Practice · Intervals differ on open paths versus closed loops · Sensim Math

Variant 1 easy

Trees are to be planted along a straight road that is $60$ m long, spaced $15$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $15$ m, and the total length of the road is labeled $60$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 60 m road, trees are planted every 15 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 60 m long
Trees are spaced 15 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 15 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 15 m gaps fit: 60 / 15 = 4 gaps.

60 \div 15 = 4 \text{ gaps}

Each 15 m piece is one gap, so dividing the total length by 15 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 4 + 1 = 5.

4 + 1 = 5 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 5 trees

4 · Reviewdoes it hold up?

Check with the spacing: 5 trees make 4 gaps of 15 m, which is 4 x 15 = 60 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 2 easy

Trees are to be planted along a straight road that is $84$ m long, spaced $12$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $12$ m, and the total length of the road is labeled $84$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 84 m road, trees are planted every 12 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 84 m long
Trees are spaced 12 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 12 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 12 m gaps fit: 84 / 12 = 7 gaps.

84 \div 12 = 7 \text{ gaps}

Each 12 m piece is one gap, so dividing the total length by 12 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 7 + 1 = 8.

7 + 1 = 8 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 8 trees

4 · Reviewdoes it hold up?

Check with the spacing: 8 trees make 7 gaps of 12 m, which is 7 x 12 = 84 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 3 easy

Trees are to be planted along a straight road that is $90$ m long, spaced $9$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $9$ m, and the total length of the road is labeled $90$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 90 m road, trees are planted every 9 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 90 m long
Trees are spaced 9 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 9 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 9 m gaps fit: 90 / 9 = 10 gaps.

90 \div 9 = 10 \text{ gaps}

Each 9 m piece is one gap, so dividing the total length by 9 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 10 + 1 = 11.

10 + 1 = 11 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 11 trees

4 · Reviewdoes it hold up?

Check with the spacing: 11 trees make 10 gaps of 9 m, which is 10 x 9 = 90 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 4 medium

Trees are to be planted along a straight road that is $100$ m long, spaced $10$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $10$ m, and the total length of the road is labeled $100$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 100 m road, trees are planted every 10 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 100 m long
Trees are spaced 10 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 10 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 10 m gaps fit: 100 / 10 = 10 gaps.

100 \div 10 = 10 \text{ gaps}

Each 10 m piece is one gap, so dividing the total length by 10 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 10 + 1 = 11.

10 + 1 = 11 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 11 trees

4 · Reviewdoes it hold up?

Check with the spacing: 11 trees make 10 gaps of 10 m, which is 10 x 10 = 100 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 5 medium

Trees are to be planted along a straight road that is $200$ m long, spaced $20$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $20$ m, and the total length of the road is labeled $200$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 200 m road, trees are planted every 20 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 200 m long
Trees are spaced 20 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 20 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 20 m gaps fit: 200 / 20 = 10 gaps.

200 \div 20 = 10 \text{ gaps}

Each 20 m piece is one gap, so dividing the total length by 20 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 10 + 1 = 11.

10 + 1 = 11 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 11 trees

4 · Reviewdoes it hold up?

Check with the spacing: 11 trees make 10 gaps of 20 m, which is 10 x 20 = 200 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 6 medium

Trees are to be planted along a straight road that is $250$ m long, spaced $25$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $25$ m, and the total length of the road is labeled $250$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 250 m road, trees are planted every 25 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 250 m long
Trees are spaced 25 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 25 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 25 m gaps fit: 250 / 25 = 10 gaps.

250 \div 25 = 10 \text{ gaps}

Each 25 m piece is one gap, so dividing the total length by 25 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 10 + 1 = 11.

10 + 1 = 11 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 11 trees

4 · Reviewdoes it hold up?

Check with the spacing: 11 trees make 10 gaps of 25 m, which is 10 x 25 = 250 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 7 medium

Trees are to be planted along a straight road that is $300$ m long, spaced $50$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $50$ m, and the total length of the road is labeled $300$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 300 m road, trees are planted every 50 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 300 m long
Trees are spaced 50 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 50 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 50 m gaps fit: 300 / 50 = 6 gaps.

300 \div 50 = 6 \text{ gaps}

Each 50 m piece is one gap, so dividing the total length by 50 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 6 + 1 = 7.

6 + 1 = 7 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 7 trees

4 · Reviewdoes it hold up?

Check with the spacing: 7 trees make 6 gaps of 50 m, which is 6 x 50 = 300 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 8 hard

Trees are to be planted along a straight road that is $480$ m long, spaced $40$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $40$ m, and the total length of the road is labeled $480$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 480 m road, trees are planted every 40 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 480 m long
Trees are spaced 40 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 40 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 40 m gaps fit: 480 / 40 = 12 gaps.

480 \div 40 = 12 \text{ gaps}

Each 40 m piece is one gap, so dividing the total length by 40 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 12 + 1 = 13.

12 + 1 = 13 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 13 trees

4 · Reviewdoes it hold up?

Check with the spacing: 13 trees make 12 gaps of 40 m, which is 12 x 40 = 480 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 9 hard

Trees are to be planted along a straight road that is $560$ m long, spaced $70$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $70$ m, and the total length of the road is labeled $560$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 560 m road, trees are planted every 70 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 560 m long
Trees are spaced 70 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 70 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 70 m gaps fit: 560 / 70 = 8 gaps.

560 \div 70 = 8 \text{ gaps}

Each 70 m piece is one gap, so dividing the total length by 70 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 8 + 1 = 9.

8 + 1 = 9 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 9 trees

4 · Reviewdoes it hold up?

Check with the spacing: 9 trees make 8 gaps of 70 m, which is 8 x 70 = 560 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Variant 10 hard

Trees are to be planted along a straight road that is $1000$ m long, spaced $100$ m apart from one end of the road all the way to the other end. How many trees are needed in all?

(Figure) A straight road with both ends open. The gap between the left end of the road and the next tree is labeled $100$ m, and the total length of the road is labeled $1000$ m underneath. A tree stands at each end of the road, and the middle stretch is shown as "......" to indicate that the trees continue at the same regular spacing.

Your answer

Show solution

1 · Understandwhat's really being asked

Along a straight 1000 m road, trees are planted every 100 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.

Givens

The road is straight and 1000 m long
Trees are spaced 100 m apart
A tree stands at each end of the road
The road is open (not a loop)

Unknowns

The total number of trees needed

Constraints

Spacing is uniform at 100 m
On an open straight road, the number of trees is one more than the number of gaps

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #9 Solve an Easier Related Problem

Interval-counting is best seen with a diagram: trees sit at both ends of an open road, so the count of trees is the count of gaps plus 1. A tiny case makes the plus-one rule obvious before applying it.

3 · Execute2 carry out the plan

1Count the gaps

#9 Solve an Easier Related Problem 4.OA.A.3

Divide the road length by the spacing to find how many 100 m gaps fit: 1000 / 100 = 10 gaps.

1000 \div 100 = 10 \text{ gaps}

Each 100 m piece is one gap, so dividing the total length by 100 counts them.

2Add one for the open-road end tree

#1 Draw a Diagram 4.MD.A.2

On a straight open road with a tree at both ends, the number of trees is one more than the number of gaps because both endpoints get a tree. So trees = 10 + 1 = 11.

10 + 1 = 11 \text{ trees}

Drawing posts and the gaps between them shows there is always one more post than gap on an open path.

Answer: 11 trees

4 · Reviewdoes it hold up?

Check with the spacing: 11 trees make 10 gaps of 100 m, which is 10 x 100 = 1000 m, exactly the road length. The plus-one matches a tree at each end.

Another way: Solve an easier related problem (tool 9): a short road of two gaps gives 3 trees, confirming the trees-equals-gaps-plus-1 rule, then scale up.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Dividing the length by the spacing to count the gaps and adding one for the endpoint tree.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Reasoning about lengths and spacing along the road to relate gaps to trees.

💡Takeaway. This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!

Intervals differ on open paths versus closed loops · 10 practice problems

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