# MATHEMATICS

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```					                                      MATHEMATICS
Activities

Framework Strand:       Data Analysis and Statistics
Grade Level Standard:           3-6 Select, explore, and organize data.

Grade Level Benchmark:          1. Collect and explore data. (III.1.E.1)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Have children bring in favorite foods. Brainstorm ways to organize data.

Example: Color

Vocabulary:

PICTORIAL (symbolic):

   Using the children’s data, keep a classroom tally of their favorite foods.

Vocabulary:

ABSTRACT (computational):

   Use the food tally to write a sentence explaining what you discovered.

Vocabulary:

58
LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   Collect the same data from another classroom and compare.

Vocabulary:

59
MATHEMATICS
Activities

Framework Strand:                        Data Analysis and Statistics
Grade Level Standard:                            3-6 Select, explore, and organize data.

Grade Level Benchmark:                           2. Organize data using concrete objects, pictures, tallies,
tables, charts, diagrams, and graphs. (III.1.E.2)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Use a floor graph, survey the class for each student’s favorite flavor of ice cream.
Have the students stand on the name of their favorite ice cream flavor on the
mat.

Vocabulary:

PICTORIAL (symbolic):

   Survey the class, then complete the graph. Rank ice cream flavors from most
liked to least liked.

FLAVORS OF ICE CREAM
Number of Students Who

10
Like a Particular Flavor

9
8
7
6
5
4
3
2
1

Vocabulary:

60
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Using the data from the graph, state the results.

Vocabulary:

PROBLEM SOLVING:

   Have students survey their family’s favorite ice cream. Collect data, make a
graph, and record results.

Vocabulary:

61
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-6 Select, explore, and organize data.

Grade Level Benchmark:         3. Present data using a variety of appropriate
representations. (III.1.E.3)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Using a floor graph mat, create a graph by having students collect and organize
classroom materials into graph format. (i.e., pattern blocks, shoes, colored
cubes, shaped pasta).

Example:

Vocabulary:

PICTORIAL (symbolic):
   Read this circle graph of where Ann spends the hours in one day.
1. Color the place Ann spends six hours a day red.
asleep in bed
2. Color Ann’s sleeping time blue.                         at the         9 hours
ball field
3. Color the time Ann spends on the ball field green.     2 hours
4. Color Ann’s non-sleep time at home yellow.                 at home       at school
(not in bed)     6 hours
7 hours
Vocabulary:

62
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Students will make a list of 4 to 5 common pets.
1. Have members of the class vote for their favorite pets.
3. Make a graph of favorite pets for the class.
4. What will you name (title) your graph?

Vocabulary:

PROBLEM SOLVING:

   Students will construct a graph of choice with given data. They will present their
graph to the class.

Vocabulary:

63
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-6 Select, explore, and organize data.

Grade Level Benchmark:         4. Identify data needed to solve a given problem. (III.1.E.4)

LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   Give students the results of a survey that reflect which articles are most popular.
Using this data, students will determine whether or not their newspaper would
likely to be purchased. Have them explain their answers in writing. What could
they do to make their newspaper more marketable?

Vocabulary:

64
MATHEMATICS
Assessment

Framework Strand:        Data Analysis and Statistics
Grade Level Standard:            3-6 Select, explore, and organize data.

PROBLEM SOLVING ASSESSMENT:

     Give students the results of a survey that reflect which articles are most popular.
Using this data, students will determine whether or not their newspaper would
likely to be purchased. Have them explain their answers in writing. What could
they do to make their newspaper more marketable?

PROBLEM RUBRIC:
BEGINNING              DEVELOPING           ACHIEVING               EXCEEDING
1                       2                     3                       4
Appropriate      Attempts a strategy    Begins with an         Uses an                Carries appropriate
Strategy                                appropriate strategy   appropriate strategy   strategy to correct
solution
Understanding    Shows minimal          Shows some             Shows significant      Understands the
Problem          understanding of       understanding of       understanding of       content of the
the content of the     the content of the     the content of the     problem
problem                problem                problem
Errors           Makes serious          Makes some errors      Makes minor errors     Makes no
errors but shows       (requires some         (could complete the    meaningful errors
reasoning (requires    instruction prior to   task with a non-
significant            being able to          instructional hint)
instruction prior to   complete the task)
being capable of
completing the
Supporting       Provides few           Provides some (but     Provides nearly        Provides clear and
Calculations,    supporting             not complete)          complete               complete
Arguments,       calculations/          supporting             supporting             supporting
and/or           arguments/             calculations/          calculations/          calculations/
Justifications   justifications         arguments/             arguments/             arguments/
justifications         justifications         justifications
Use of Tools     Uses inappropriate     Recognizes an          Uses appropriate       Uses available
tools and/or           appropriate tool or    tools and              tools and
representations        representation but     representations        representations
uses it                correctly but reads    correctly with
inappropriately        the scale              correct results
incorrectly or has
an error in
interpretation

65
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-7 Analyze and interpret data.

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Create a list of favorite television programs for students in the classroom. Make
a graph to demonstrate this information.

Vocabulary:

PICTORIAL (symbolic):

   Look at the picture graph. What does this information tell you?

CHILDREN OF THE WORLD
(under the age of 15)

PICTOGRAPH                                                        = 20 million children
Africa
Asia

Australia
Europe
North
America
South
America

Vocabulary: picture graph

66
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):
Public School Enrollment in the US
   A line graph shows changes
over time. The one here                                 36
gives changes for two                                   34
32
groups. Name the groups.                                30
The numbers across the                                  28

Millions of Students
bottom identify the years.                              26
24
The numbers on the side                                 22
represent millions of                                   20
18
students. The most students                             16
ever in elementary school at                            14
once was 33 million                                     12
10
(33,000,000). In what year                               8
were they enrolled?                                      6
4
2

*
30

40

50

60

70

80

90
19

19

19

19

19

19

19
Vocabulary:

PROBLEM SOLVING:

   Using the graph above, tell how many more elementary students than secondary
students were enrolled in 1950?

Answer: 12 million more elementary students.

   Write 2 problems using the graph above.

Vocabulary:

67
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-7 Analyze and interpret data.

Grade Level Benchmark:         2. Describe the shape of the data using informal language.
(III.2.E.2)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Divide students into cooperative groups. Using the same data, have the students
construct various types of graphs. (i.e. pie, bar, line (vertical or horizontal) etc.).

Vocabulary:

PICTORIAL (symbolic):

   As a group, compare and contrast the various graphs and charts (i.e. were some
easier to understand than others?). Is the information the best presented in the
form of a pie chart, a bar graph, etc.

Vocabulary:

ABSTRACT (computational):
   Give the students a new set(s) of data from the class bake sale. Have them
decide which graph or chart would be the best choice for representation.
Vocabulary:

PROBLEM SOLVING:
   From the above graph, students will then write a word problem and have their
partner solve it.
Vocabulary:

68
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-7 Analyze and interpret data.

Grade Level Benchmark:         3. Draw, explain, and justify conclusions using data.
(III.2.E.3)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   In small groups, students will observe another class on the playground. They will
keep a count of the children using various pieces of playground equipment by
dropping a manipulative into a bag.

Example: red unifix cubes for swings, blue cubes for the jungle gym, etc. In the
classroom, cubes can be used to derive a graph.

Slide (yellow)
Swings (red)
Jungle Gym (blue)

Vocabulary:

PICTORIAL (symbolic):

   Students will look at the information on the chart to determine which piece of
playground equipment is used most?

   The table shows the population of five major cities in the United States. Study
the table, then answer the questions.

City          Number of People
Atlanta                428,153
Boston                 560,847
Dallas                 943,484
Miami                  382,726
New York              7,086,096

69
LEARNING ACTIVITY/FACTS/INFORMATION
PICTORIAL (symbolic): (cont)

1) Which city has the most people?
a) Atlanta b) Boston c) Miami d) New York              Answer: d

2) Which city has nearly 600,000 people?
a) Atlanta b) Boston c) Miami d) New York              Answer: b

3) How many people live in Atlanta and Miami?
a) 800,079 b) 710,899 c) 810,879 d) 700,789            Answer: c

Vocabulary: population

ABSTRACT (computational):

   Jane’s father bought her 30 ride tickets at the carnival. Some rides cost four
tickets and some cost five tickets. Complete the table. Use it to determine how
many different combinations of rides there are and which combinations(s) allow
the most rides. Use data trends to complete the table.

Number of 4     Number of 5 ticket    Total number of
ticket rides         rides                tickets
7                 0                     28
6                 1                     29
5                 5                     30
0                 6                     30

Vocabulary:

PROBLEM SOLVING:

   Students will speculate as to why the number of campers dropped in weeks 3
and 4. Why might the campers have increased in week 5?

This graph shows how many campers at Jewel Lake during five weeks. Study
the graph; then answer the questions.

1. How many campers camped at Jewel Lake during week 4?
a) 20
b) 25
c) 40
d) 35

70
LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING: (cont)

2. Which week had the most                             Jewel Lake Camper Attendance
campers?

Number of Campers
a) week 5                                        40
b) week 2                                        30
c) week 3                                        20
d) week 1                                        10
0
Answer: b                                                   1   2   3     4     5
Weeks
3. What was the total number of
campers at Jewel Lake for the
five weeks?
a) 125
b) 150
c) 140
d) 155

Vocabulary:

71
MATHEMATICS
Activities

Framework Strand:     Data Analysis and Statistics
Grade Level Standard:         3-7 Analyze and interpret data.

Grade Level Benchmark:        4. Analyze validity of data. (III.2.E.4)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Have students decide what toppings they should choose for a pizza party. They
should survey three or more people to find out their preferences. Graph the
results. Compare with other students. Decide on the best choice for the sample
survey population. Determine why this is the most valid choice.

Vocabulary: sample survey population, validity

PICTORIAL (symbolic):

   Use the class graph to answer questions.

1. Which topping did 7 of the        14
students prefer?                  13
12
11
pepper                                9
8
2. Which pizza is the most            7
6
popular?                           5
4
2
1
3. How many students liked            0
the plain cheese pizza?                  Plain    Pepperoni Sausage
Cheese       and    and Green
Answer: 13 students                         Pizza     Cheese    Pepper
Pizza     Pizza

72
LEARNING ACTIVITY/FACTS/INFORMATION
PICTORIAL (symbolic): (cont)

4. How many students liked the pepperoni and cheese pizza?

Vocabulary:

ABSTRACT (computational):

   Use this graph to generate valid conclusions.

Example:
Classroom 8 has the highest percentages of spelling scores. (valid conclusion)
Classroom 8 are the best spellers. (valid conclusion)

Classroom 5

Classroom 7

Classroom 8

Classroom 9

40   50   60   70   80   90   100

Vocabulary:

PROBLEM SOLVING:

Team 1

Team 2

Team 3

   In using the graphs, determine the validity of the statements:
1. In different basketball games, Team 1, 2, and 3 scored the amount of points
noted on the graph; therefore, Team 1 must be the best basketball team. Is
this a valid statement?

Vocabulary:

73
MATHEMATICS
Activities

Framework Strand:       Data Analysis and Statistics
Grade Level Standard:           3-7 Analyze and interpret data.

Grade Level Benchmark:          5. Formulate questions, and gather and interpret data to
solve problems. (III.2.E.5)

LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

    Students formulate question (hypothesis) regarding conditions under which
plants will grow. Students plant one lima bean in a Styrofoam cup placed in
sunlight (water plant); another under same conditions but without sunlight.
Observe for two weeks.

1. Follow instructions above. Chart progress in graph format. Make identical
charts for each plant.

Height in cm.   Day 2       Day 4    Day 6      Day 8      Day 10   Day 12
5
4
3
2
1

2. Interpret data on the plant graph.
a) Draw conclusions based on the plant graph data. Did the results support

With Light          Without light

b) How might a change in another variable affect the outcome of plant
growth? (i.e., the presence of oxygen)

Vocabulary:

74
MATHEMATICS
Assessment

Framework Strand:        Data Analysis and Statistics
Grade Level Standard:            3-7 Analyze and interpret data.

PROBLEM SOLVING ASSESSMENT:

     Generate questions, and then collect and interpret data about topics relevant to
students.
- Interests (hobbies, favorite food, favorite book)
- Current content or event
- School issues/events (class rules, spelling scores)

PROBLEM RUBRIC:
BEGINNING              DEVELOPING           ACHIEVING               EXCEEDING
1                       2                     3                       4
Appropriate      Attempts a strategy    Begins with an         Uses an                Carries appropriate
Strategy                                appropriate strategy   appropriate strategy   strategy to correct
solution
Understanding    Shows minimal          Shows some             Shows significant      Understands the
Problem          understanding of       understanding of       understanding of       content of the
the content of the     the content of the     the content of the     problem
problem                problem                problem
Errors           Makes serious          Makes some errors      Makes minor errors     Makes no
errors but shows       (requires some         (could complete the    meaningful errors
reasoning (requires    instruction prior to   task with a non-
significant            being able to          instructional hint)
instruction prior to   complete the task)
being capable of
completing the
Supporting       Provides few           Provides some (but     Provides nearly        Provides clear and
Calculations,    supporting             not complete)          complete               complete
Arguments,       calculations/          supporting             supporting             supporting
and/or           arguments/             calculations/          calculations/          calculations/
Justifications   justifications         arguments/             arguments/             arguments/
justifications         justifications         justifications

75
BEGINNING           DEVELOPING           ACHIEVING            EXCEEDING
1                     2                     3                     4
Use of Tools   Uses inappropriate   Recognizes an         Uses appropriate      Uses available
tools and/or         appropriate tool or   tools and             tools and
representations      representation but    representations       representations
uses it               correctly but reads   correctly with
inappropriately       the scale             correct results
incorrectly or has
an error in
interpretation

76
MATHEMATICS
Activities

Framework Strand:     Data Analysis and Statistics
Grade Level Standard:         3-8 Make predictions and formulate hypotheses.

Grade Level Benchmark:        1. Make and test hypotheses. (III.3.E.1)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Explore graphs of interest and formulate hypotheses based on information. Test
hypotheses (wait for outcome) for validity.
Example: The high school basketball team has scored 54 points the last three
games. What do you think the score of the next game will be?

Vocabulary: hypothesis

PICTORIAL (symbolic):

   Continue following the team’s progress. Graph results. Conclude chances for
going to a championship or winning a championship based on data checked.

Vocabulary:

ABSTRACT (computational):

   Use the graph below to predict sunrise time.
1. Predict the time of sunrise on August 6.
2. What pattern helps to make this prediction?
3. Predict the time of sunrise for August 7.
4. Use a red pencil or pen to show your prediction for August 6 and 7 on the
graph.

77
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational): (cont)

Predicting Sunrise
5:06 a.m. _________________________________________
5:05 a.m. _________________________________________
5:04 a.m. _________________________________________
5:03 a.m. _________________________________________
5:02 a.m. _________________________________________
5:01 a.m. _________________________________________
5:00 a.m. _________________________________________
_________________________________________
August       1    2     3     4     5      6 7

1. 5:05
2. The time is rising, one minute per day.
3. 5:06
4. Graph should be extended as shown to include 5:05 and 5:06.

Predicting Sunrise
5:06 a.m. _________________________________________
5:05 a.m. _________________________________________
5:04 a.m. _________________________________________
5:03 a.m. _________________________________________
5:02 a.m. _________________________________________
5:01 a.m. _________________________________________
5:00 a.m. _________________________________________
_________________________________________
August       1    2     3     4      5    6  7

Vocabulary:

PROBLEM SOLVING:

   See Abstract.

Vocabulary:

78
MATHEMATICS
Activities

Framework Strand:     Data Analysis and Statistics
Grade Level Standard:         3-8 Make predictions and formulate hypotheses.

Grade Level Benchmark:        2. Conduct surveys, samplings, and experiments. (III.3.E.2)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Collect data on hair and eye color. Create a graph.

Eye Color       Number with light hair   Number with dark hair

Vocabulary:

PICTORIAL (symbolic):

   Use the information from the above table to complete each of the following:
How many?
1. Total                             ____
2. Light hair                        ____
3. Dark hair                         ____
4. Brown eyes                        ____
5. Blue eyes                         ____
6. Light hair and brown eyes         ____
7. Light hair and blue eyes          ____
8. Dark hair and brown eyes          ____
9. Dark hair and blue eyes           ____
Vocabulary:

79
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Complete the graph using the information gathered above.

____ Hair    ____ Hair
____ Eyes    ____ Eyes
____ %       ____ %

____ Hair    ____ Hair
____ Eyes    ____ Eyes
____ %       ____ %

Vocabulary:

PROBLEM SOLVING:

   Suppose there are 2,000 students in your school. Predict the number of students
who have the following:

Light hair and brown eyes              ____
Dark hair and brown eyes               ____
Light hair and blue eyes               ____
Dark hair and blue eyes                ____

Vocabulary:

80
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-8 Make predictions and formulate hypotheses.

Grade Level Benchmark:         3. Formulate and communicate arguments and conclusions
based on data and evaluate their arguments and those of others. (III.3.E.3)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   N/A

Vocabulary:

PICTORIAL (symbolic):

   N/A

Vocabulary:

ABSTRACT (computational):

   Students develop questions similar to those listed based on their data, looking for
1. What is the title of the graph?
2. What are the labels on the graph?
3. How many different kinds of shows are recorded?
4. How many half-hours of news were counted?
5. How many half-hours of game shows were counted?
6. Which kind of show was on for the most amount of time?
7. Which kind of show was on for the least amount of time?
8. Was there more time counted for sit-coms or drama?
9. Do you think the record was on a Saturday, a Sunday, or a weekday? If
you are not sure, how could you find out?

Vocabulary:

81
LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   Look at the table. Predict for 9/16 the time of sunrise, time of sunset, and length
of day.

Date           Time of Sunrise       Time of Sunset        Length of Day
9/12                6:24                  6:54               12h 30m
9/13                6:25                  6:52               12h 27m
9/14                6:26                  6:50               12h 24m
9/15                6:27                  6:48               12h 21m
9/16

Vocabulary:

82
MATHEMATICS
Activities

Framework Strand:     Data Analysis and Statistics
Grade Level Standard:         3-8 Make predictions and formulate hypotheses.

Grade Level Benchmark:        4. Make and explain predictions based on data. (III.3.E.4)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Students will make a prediction as to whether rainy days affect people’s
emotions. They will collect data to make a chart.

RAIN MAKES ME
Katie                Julio
Kayla                David
Jim                  Kenji
Carol                Maria
Jamel                Kim
George               Charles

Vocabulary:

PICTORIAL (symbolic):

   Students draw numerical conclusions based on data presented in the graph.

Compare results to original predictions.

Vocabulary:

83
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Create < or > equations (number sentences) based on data collected.
   Use data obtained from the rain survey to make a numerical graph.

12
Number of People   10
8
6
4
2

Vocabulary:

PROBLEM SOLVING:

   Students will use math journals and write word problems from data. Partners will
solve.

Vocabulary:

84
MATHEMATICS
Activities

Framework Strand:      Data Analysis and Statistics
Grade Level Standard:          3-8 Make predictions and formulate hypotheses.

problems. (III.3.E.5)

LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

1. Predict the number and types of plants owned by your classmates. Then make a
plan to systematically collect and report the number and type of plants owned by

Rubber plants                       IIIII    IIIII I
Snake plants                        IIIII    III
Geraniums                           IIIII    IIIII III
Begonias                            IIIII    IIIII
Cacti                               IIIII    IIIII IIIII I
Palm trees                          IIIII    IIIII I
Other                               IIIII    IIIII

2. Use data obtained from your survey to make a graph. Make a pictograph.

Plants                            How many
Rubber plants                                    11
Snake plants                                     8
Geraniums                                        13
Begonias
Cacti
Palm trees
Other

85
LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING: (cont)

3. Draw a circle graph with sections for each type of plant and label:

Other    Rubber
12%    Plants 13%

13%                  9%

7%                 15%

19%
12%

4. Use the graphs to answer questions, write word problems, etc.

Example:

Rank plants in order from most popular to least popular.
1) ___________________________ 5) ___________________________

2) ___________________________           6) ___________________________

3) ___________________________           7) ___________________________

4) ___________________________           8) ___________________________

Vocabulary:

86
MATHEMATICS
Assessment

Framework Strand:        Data Analysis and Statistics
Grade Level Standard:            3-8 Make predictions and formulate hypotheses.

PROBLEM SOLVING ASSESSMENT:

     Predict the number and types of plants owned by your classmates. Then make a
plan to systematically collect and report the number and type of plants owned by
     Use the data obtained from your survey to make a graph. Make a pictograph.
     Draw a circle graph with sections for each type of plant and label.
     Use the graphs to answer questions, write word problems, etc.
Example: Rank plants in order from most popular to least popular.

PROBLEM RUBRIC:
BEGINNING              DEVELOPING           ACHIEVING               EXCEEDING
1                       2                     3                       4
Appropriate      Attempts a strategy    Begins with an         Uses an                Carries appropriate
Strategy                                appropriate strategy   appropriate strategy   strategy to correct
solution
Understanding    Shows minimal          Shows some             Shows significant      Understands the
Problem          understanding of       understanding of       understanding of       content of the
the content of the     the content of the     the content of the     problem
problem                problem                problem
Errors           Makes serious          Makes some errors      Makes minor errors     Makes no
errors but shows       (requires some         (could complete the    meaningful errors
reasoning (requires    instruction prior to   task with a non-
significant            being able to          instructional hint)
instruction prior to   complete the task)
being capable of
completing the
Supporting       Provides few           Provides some (but     Provides nearly        Provides clear and
Calculations,    supporting             not complete)          complete               complete
Arguments,       calculations/          supporting             supporting             supporting
and/or           arguments/             calculations/          calculations/          calculations/
Justifications   justifications         arguments/             arguments/             arguments/
justifications         justifications         justifications

87
BEGINNING           DEVELOPING           ACHIEVING            EXCEEDING
1                     2                     3                     4
Use of Tools   Uses inappropriate   Recognizes an         Uses appropriate      Uses available
tools and/or         appropriate tool or   tools and             tools and
representations      representation but    representations       representations
uses it               correctly but reads   correctly with
inappropriately       the scale             correct results
incorrectly or has
an error in
interpretation

88
MATHEMATICS
Activities

Framework Strand:       Number Sense and Numeration
Grade Level Standard:           3-9 Develop understanding of number properties.

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Using flash cards, play a game of concentration with students.
Example: Cards labeled with the months of year January through December will
be matched with the first twelve ordinal numbers: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th,
9th, 10th, 11th, 12th.
Possible matches: 1st and January; 7th and July, etc.

Vocabulary:

PICTORIAL (symbolic):

Whole numbers: 256, 315, 067, 87, 5, 216
Ordinal numbers: 51st, 75th, 82nd, 100th
Fraction numbers: 1/2, 2/3, 9/10, 6/100
Decimal numbers: 0.9, 0.2, 1.2, 6.9

Vocabulary: whole numbers, ordinal numbers, fraction numbers, decimal numbers

ABSTRACT (computational):

1. Write the following whole numbers:
Two hundred fifty-six; three hundred fifteen thousand; sixty-seven, eighty-seven;
five thousand two hundred sixteen
2. Write the following ordinal numbers:
Fifty-first; seventy-fifth; eighty-second; one hundredth
89
LEARNING ACTIVITY/FACTS/INFORMATION

ABSTRACT (computational): (cont)

3. Write the following fractions:
One-half; two-thirds; nine-tenths; six hundredths
4. Write the following decimals:
Eight-tenths, two-tenths, one and two-tenths, six and nine-tenths

Vocabulary: fraction

PROBLEM SOLVING:

1. Match the correct numeral with the written number.

_____ 67                   a. fifty-third
_____ 53rd                 b. six-tenths
_____ .6                   c. seven hundredths
_____ 7/100                d. sixty-seven

2. Using a newspaper, cut out and categorize examples of whole numbers, ordinal
numbers, fractions, and decimals.

Whole Numbers          Ordinal Numbers         Fractions           Decimals
st
Lions 7 Packers 0     1 Annual City Meeting   ½ off sale   .500 Mark McGwire batting
average

Vocabulary: decimal

90
MATHEMATICS
Activities

Framework Strand:     Number Sense and Numeration
Grade Level Standard:         3-9 Develop understanding of number properties.

Grade Level Benchmark:        2. Write whole numbers, fractions, and decimals. (IV.1.E.1)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):
   Have students write numbers dictated by teacher. The teacher will use phrases
like 1st Monday, 3rd Wednesday, 345, one-tenth, and one hundredth.
Vocabulary: tenth, hundredth

PICTORIAL (symbolic):
   Have students write numbers dictated by teacher, including whole numbers up to
six digits.
- 10, 100 and 1000 more than a given number
- ordinal numbers 50th-100th
- fractions – parts of a whole through hundredths
   Have students write the fractions shown. Use base ten blocks to show 1/100,
1/10, 1/1000.
Vocabulary:

ABSTRACT (computational):

   Students use words to write numbers dictated by the teacher. Include whole
numbers up to six digits.
-   10,100, and 1000 more than a given number
-   ordinal numbers 50th-100th
-   fractions – parts of a whole through hundredths
-   mixed numbers
-   decimals in tenths and amounts greater than one.

Vocabulary: ordinal, fractions, decimal, mixed number

91
LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   Use the picture to answer the questions.

1. Al lives in the first house. Who lives in the eighth? (Ann)
2. Which house does Jo live in? (third)
3. Two people’s names start with S. Which houses do they live in? (fifth and
sixth)
4. A cat lives in the fourth house. Whose house is it? (Luz’s)
5. Which house does Ti live in? (second)
6. Tom walks from the tree to his house. How many houses does he walk by?
(6)
7. Two people’s names start with L. Which houses do they live in? (fourth and
tenth)
8. There are 21 houses on the street. Steve lives in the next to last house. What
is his place on the street? (twentieth)

Vocabulary:

92
MATHEMATICS
Activities

Framework Strand:         Number Sense and Numeration
Grade Level Standard:             3-9 Develop understanding of number properties.

Grade Level Benchmark:            3. Count whole numbers, fractions, and decimals.
(IV.1.E.1)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Use manipulatives to find the missing number. Complete by counting aloud.

31              33        34                  37

   Circle the greater number.

58             ½
42             ¾

   Place the next four numbers in this sequence:

1, 2, 3, 4 . . .
56, 57, 58 . . .
10, 20, 30 . . .
5, 10, 15 . . .

Vocabulary: fraction, greater than, less than

PICTORIAL (symbolic):

   Which picture shows the larger fraction?

¾      or      ¼

Vocabulary:

93
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Have students count the multiples of 3, 4, 6, 7, 8, 9, 50, 100, and 1000.
   Have students count backwards from a given number by 100s and 1000s.
Students count forward and backward from any 5-digit number. Count by halves,
fourths, tenths, and hundredths.
   How many ways can you write or show a half?
½, .5,

Vocabulary:

PROBLEM SOLVING:

   Have students list 20 ways to represent 100 using base ten blocks. Draw and
write each response.

Vocabulary:

94
MATHEMATICS
Activities

Framework Strand:     Number Sense and Numeration
Grade Level Standard:         3-9 Develop understanding of number properties.

Grade Level Benchmark:        4. Investigate and develop an understanding of the base-10
place value system. (IV.1.E.2)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Use base ten blocks to build models to demonstrate place value, e.g. 1,324

Vocabulary:

PICTORIAL (symbolic):

1. Draw place value blocks to show the following number: 25.
2. Round 25 to the nearest ten and draw the base ten blocks.
3. Round 156 to the nearest ten then hundred. Draw the base ten blocks for each.

1)               2)                3)

Vocabulary:

95
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Given a number, such as 1,345, have students write an expanded notation and
word form.
   Have students give the number of thousands, hundreds, tens, and ones. Then
the students will write the number.

Vocabulary:

PROBLEM SOLVING:

   Give students a real estate magazine. Assign each child a number (1-4), have
them find their number, and identify the place value of their number (ones, tens,
hundreds, etc…).

Vocabulary:

96
MATHEMATICS
Activities

Framework Strand:      Number Sense and Numeration
Grade Level Standard:          3-9 Develop understanding of number properties.

Grade Level Benchmark:         5. Examine properties of operations. (IV.1.E.3)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Using unifix cubes, set up multiplication problems and 2 division problems using
zero as a factor, then one as a factor.
   Use counters to set up multiplication problems and division problems.

Vocabulary: factor

PICTORIAL (symbolic):

   Draw examples of the following problems:
8 x 10,   20 x 0,   7  0,     12  0,   12 x 1,   15 x 1

Vocabulary:

ABSTRACT (computational):

   NA

Vocabulary:

PROBLEM SOLVING:

   NA

Vocabulary:

97
MATHEMATICS
Activities

Framework Strand:     Number Sense and Numeration
Grade Level Standard:         3-9 Develop understanding of number properties.

Grade Level Benchmark:        6. Use prior knowledge of number systems to solve
problems. (IV.1.E.4)

LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   Students go around the classroom or school and look for other “names” for the
numbers 12-25. For example: The number 12 could be represented as:
12 (whole number)
XII (Roman numeral)
24/2 (fraction)
twelve (word form)
twelfth (ordinal number)
5 + 7 = 12 (number sentence - addition)
18 – 6 = 12 (number sentence –subtraction)
(6 + 9) –3 = 12 (distributive property)
12.0 = decimal
   Record the various “names” for each number on charts to be displayed in the
classroom. Discuss the various ways for numerical representation.

Vocabulary:

98
MATHEMATICS
Assessment

Framework Strand:        Number Sense and Numeration
Grade Level Standard:            3-9 Develop understanding of number properties.

PROBLEM SOLVING ASSESSMENT:

     Students go around the classroom or school and look for other “names” for the
numbers 12-25. For example: The number 12 could be represented as:
12 (whole number)
XII (Roman numeral)
24/2 (fraction)
twelve (word form)
twelfth (ordinal number)
5 + 7 = 12 (number sentence - addition)
18 – 6 = 12 (number sentence –subtraction)
(6 + 9) –3 = 12 (distributive property)
12.0 = decimal
     Record the various “names” for each number on charts to be displayed in the
classroom. Discuss the various ways for numerical representation.

PROBLEM RUBRIC:
BEGINNING              DEVELOPING           ACHIEVING               EXCEEDING
1                       2                     3                       4
Appropriate      Attempts a strategy    Begins with an         Uses an                Carries appropriate
Strategy                                appropriate strategy   appropriate strategy   strategy to correct
solution
Understanding    Shows minimal          Shows some             Shows significant      Understands the
Problem          understanding of       understanding of       understanding of       content of the
the content of the     the content of the     the content of the     problem
problem                problem                problem
Errors           Makes serious          Makes some errors      Makes minor errors     Makes no
errors but shows       (requires some         (could complete the    meaningful errors
reasoning (requires    instruction prior to   task with a non-
significant            being able to          instructional hint)
instruction prior to   complete the task)
being capable of
completing the

99
BEGINNING            DEVELOPING         ACHIEVING             EXCEEDING
1                    2                     3                     4
Supporting       Provides few         Provides some (but    Provides nearly       Provides clear and
Calculations,    supporting           not complete)         complete              complete
Arguments,       calculations/        supporting            supporting            supporting
and/or           arguments/           calculations/         calculations/         calculations/
Justifications   justifications       arguments/            arguments/            arguments/
justifications        justifications        justifications
Use of Tools     Uses inappropriate   Recognizes an         Uses appropriate      Uses available
tools and/or         appropriate tool or   tools and             tools and
representations      representation but    representations       representations
uses it               correctly but reads   correctly with
inappropriately       the scale             correct results
incorrectly or has
an error in
interpretation

100
MATHEMATICS
Activities

Framework Strand:     Number Sense and Numeration
Grade Level Standard:         3-10 Develop, examine, and investigate ways numbers are
used.
Grade Level Benchmark:        1. Represent whole numbers, fractions, and decimals using
concrete, pictorial, and symbolic representations. (IV.2.E.1)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Using pattern block pictures (pre-made) identify the shapes used. Orally express
the amount of shapes in the following ways: whole number, fraction, and
decimals.

Number of triangles = 4 = 4/5 = .20

   Use models, e.g. Kids, shoes, and blocks to show forms of numbers. Use graph
paper to visualize decimals.

Vocabulary:

PICTORIAL (symbolic):

   Using the same pattern block pictures, students should draw a chart to show the
amount of shapes in whole numbers, fractions, and decimals.

Vocabulary: transpose

101
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

   Given a set of numbers, students should transpose them into whole numbers,
fractions, or decimals.

Example:

Whole Number                  Fraction                  Decimal
20                         2/10                      .2
50                       5/10, 1/2                   .5

Vocabulary:

PROBLEM SOLVING:

   Bring in various bags of candy. Students will determine which bags would have
enough candy for everyone in the classroom. Possible ways would be to use
prior knowledge, compare to a bag of candy they know the amount of.

Extension: Discuss if it would be more economical to purchase 1bag or 2 of the
smaller bags. How do you know?

Vocabulary:

102
MATHEMATICS
Activities

Framework Strand:     Number Sense and Numeration
Grade Level Standard:         3-10 Develop, examine, and investigate ways numbers are
used.
Grade Level Benchmark:        2. Explore representations of a number. (IV.2.E.2)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Using math counters, have students organize counters in 3 rows and 8 columns.

XXXXXXXX
XXXXXXXX
XXXXXXXX

What multiplication fact does it show?

   Using math counters, show the following problems:

2x5          4x4            3x3           5x2

Vocabulary:

PICTORIAL (symbolic):

   Demonstrate number operations using manipulatives.

+                2+3=5                                   4 1 = 3

Division

6÷2=3

Vocabulary:

103
LEARNING ACTIVITY/FACTS/INFORMATION
ABSTRACT (computational):

1. Know how to add, subtract, multiply, and divide whole numbers.
13       14               521    393         8             18  3 = 6
+6       +6              -211   +227       x4              6 x 2 = 12
19       20               310    620        32             20 ÷ 5 = 4

2. What means the same as 4 x 5 = 20?
a.) 5 + 4 = 20
b.) 5 + 5 + 5 + 5 = 20
c.) 4 + 5 + 4 + 5 = 20

Vocabulary:

PROBLEM SOLVING:

   If you make 20¢ from each candy bar, how many candy bars must your class sell
so that everyone can go to the Anderson Water Park? It costs \$1.00 per child to
get into the park.

Answer: dependent on the number of students in the class (x) 20¢ ● x = ?

Vocabulary:

104
MATHEMATICS
Activities

Framework Strand:      Number Sense and Numeration
Grade Level Standard:          3-10 Develop, examine, and investigate ways numbers are
used.
Grade Level Benchmark:         3. Investigate ways numbers are used. (IV.2.E.3)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Students will represent a given number using a variety of manipulatives.
Example: dominoes, dice, base ten blocks

Vocabulary:

PICTORIAL (symbolic):

   Students walk around the room observing and recording ways numbers are
used.
Example: clock to measure time, calendar to measure time

Vocabulary:

ABSTRACT (computational):

   Students will use an analog clock to calculate time passed within a half-hour.
Example: 12:00-12:15
Count by 5’s from the number 1 on the clock to the number 3.

Vocabulary:

PROBLEM SOLVING:

   Given a menu, students will work in cooperative groups with a set amount of
money. Together they will determine a group order they can afford.

Vocabulary:

105
MATHEMATICS
Activities

Framework Strand:     Number Sense and Numeration
Grade Level Standard:         3-10 Develop, examine, and investigate ways numbers are
used.
Grade Level Benchmark:        4. Develop and evaluate strategies for estimating quantity.
(IV.2.E.4)

LEARNING ACTIVITY/FACTS/INFORMATION
CONCRETE (conceptualizing):

   Give groups of students a small jar of buttons. How many buttons are in the jar?

   Give groups 2 jars. One jar should be labeled with the amount of buttons. Using
this jar as a benchmark, students can estimate the number of buttons in the
second jar.

Benchmark          5 buttons               20 buttons

Vocabulary:

PICTORIAL (symbolic):

   How many squares are in the picture?

Vocabulary:

ABSTRACT (computational):

   Have students count the number of students in their class? If all the rooms have
the same number of children in them, how many children are in the school?
Students need to know how many classrooms are in the school.

Vocabulary:

106
LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   There are 500 seats in the school auditorium. If each classroom has 22-25
students, about how many classrooms can attend the assembly at one time?

Vocabulary: estimate

107
MATHEMATICS
Activities

Framework Strand:      Number Sense and Numeration
Grade Level Standard:          3-10 Develop, examine, and investigate ways numbers are
used.
Grade Level Benchmark:         5. Select appropriate numbers and representations in order
to solve problems. (IV.2.E.5)

LEARNING ACTIVITY/FACTS/INFORMATION
PROBLEM SOLVING:

   Given the information of teachers’ names and the amount of students in their
classrooms, compare them to your homeroom class. Use the words “greater
than, less than, or equal to.” Next rank the names of the teachers in order from
smallest to largest class sizes.

Vocabulary:

108
MATHEMATICS
Assessment

Framework Strand:        Number Sense and Numeration
Grade Level Standard:            3-10 Develop, examine, and investigate ways numbers
are used.

PROBLEM SOLVING ASSESSMENT:

     Given the information of teachers’ names and the amount of students in their
classrooms, compare them to your homeroom class. Use the words “greater
than, less than, or equal to.” Next rank the names of the teachers in order from
smallest to largest class sizes.

PROBLEM RUBRIC:
BEGINNING              DEVELOPING           ACHIEVING               EXCEEDING
1                       2                     3                       4
Appropriate      Attempts a strategy    Begins with an         Uses an                Carries appropriate
Strategy                                appropriate strategy   appropriate strategy   strategy to correct
solution
Understanding    Shows minimal          Shows some             Shows significant      Understands the
Problem          understanding of       understanding of       understanding of       content of the
the content of the     the content of the     the content of the     problem
problem                problem                problem
Errors           Makes serious          Makes some errors      Makes minor errors     Makes no
errors but shows       (requires some         (could complete the    meaningful errors
reasoning (requires    instruction prior to   task with a non-
significant            being able to          instructional hint)
instruction prior to   complete the task)
being capable of
completing the
Supporting       Provides few           Provides some (but     Provides nearly        Provides clear and
Calculations,    supporting             not complete)          complete               complete
Arguments,       calculations/          supporting             supporting             supporting
and/or           arguments/             calculations/          calculations/          calculations/
Justifications   justifications         arguments/             arguments/             arguments/
justifications         justifications         justifications
Use of Tools     Uses inappropriate     Recognizes an          Uses appropriate       Uses available
tools and/or           appropriate tool or    tools and              tools and
representations        representation but     representations        representations
uses it                correctly but reads    correctly with
inappropriately        the scale              correct results
incorrectly or has
an error in
interpretation

109

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