Estimate an unmeasured midpoint value on a line graph
5.MD.B.2
Generated variants — 8
The line graph shows the garden temperature recorded in a town. Estimate the value at about 11 a.m., in .
The graph is titled "Garden Temperature." The horizontal axis shows the time (6, 8, 10, 12, 2), and the vertical axis shows the value in . The vertical axis is labeled 5, 10, 15; since 5 grid squares represent 5, each grid square represents . The recorded values are: 6 , 8 , 10 , 12 , 2 . The value at 11 a.m. was not recorded, so estimate it as the midpoint of the values at 10 a.m. and 12 noon.
Show solution
1 · Understandwhat's really being asked
A line graph of garden temperature shows 6 = 4, 8 = 7, 10 = 10, 12 = 16, 2 = 14 degrees C (each square = 1 degrees C). 11 a.m. was not measured; I estimate it as the midpoint of the 10 a.m. and 12 noon readings.
Givens
- 6 = 4 degrees C, 8 = 7 degrees C, 10 = 10 degrees C, 12 = 16 degrees C, 2 = 14 degrees C
- Each small grid square = 1 degrees C
- 11 a.m. is exactly halfway between 10 a.m. and 12 noon
- Estimate 11 a.m. as the midpoint of the 10 a.m. and 12 noon values
Unknowns
- The estimated value at about 11 a.m. in degrees C
Constraints
- 11 a.m. lies between the two measured times, so its value should sit between 10 and 16
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. 11 a.m. is the halfway time between 10 a.m. and 12 noon, so I take the midpoint of 10 and 16.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
13 lies between 10 (10 a.m.) and 16 (12 noon), as it must for a time in between, and it is exactly in the middle, which fits 11 a.m. being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the road temperature recorded in a town. Estimate the value at about 12 noon, in .
The graph is titled "Road Temperature." The horizontal axis shows the time (7, 9, 11, 1, 3), and the vertical axis shows the value in . The vertical axis is labeled 5, 10, 15; since 5 grid squares represent 5, each grid square represents . The recorded values are: 7 , 9 , 11 , 1 , 3 . The value at 12 noon was not recorded, so estimate it as the midpoint of the values at 11 a.m. and 1 p.m..
Show solution
1 · Understandwhat's really being asked
A line graph of road temperature shows 7 = 3, 9 = 6, 11 = 9, 1 = 17, 3 = 14 degrees C (each square = 1 degrees C). 12 noon was not measured; I estimate it as the midpoint of the 11 a.m. and 1 p.m. readings.
Givens
- 7 = 3 degrees C, 9 = 6 degrees C, 11 = 9 degrees C, 1 = 17 degrees C, 3 = 14 degrees C
- Each small grid square = 1 degrees C
- 12 noon is exactly halfway between 11 a.m. and 1 p.m.
- Estimate 12 noon as the midpoint of the 11 a.m. and 1 p.m. values
Unknowns
- The estimated value at about 12 noon in degrees C
Constraints
- 12 noon lies between the two measured times, so its value should sit between 9 and 17
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. 12 noon is the halfway time between 11 a.m. and 1 p.m., so I take the midpoint of 9 and 17.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
13 lies between 9 (11 a.m.) and 17 (1 p.m.), as it must for a time in between, and it is exactly in the middle, which fits 12 noon being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the plant height recorded in a town. Estimate the value at about week 3.5, in .
The graph is titled "Plant Height." The horizontal axis shows the week (1, 2, 3, 4, 5), and the vertical axis shows the value in . The vertical axis is labeled 5, 10, 15; since 5 grid squares represent 5, each grid square represents . The recorded values are: 1 , 2 , 3 , 4 , 5 . The value at week 3.5 was not recorded, so estimate it as the midpoint of the values at week 3 and week 4.
Show solution
1 · Understandwhat's really being asked
A line graph of plant height shows 1 = 4, 2 = 8, 3 = 12, 4 = 20, 5 = 18 cm (each square = 1 cm). week 3.5 was not measured; I estimate it as the midpoint of the week 3 and week 4 readings.
Givens
- 1 = 4 cm, 2 = 8 cm, 3 = 12 cm, 4 = 20 cm, 5 = 18 cm
- Each small grid square = 1 cm
- week 3.5 is exactly halfway between week 3 and week 4
- Estimate week 3.5 as the midpoint of the week 3 and week 4 values
Unknowns
- The estimated value at about week 3.5 in cm
Constraints
- week 3.5 lies between the two measured times, so its value should sit between 12 and 20
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. week 3.5 is the halfway time between week 3 and week 4, so I take the midpoint of 12 and 20.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
16 lies between 12 (week 3) and 20 (week 4), as it must for a time in between, and it is exactly in the middle, which fits week 3.5 being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the snow depth recorded in a town. Estimate the value at about day 3.5, in .
The graph is titled "Snow Depth." The horizontal axis shows the day (1, 2, 3, 4, 5), and the vertical axis shows the value in . The vertical axis is labeled 5, 10, 15; since 5 grid squares represent 5, each grid square represents . The recorded values are: 1 , 2 , 3 , 4 , 5 . The value at day 3.5 was not recorded, so estimate it as the midpoint of the values at day 3 and day 4.
Show solution
1 · Understandwhat's really being asked
A line graph of snow depth shows 1 = 6, 2 = 10, 3 = 14, 4 = 22, 5 = 18 cm (each square = 1 cm). day 3.5 was not measured; I estimate it as the midpoint of the day 3 and day 4 readings.
Givens
- 1 = 6 cm, 2 = 10 cm, 3 = 14 cm, 4 = 22 cm, 5 = 18 cm
- Each small grid square = 1 cm
- day 3.5 is exactly halfway between day 3 and day 4
- Estimate day 3.5 as the midpoint of the day 3 and day 4 values
Unknowns
- The estimated value at about day 3.5 in cm
Constraints
- day 3.5 lies between the two measured times, so its value should sit between 14 and 22
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. day 3.5 is the halfway time between day 3 and day 4, so I take the midpoint of 14 and 22.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
18 lies between 14 (day 3) and 22 (day 4), as it must for a time in between, and it is exactly in the middle, which fits day 3.5 being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the library visitors recorded in a town. Estimate the value at about hour 3.5, in .
The graph is titled "Library Visitors." The horizontal axis shows the hour (1, 2, 3, 4, 5), and the vertical axis shows the value in . The vertical axis is labeled 10, 20, 30; since 5 grid squares represent 10, each grid square represents . The recorded values are: 1 , 2 , 3 , 4 , 5 . The value at hour 3.5 was not recorded, so estimate it as the midpoint of the values at hour 3 and hour 4.
Show solution
1 · Understandwhat's really being asked
A line graph of library visitors shows 1 = 10, 2 = 16, 3 = 20, 4 = 30, 5 = 24 people (each square = 2 people). hour 3.5 was not measured; I estimate it as the midpoint of the hour 3 and hour 4 readings.
Givens
- 1 = 10 people, 2 = 16 people, 3 = 20 people, 4 = 30 people, 5 = 24 people
- Each small grid square = 2 people
- hour 3.5 is exactly halfway between hour 3 and hour 4
- Estimate hour 3.5 as the midpoint of the hour 3 and hour 4 values
Unknowns
- The estimated value at about hour 3.5 in people
Constraints
- hour 3.5 lies between the two measured times, so its value should sit between 20 and 30
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. hour 3.5 is the halfway time between hour 3 and hour 4, so I take the midpoint of 20 and 30.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
25 lies between 20 (hour 3) and 30 (hour 4), as it must for a time in between, and it is exactly in the middle, which fits hour 3.5 being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the town temperature recorded in a town. Estimate the value at about 1:00 p.m., in .
The graph is titled "Town Temperature." The horizontal axis shows the time (8, 10, 12, 2, 4), and the vertical axis shows the value in . The vertical axis is labeled 5, 10, 15; since 5 grid squares represent 5, each grid square represents . The recorded values are: 8 , 10 , 12 , 2 , 4 . The value at 1:00 p.m. was not recorded, so estimate it as the midpoint of the values at 12 noon and 2 p.m..
Show solution
1 · Understandwhat's really being asked
A line graph of town temperature shows 8 = 6, 10 = 8, 12 = 11, 2 = 15, 4 = 12 degrees C (each square = 1 degrees C). 1:00 p.m. was not measured; I estimate it as the midpoint of the 12 noon and 2 p.m. readings.
Givens
- 8 = 6 degrees C, 10 = 8 degrees C, 12 = 11 degrees C, 2 = 15 degrees C, 4 = 12 degrees C
- Each small grid square = 1 degrees C
- 1:00 p.m. is exactly halfway between 12 noon and 2 p.m.
- Estimate 1:00 p.m. as the midpoint of the 12 noon and 2 p.m. values
Unknowns
- The estimated value at about 1:00 p.m. in degrees C
Constraints
- 1:00 p.m. lies between the two measured times, so its value should sit between 11 and 15
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. 1:00 p.m. is the halfway time between 12 noon and 2 p.m., so I take the midpoint of 11 and 15.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
13 lies between 11 (12 noon) and 15 (2 p.m.), as it must for a time in between, and it is exactly in the middle, which fits 1:00 p.m. being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the pool temperature recorded in a town. Estimate the value at about 11:30 a.m., in .
The graph is titled "Pool Temperature." The horizontal axis shows the time (9, 10, 11, 12, 1), and the vertical axis shows the value in . The vertical axis is labeled 15, 20, 25; since 5 grid squares represent 5, each grid square represents . The recorded values are: 9 , 10 , 11 , 12 , 1 . The value at 11:30 a.m. was not recorded, so estimate it as the midpoint of the values at 11 a.m. and 12 noon.
Show solution
1 · Understandwhat's really being asked
A line graph of pool temperature shows 9 = 18, 10 = 20, 11 = 22, 12 = 26, 1 = 28 degrees C (each square = 1 degrees C). 11:30 a.m. was not measured; I estimate it as the midpoint of the 11 a.m. and 12 noon readings.
Givens
- 9 = 18 degrees C, 10 = 20 degrees C, 11 = 22 degrees C, 12 = 26 degrees C, 1 = 28 degrees C
- Each small grid square = 1 degrees C
- 11:30 a.m. is exactly halfway between 11 a.m. and 12 noon
- Estimate 11:30 a.m. as the midpoint of the 11 a.m. and 12 noon values
Unknowns
- The estimated value at about 11:30 a.m. in degrees C
Constraints
- 11:30 a.m. lies between the two measured times, so its value should sit between 22 and 26
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. 11:30 a.m. is the halfway time between 11 a.m. and 12 noon, so I take the midpoint of 22 and 26.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
24 lies between 22 (11 a.m.) and 26 (12 noon), as it must for a time in between, and it is exactly in the middle, which fits 11:30 a.m. being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point
The line graph shows the cafe customers recorded in a town. Estimate the value at about 10:30 a.m., in .
The graph is titled "Cafe Customers." The horizontal axis shows the hour (8, 9, 10, 11, 12), and the vertical axis shows the value in . The vertical axis is labeled 10, 20, 30; since 5 grid squares represent 10, each grid square represents . The recorded values are: 8 , 9 , 10 , 11 , 12 . The value at 10:30 a.m. was not recorded, so estimate it as the midpoint of the values at 10 a.m. and 11 a.m..
Show solution
1 · Understandwhat's really being asked
A line graph of cafe customers shows 8 = 12, 9 = 18, 10 = 24, 11 = 36, 12 = 30 people (each square = 2 people). 10:30 a.m. was not measured; I estimate it as the midpoint of the 10 a.m. and 11 a.m. readings.
Givens
- 8 = 12 people, 9 = 18 people, 10 = 24 people, 11 = 36 people, 12 = 30 people
- Each small grid square = 2 people
- 10:30 a.m. is exactly halfway between 10 a.m. and 11 a.m.
- Estimate 10:30 a.m. as the midpoint of the 10 a.m. and 11 a.m. values
Unknowns
- The estimated value at about 10:30 a.m. in people
Constraints
- 10:30 a.m. lies between the two measured times, so its value should sit between 24 and 36
2 · Planchoose the strategy
#5 Look for a Pattern
On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. 10:30 a.m. is the halfway time between 10 a.m. and 11 a.m., so I take the midpoint of 24 and 36.
3 · Execute2 carry out the plan
1Add the two endpoint values
2Halve to get the midpoint
4 · Reviewdoes it hold up?
30 lies between 24 (10 a.m.) and 36 (11 a.m.), as it must for a time in between, and it is exactly in the middle, which fits 10:30 a.m. being the middle time.
Standardsmin grade 5
5.MD.B.2Make a line plot to display a data set and solve problems using the data — Reading the two endpoint values and estimating the in-between point