4th Grade - Use Graphs, Diagrams, And Other Methods

 
     
 
     
 
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4th
Reasoning
Use Graphs, Diagrams, and Other Methods
Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
Use different methods to explain how to solve math problems, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models.
 

Sample Problems

(1)

Use the Venn diagram to determine what are the numbers divisible by:

(2)

Use the stem and leaf plot to find the median score.

Football Scores 2007

Stem

Leaves

1

2

3

4

5






4 4 7 9

1 1 1 8

0 1 5 5 7

2 2 3

0 1 2

Write the scores shown on the stem and leaf plot: ______________

What is the median score? ________________

(3)

Describe the relationship between x and y. ___________________


Input

1

2

3

4

5

6

Output

3

6

9

12

15

18

(4)

Use the formula (V = length x width x height) to find the volume of the rectangular prism. __________________________


7in6 in

9 in.


(5)

Use the table to answer the following questions.

When Is Your Birthday

Month

Frequency

January

10

February

5

March

4

April

11

May

17

June

3

July

9

August

12

September

15

October

6

November

16

December

5


How many people were surveyed? __________________

Does this represent the majority of the school population with 671 students? ____________________


Learning Tips

(1)

Graph types

Line graph- shows change over time; Use a line graph to show whether data increases or decreases.


Bar graph- compares data. Use a bar graph to see how may of each type of item are in the data.


Double bar graph- Compares 2 sets of data. You can compare how two items are represented in the data.


Line plot- shows how many times each number occurs in the data


Stem and leaf plot- shows data arranged by place value. Use the plot to organize a long list of numbers

(2)


Line Plot- A graph that shows the frequency of data along a number line

Used to determine mode, range, and outliers.

x

x x

x x x x

x x x x x

x x x x x x

--׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀---

0 1 2 3 4 5 6 7 8 9





Stem & Leaf Plot- A table that shows groups of data arranged by place value

  • Group the data by the tens digits

  • Order the tens digits in a column from least to greatest to form the stems

  • Write each ones digit to the right of the stem (from least to greatest)

  • Used to determine median, mode, and range


Stem

Leaves

Tens digit







Ones digit


Mode- the number that is listed the most often in a set of data

Median- the middle number in an ordered series of numbers

Range- the difference between the highest and lowest number in the data

(3)

Practice finding volume

Volume- the measure of the space that a solid figure occupies.


Use cubic units (similar to base ten block, but in cube form) to count the cubes in order to measure the volume.


Use the formula for volume:

Volume = length x width x height (use cubic units)


You can measure various boxes, using a ruler in order to determine the volume. Have your child measure the length, width, and height of the boxes and then find the volume by multiplying.

(4)

Venn diagrams: Explain how to use Venn diagrams. The one color explains how the items are different and the combined colors in the middle identify how the items are the same.


Practice using the Venn diagrams by comparing and contrasting you and your child (or information he/she can easily identify with). Then, move into math concepts.


(5)

How to find a rule for the input/output table:

  • Look at the pattern from a to b

  • Is the number increasing or decreasing

  • If number is increasing (a + □ = b) or (a x □ = b)

  • If number is decreasing (a -□ = b) or (a ÷ □ = b)

  • Test the rules by plugging in the number you think is making the pattern, to see if it works for all numbers in the table.


Input

a

1

2

3

4

Output

b

2

4

6

8

Extra Help Problems

(1)

Use the diagram to answer the questions: Label the Venn diagram. Are there any similarities between the two types of shapes? ____________

(Green = Triangles, Blue = quadrilaterals; no similarities)

(2)

Compare and contrast the factors of 32 and 36.

(32: 8, 16, 32---36: 6, 9, 18, 36 Same: 1,2,4)

(3)

How would you draw a diagram to determine the answer:



Janey read 8 books; Jody read 5 more books that Janey, Bob read 3 less book than Jody. How many books did each person read?


  1. Venn diagram

  2. Line plot

  3. Picture graph


(c)

(4)

How would you draw a diagram to determine the answer:


I need to transfer my measurements from feet to inches.

(a) Bar graph

(b) Venn diagram

(c) table


(c)

(5)

Use the stem and leaf plot to answer questions about the data.

Reading Scores

Stem

Leaves

4

5

6

7

8

9

10




8 9

4 4 8 9

0

2 2 3 5 6 7 7

0 1 2 6 6 6 9

3 3 3 5 5 7 7 7 7

0

Write the reading scores from the stem-and leaf plot. ___________

What is the mode? _____________

(scores: 48, 49, 54, 54, 58, 59, 60, 72, 72, 73, 75, 76, 77, 77, 80, 81, 82, 86, 86, 86, 89, 93, 93, 93, 95, 95, 97, 97, 97, 97, 100; The mode is 97)

(6)

Use the stem and leaf plot to answer questions about the data.

Reading Scores

Stem

Leaves

4

5

6

7

8

9

10




8 9

4 4 8 9

0

2 2 3 5 6 7 7

0 1 2 6 6 6 9

3 3 3 5 5 7 7 7 7

0

What is the median score? _____________


(81)

(7)

What information can be determined from the stem and leaf plot?

________________________________________







(8)

Use the line plot to answer questions about data.

x

x x x x

x x x x x x

x x x x x x x

--׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀---

0 1 2 3 4 5 6 7 8 9

Homeruns

Each x represents the number of homeruns made for each game.


How many games were played? ____________

What is the mode for the data? ____________

(18 games were played; Mode =3)

(9)

Stem & Leaf Plot


Football Scores 2007

Stem

Leaves

1

2

3

4

5






4 4 7 9

1 1 1 8

0 1 5 5 7

2 2 3

0 1 2


Line Plot

x

x x x x

x x x x x x

x x x x x x x

--׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀---

0 1 2 3 4 5 6 7 8 9

Homeruns

Each x represents the number of homeruns made for each game.


Compare and contrast how the stem and leaf plot and line plot are used to analyze data.

(10)

Use the formula (V = length x width x height) to find the volume of the rectangular prism. __________________________


6 in3 in.

7 in.


(6 x 7 x 3 = 126 in3)

(11)

Complete the table to find volume:


Length

Width

Height

Volume

4 in.

3 in.

2 in.

(24 in3)

5 in.

6 in.

7 in.

(210 in3)

9 in.

5 in

5 in.

(225 in3)



(12)

Complete the table to find measurements for volume:


Length

Width

Height

Volume

3 in

(3 in)

2 in.

18 in.3

4 in

(4 in)

(2 in)

32 in.3

(4 in)

3 in.

(3 in)

36 in.3



(13)

Make a rectangular prism with the volume of 24 cubic units.


Length = _________

Width = __________

Height = __________


(4 x 3 x 2—answers may vary)

(14)

Make a rectangular prism with the volume of 12 cubic units.


Length = _________

Width = __________

Height = __________


(2 x 2 x 3)

(15)

Describe the relationship between x and y. ___________________


Input

1

4

9

16

25

36

Output

1

2

3

4

5

6


(Divide by its double factor)

(16)

Describe the relationship between x and y. ___________________


Input

6

7

8

9

10

11

Output

12

14

16

18

20

22


(Multiply by 2)

(17)

Describe the relationship between x and y. ___________________


Input

1

2

3

4

5

6

Output

4

5

6

7

8

9


(add 3)

(18)

Describe the relationship between x and y. ___________________


Input

14

21

28

35

42

49

Output

2

3

4

5

6

7


(divide by 7)

(19)

Describe the relationship between x and y. ___________________


Input

17

18

19

20

21

22

Output

12

13

14

15

16

17


(subtract 5)

(20)

Use the table to answer the following questions.

When Is Your Birthday

Month

Frequency

January

10

February

5

March

4

April

11

May

17

June

3

July

9

August

12

September

15

October

6

November

16

December

5


What type of graph would be best to use for the data in the table? ________

(bar graph, it compares data)

(21)

Use the table to answer the following questions.

When Is Your Birthday

Month

Frequency

January

10

February

5

March

4

April

11

May

17

June

3

July

9

August

12

September

15

October

6

November

16

December

5


What scale would you use for the graph? ________________

What intervals would you use for the graph? ______________


(Scale- 0 -20; Intervals 2)

(22)

Use the table to answer the following questions.

At dog training, if a dog follows a command he/she receives treats. Look at the table to see the number of treats given for the dogs.

Number of Dogs

Dog Treats

1

7

2

3

3

1

4

6

5

2


What type of graph can be used to organize the data in the table?

________________


(Line plot)

(23)

Use the table to answer the following questions.

At dog training, if a dog follows a command he/she receives treats. Look at the table to see the number of treats given for the dogs.

Number of Dogs

Dog Treats

1

7

2

3

3

1

4

6

5

2


What is the range of the number of dog treats given? _____________

(Range = 7 – 1 = 6)

(24)

The fifth grade class was surveyed about their favorite ice cream; in order give them an ice cream party. Which ice cream was their favorite? Explain how you know? _______________________



(Cookies and cream, the graph shows the bar being the highest)

(25)

We use ____________ to help determine information more easily.

  1. words

  2. numbers

  3. graphs


(c)

 

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