← 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 medium 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
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Trace the outer frame

#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.

2Walk along the notched bottom

#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+9=112 + 9 = 11
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.

3Close the loop with the left edge

#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
4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.
💡Takeaway. Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 2 medium 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
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Trace the outer frame

#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.

2Walk along the notched bottom

#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+25=272 + 25 = 27
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.

3Close the loop with the left edge

#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
4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.
💡Takeaway. Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 3 medium 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
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Trace the outer frame

#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.

2Walk along the notched bottom

#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+17=192 + 17 = 19
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.

3Close the loop with the left edge

#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
4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.
💡Takeaway. Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 4 medium 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
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Trace the outer frame

#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.

2Walk along the notched bottom

#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+13=152 + 13 = 15
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.

3Close the loop with the left edge

#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
4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.
💡Takeaway. Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!
Variant 5 medium 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
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Trace the outer frame

#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.

2Walk along the notched bottom

#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+21=232 + 21 = 23
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.

3Close the loop with the left edge

#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
4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.
💡Takeaway. Walk the outline like a pencil and count every time it turns -- each straight stretch between turns is one line segment!