102 + 8 = 10
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.
#1 Draw a Diagram 3.OA.D.9
Finally the left edge goes up to the top-left corner, the last segment that closes the outline.
11+1=1211 + 1 = 12
Counting the final closing side is simple addition, and the walk returning to its start confirms the loop is complete.
Answer: 12 line segments

Review

A plain rectangle has 4 segments. Cutting a battlement notch with 1 tab(s) into the bottom adds 8 extra corners, giving 12. Because the shape is closed and rectilinear, segments equal corners.

Each rectangular bump or dip added to a straight edge adds 2 segments; count the steps in the bottom profile and add 2 per step to the base 4, getting the same total.

Standards · min grade 4

  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Identifying each straight stretch of the outline as one line segment between corners.
  • 3.OA.D.9 Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
💡 Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 2 answer: 28 line segments

How many line segments are there in the figure below?

The figure is a closed shape made entirely of straight lines. It is a large rectangle whose bottom edge is interrupted by an inward battlement-shaped notch (a crown-like cutout), so the outline runs through a sequence of horizontal and vertical segments. Count every line segment (a straight stretch joining one corner point to the next) along the outline of the figure.

Show solution

Understand

The figure is a rectangle whose bottom edge is cut by an inward battlement notch with 5 raised tab(s). I must count how many straight line segments make up the whole outline.

Givens
  • The figure is a single closed shape made only of straight horizontal and vertical lines.
  • It is a large rectangle with an inward battlement notch cut into the bottom middle.
  • The notch profile contains 5 upward tab(s).
Unknowns
  • The number of straight line segments along the outline.
Constraints
  • A line segment is one straight stretch between two neighboring corner points.
  • Each corner is where the outline changes direction.

Plan

#1 Draw a Diagram · also uses: #2 Make a Systematic List

Trace the outline like a pencil walk and mark every corner where the direction changes; for a closed rectilinear shape the number of segments equals the number of corners.

Execute

#1 Draw a Diagram 4.G.A.1
Start at the top-left corner and walk clockwise. The top edge is one segment and the right edge down is one segment.
22
Each straight side counts as one line segment, the Grade 4 idea of identifying line segments in a figure.
#2 Make a Systematic List 4.G.A.1
Continuing clockwise across the crenellated bottom, each horizontal ledge and vertical tab wall is one segment. The bottom profile uses 25 segments in all.
2+24=262 + 24 = 26
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.
#1 Draw a Diagram 3.OA.D.9
Finally the left edge goes up to the top-left corner, the last segment that closes the outline.
27+1=2827 + 1 = 28
Counting the final closing side is simple addition, and the walk returning to its start confirms the loop is complete.
Answer: 28 line segments

Review

A plain rectangle has 4 segments. Cutting a battlement notch with 5 tab(s) into the bottom adds 24 extra corners, giving 28. Because the shape is closed and rectilinear, segments equal corners.

Each rectangular bump or dip added to a straight edge adds 2 segments; count the steps in the bottom profile and add 2 per step to the base 4, getting the same total.

Standards · min grade 4

  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Identifying each straight stretch of the outline as one line segment between corners.
  • 3.OA.D.9 Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
💡 Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 3 answer: 20 line segments

How many line segments are there in the figure below?

The figure is a closed shape made entirely of straight lines. It is a large rectangle whose bottom edge is interrupted by an inward battlement-shaped notch (a crown-like cutout), so the outline runs through a sequence of horizontal and vertical segments. Count every line segment (a straight stretch joining one corner point to the next) along the outline of the figure.

Show solution

Understand

The figure is a rectangle whose bottom edge is cut by an inward battlement notch with 3 raised tab(s). I must count how many straight line segments make up the whole outline.

Givens
  • The figure is a single closed shape made only of straight horizontal and vertical lines.
  • It is a large rectangle with an inward battlement notch cut into the bottom middle.
  • The notch profile contains 3 upward tab(s).
Unknowns
  • The number of straight line segments along the outline.
Constraints
  • A line segment is one straight stretch between two neighboring corner points.
  • Each corner is where the outline changes direction.

Plan

#1 Draw a Diagram · also uses: #2 Make a Systematic List

Trace the outline like a pencil walk and mark every corner where the direction changes; for a closed rectilinear shape the number of segments equals the number of corners.

Execute

#1 Draw a Diagram 4.G.A.1
Start at the top-left corner and walk clockwise. The top edge is one segment and the right edge down is one segment.
22
Each straight side counts as one line segment, the Grade 4 idea of identifying line segments in a figure.
#2 Make a Systematic List 4.G.A.1
Continuing clockwise across the crenellated bottom, each horizontal ledge and vertical tab wall is one segment. The bottom profile uses 17 segments in all.
2+16=182 + 16 = 18
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.
#1 Draw a Diagram 3.OA.D.9
Finally the left edge goes up to the top-left corner, the last segment that closes the outline.
19+1=2019 + 1 = 20
Counting the final closing side is simple addition, and the walk returning to its start confirms the loop is complete.
Answer: 20 line segments

Review

A plain rectangle has 4 segments. Cutting a battlement notch with 3 tab(s) into the bottom adds 16 extra corners, giving 20. Because the shape is closed and rectilinear, segments equal corners.

Each rectangular bump or dip added to a straight edge adds 2 segments; count the steps in the bottom profile and add 2 per step to the base 4, getting the same total.

Standards · min grade 4

  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Identifying each straight stretch of the outline as one line segment between corners.
  • 3.OA.D.9 Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
💡 Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 4 answer: 16 line segments

How many line segments are there in the figure below?

The figure is a closed shape made entirely of straight lines. It is a large rectangle whose bottom edge is interrupted by an inward battlement-shaped notch (a crown-like cutout), so the outline runs through a sequence of horizontal and vertical segments. Count every line segment (a straight stretch joining one corner point to the next) along the outline of the figure.

Show solution

Understand

The figure is a rectangle whose bottom edge is cut by an inward battlement notch with 2 raised tab(s). I must count how many straight line segments make up the whole outline.

Givens
  • The figure is a single closed shape made only of straight horizontal and vertical lines.
  • It is a large rectangle with an inward battlement notch cut into the bottom middle.
  • The notch profile contains 2 upward tab(s).
Unknowns
  • The number of straight line segments along the outline.
Constraints
  • A line segment is one straight stretch between two neighboring corner points.
  • Each corner is where the outline changes direction.

Plan

#1 Draw a Diagram · also uses: #2 Make a Systematic List

Trace the outline like a pencil walk and mark every corner where the direction changes; for a closed rectilinear shape the number of segments equals the number of corners.

Execute

#1 Draw a Diagram 4.G.A.1
Start at the top-left corner and walk clockwise. The top edge is one segment and the right edge down is one segment.
22
Each straight side counts as one line segment, the Grade 4 idea of identifying line segments in a figure.
#2 Make a Systematic List 4.G.A.1
Continuing clockwise across the crenellated bottom, each horizontal ledge and vertical tab wall is one segment. The bottom profile uses 13 segments in all.
2+12=142 + 12 = 14
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.
#1 Draw a Diagram 3.OA.D.9
Finally the left edge goes up to the top-left corner, the last segment that closes the outline.
15+1=1615 + 1 = 16
Counting the final closing side is simple addition, and the walk returning to its start confirms the loop is complete.
Answer: 16 line segments

Review

A plain rectangle has 4 segments. Cutting a battlement notch with 2 tab(s) into the bottom adds 12 extra corners, giving 16. Because the shape is closed and rectilinear, segments equal corners.

Each rectangular bump or dip added to a straight edge adds 2 segments; count the steps in the bottom profile and add 2 per step to the base 4, getting the same total.

Standards · min grade 4

  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Identifying each straight stretch of the outline as one line segment between corners.
  • 3.OA.D.9 Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
💡 Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 5 answer: 24 line segments

How many line segments are there in the figure below?

The figure is a closed shape made entirely of straight lines. It is a large rectangle whose bottom edge is interrupted by an inward battlement-shaped notch (a crown-like cutout), so the outline runs through a sequence of horizontal and vertical segments. Count every line segment (a straight stretch joining one corner point to the next) along the outline of the figure.

Show solution

Understand

The figure is a rectangle whose bottom edge is cut by an inward battlement notch with 4 raised tab(s). I must count how many straight line segments make up the whole outline.

Givens
  • The figure is a single closed shape made only of straight horizontal and vertical lines.
  • It is a large rectangle with an inward battlement notch cut into the bottom middle.
  • The notch profile contains 4 upward tab(s).
Unknowns
  • The number of straight line segments along the outline.
Constraints
  • A line segment is one straight stretch between two neighboring corner points.
  • Each corner is where the outline changes direction.

Plan

#1 Draw a Diagram · also uses: #2 Make a Systematic List

Trace the outline like a pencil walk and mark every corner where the direction changes; for a closed rectilinear shape the number of segments equals the number of corners.

Execute

#1 Draw a Diagram 4.G.A.1
Start at the top-left corner and walk clockwise. The top edge is one segment and the right edge down is one segment.
22
Each straight side counts as one line segment, the Grade 4 idea of identifying line segments in a figure.
#2 Make a Systematic List 4.G.A.1
Continuing clockwise across the crenellated bottom, each horizontal ledge and vertical tab wall is one segment. The bottom profile uses 21 segments in all.
2+20=222 + 20 = 22
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.
#1 Draw a Diagram 3.OA.D.9
Finally the left edge goes up to the top-left corner, the last segment that closes the outline.
23+1=2423 + 1 = 24
Counting the final closing side is simple addition, and the walk returning to its start confirms the loop is complete.
Answer: 24 line segments

Review

A plain rectangle has 4 segments. Cutting a battlement notch with 4 tab(s) into the bottom adds 20 extra corners, giving 24. Because the shape is closed and rectilinear, segments equal corners.

Each rectangular bump or dip added to a straight edge adds 2 segments; count the steps in the bottom profile and add 2 per step to the base 4, getting the same total.

Standards · min grade 4

  • 4.G.A.1 Draw points, lines, line segments, rays, angles, and identify in figures — Identifying each straight stretch of the outline as one line segment between corners.
  • 3.OA.D.9 Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
💡 Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!