Count segments between points on a line
4.G.A.13.OA.D.9
Generated variants — 5
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
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
2Walk along the notched bottom
3Close the loop with the left edge
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.
Standardsmin grade 4
4.G.A.1Draw 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.9Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
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
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
2Walk along the notched bottom
3Close the loop with the left edge
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.
Standardsmin grade 4
4.G.A.1Draw 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.9Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
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
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
2Walk along the notched bottom
3Close the loop with the left edge
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.
Standardsmin grade 4
4.G.A.1Draw 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.9Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
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
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
2Walk along the notched bottom
3Close the loop with the left edge
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.
Standardsmin grade 4
4.G.A.1Draw 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.9Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
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
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
2Walk along the notched bottom
3Close the loop with the left edge
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.
Standardsmin grade 4
4.G.A.1Draw 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.9Identify arithmetic patterns and explain using properties of operations — Adding the segment counts and using the bump-adds-two pattern to check the total.
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