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

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

## Building Blocks/Prerequisites

### 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.

 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.

 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.

 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)

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

(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.

 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.

 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)