Data management - Ottawa Bansho



Data management

Lesson 1: Introduction –

We are going to gather data amongst our classes. Think of something you would like to know about concerning this age group, choose something they like, or don’t like, to do (How much time they watch tv, play video games, computer time, etc…)

Once topics are chosen, make a prediction. Are you average? Will the classes differ from one another? Will ages matter? Does it go up or down with age? Why? Explain.

Write topic and predictions in notebook.

Lesson 2: Design a survey that will answer you question.

Possible problems – how do you represent ½ hours?

Track how much you do it a week.

Do survey.

Lesson 3: Introduce Stem and Leaf plot (grade 4) and Broken-line Graph (grade 5)

Grade 4 – page 64, Nelson text; self generated worksheet below (to be evaluated)

Grade 5 – page 64, Nelson text

Make a graph of our data.

Consolidation: analyzing the data

• What is the general shape of the data?

• How is the data spread out?

• What have you learned about topic?

• Are you average?

|Name: _______________________ |[pic] |

|Date: ________________________ | |

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|Stem-and-Leaf Plots | |

Mr. Wendler’s class tried having a pizza throwing contest. They used small pizzas which have 4 pieces each. They tried throwing one piece at a time into Mr. Wendler’s very large hat. Here are their results.

12½, 12¼, 12¾, 13, 13, 13, 13¼, 13¼, 13½, 13¾, 14½, 14½, 15, 15, 15¾

Make a Stem-and-Leaf Plot of the results.

|Stem |Leaf |

|15 | |

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| | |

(Don’t worry, they didn’t waste the pizza. They had a pizza party when they were done and ate it.)

Mr. Wendler’s class also had a balancing contest to see who could stand on their head the longest. Here are the results in hours.

1, 1 ¼, 1 ½, 2, 2, 2 ¼, 2 ¼, 2 ¼, 2 ¼, 2 ½, 3 ½, 4

Make a Stem-and-Leaf Plot of the results.

|Stem |Leaf |[pic] |

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|Name: _______________________ |[pic] |

|Date: ________________________ | |

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|Stem-and-Leaf Plots | |

Mr. Wendler’s class tried linking paper clips together in two minutes. Here are their results.

11 12 12 14 16 17 17 17 19 21 22 22 23 24 26 26 28 28 28 28 28 30 31 33 33 35 36 38 43

Make a Stem-and-Leaf Plot of the results.

|Stem |Leaf |

|4 | |

|3 | |

|2 | |

|1 | |

Mr. Wendler’s class also had a worm eating contest. Students had to see how many worms they could eat in 1 minute. Here are the results.

21 24 29 32 32 35 36 36 39 41 41 43 43 43 43 43 43 45 46 46 47 49 50 51 51 53 55 56 56 59 67

Make a Stem-and-Leaf Plot of the results.

|Stem |Leaf |[pic] |

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Lesson 4: Introduce Mean, Mode (grade5) and Median (grade 4)

Notes: (I wonder if we can bansho this?)

Median:

• The Median is the physical centre of a set of data.

• Put the data in order from smallest to largest.

• Odd numbered data, find the middle (halfway point).

(Use examples on board)

• 9 people surveyed – hours of television watched this week. What is the median? (18)

|2 |4.5 |

The median is the number in the middle. Take a set of numbers, put them in order from smallest to largest, and then find the one in the middle.

4, 5, 7, 8, 9, 11, 13

Here are some numbers. If I cross out the numbers on the end (the 4 and the 13) and then do it again (the 5 and 11) and then again (the 7 and 9), the number in the middle is: 8

Therefore the MEDIAN is 8.

If there are 2 numbers in the middle, you find the average of the two numbers and that is the median.

4, 5, 7, 8, 10, 15, 17, 19

Here are some numbers. If I cross out the ones on the end (one at a time) I am left with 8 and 10. The average of 8 and 10 (add them together and then divide by 2) is 9. Therefore the MEDIAN is 9.

Question 1:

Find the median of these numbers.

1, 22, 27, 6, 29, 2, 13, 17, 22, 12, 17, 8, 8, 8, 9

Step one, place them in order:

_________________________________________________________

Step two, find the middle number: ______

The median is: ________

Question 2:

Find the median: 2, 4, 4, 9, 6, 7, 5, 6, 3, 9, 10, 6, 6, 14

Step one: _________________________________________________

Step two: ____________________________

The median is: _______

The mode is the number that occurs the most often.

What is the mode of question 1: ________

What is the mode of question 2: ________

Grade 5’s

The mean is the average. To find the average you have to add all the numbers together and then divide them by the number of “numbers”.

For example:

Here are number of cookies found in 5 children’s lunches.

3, 1, 3, 3, 5

To find the MEAN:

Step 1 - add the numbers together.

3 + 1 + 3 + 3 + 5 = 15

Step 2 – divide the answer by the number of children’s lunches.

15 ÷ 5 = 3

Therefore the MEAN is 3.

Find the MEAN.

Find the MEAN from question 1:

Show your work.

You may use a calculator.

Find the MEAN from question 2:

Show your work.

You may use a calculator.

Lesson 5: Bar graphs (intervals)

How do you compare data using bar graphs?

How do you graph data into 5 or 6 categories when there is too much information?

Bar graphs with intervals; (I think we can bansho this… give them a set of data and ask how they can display the data using a bar graph)

Grade 4: Nelson text page 66

Grade 5: Nelson text page 68

Teacher generated sheets below (to be handed in – evaluated):

Lesson 6: How do you compare data using a bar graph? (double bar)

(Could bansho)

Use teacher generated sheets below (evaluated)

Lesson 7: Final task (see assignment below)

|Name: _____________________ |[pic] |

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|Date: ______________________ | |

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|Bar Graph With Intervals (4) | |

Mr. Wendler asked the class to estimate the number of shoes he had in his closet. Here are the results.

15 10 29 11 15 16 29 18 12 15

25 12 18 21 13 17 24 23 15 24

How do you calculate the range? ________________________________

What is the RANGE of this data: ___________

Round off the range to an easy number: ____________

How can you use the range to make a bar graph with about 4 bars? What would be the interval of each bar?

__________________________________________________________________________________________________________________

_________________________________________________________

Make a T-chart of the data:

|Number of shoes (intervals from above question) |Number of people (to guess within that interval) |

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Make a bar graph of the data.

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Mr. Wendler asked the class to estimate the number of grasshoppers he had in his terrarium. Here are the results.

150. 100 299 104 105 150 160 299 100 115 150

250. 120 120 180 204 123 125 240 145 150 240

What is the RANGE of this data: ___________________________

How can you use the range to make a bar graph with about 4 bars? What would be the interval of each bar?

__________________________________________________________________________________________________________________

_________________________________________________________

Make a T-chart of the data:

|Number of grasshoppers (4 intervals from above question) |Number of people (to guess within that interval) |

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| | |

| | |

Make a bar graph of the data.

| | | | | |

|Knowledge and Understanding – demonstrates considerable knowledge of| | | | |

|how to calculate the range, intervals, and creating a bar graph. |1 |2 |3 |4 |

|Thinking – makes and carried out a plan (making a bar graph). All | | | | |

|the parts of a bar graph were included (title, labels, good scale) |1 |2 |3 |4 |

|Communication – expresses mathematical thinking (using conventions | | | | |

|and vocabulary). (WIN) |1 |2 |3 |4 |

|Application – applies knowledge making as few errors as possible. | | | | |

| |1 |2 |3 |4 |

|Mark: |4=D |6=C- |10=B- |14=A- |

| |5=D+ |7-8=C |11-12=B |15=A |

| | |9=C+ |13=B+ |16=A+ |

Notes:

Problem solving assessment sheet Name: __________________

Problem: Bar Graph using intervals.

| |With limited |With some |With |With high |

| |effectiveness |effectiveness |considerable |degree of |

| | | |effectiveness |effectiveness |

|Knowledge and Understanding – demonstrates considerable knowledge of| | | | |

|how to calculate the range, intervals, and creating a bar graph. |1 |2 |3 |4 |

|Thinking – makes and carried out a plan (making a bar graph). All | | | | |

|the parts of a bar graph were included (title, labels, good scale) |1 |2 |3 |4 |

|Communication – expresses mathematical thinking (using conventions | | | | |

|and vocabulary). (WIN) |1 |2 |3 |4 |

|Application – applies knowledge making as few errors as possible. | | | | |

| |1 |2 |3 |4 |

|Mark: |4=D |6=C- |10=B- |14=A- |

| |5=D+ |7-8=C |11-12=B |15=A |

| | |9=C+ |13=B+ |16=A+ |

Notes:

|Name: _____________________ |[pic] |

|Date: _____________________ | |

| | |

|Double Bar Graphs | |

When comparing data, one good way to display the information is by using double bar graphs.

For example: A school had a walk-a-thon. The children walked laps around a field for 15 minutes each day for 3 weeks. The primary children wanted to compare their results to the junior children. Here are the results:

|Week 1 |Week 2 |Week 3 |

|Primaries: 30 laps |Primaries: 40 laps |Primaries: 50 laps |

|Juniors: 50 laps |Juniors: 55 laps |Juniors: 60 laps |

Here is a double bar graph showing the information side by side.

Laps walked by students in walk-a-thon

|Number | | | | | | |

|of Laps |70 | | | | | |

| |60 | | | | | |

| |50 | | | | | |

| |40 | | | | | |

| |30 | | | | | |

| |20 | | | | | |

| |10 | | | | | |

| |0 | | | | | |

| | |P |

Comparing the results, what can you conclude?

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Here are some results from a survey of the number of teeth that fell out of the mouths of the boys and girls in Mr. Wendler’s class, over term 1, 2 and 3 of last year.

Boys Term 1 – 18 Girls Term 1 - 24

Boys Term 2 – 10 Girls Term 2 - 18

Boys Term 3 – 6 Girls Term 3 - 12

Make a Double Bar Graph of the results, comparing the boys and girls in Mr. Wendler’s class.

_____________________________

| | | | | |

|Knowledge and Understanding – demonstrates considerable knowledge of| | | | |

|how to create and interpret a double-bar graph. |1 |2 |3 |4 |

|Thinking – makes and carried out a plan (making a bar graph). All | | | | |

|the parts of a bar graph were included (title, labels, good scale) |1 |2 |3 |4 |

|Communication – expresses mathematical thinking using conventions | | | | |

|and vocabulary. |1 |2 |3 |4 |

|Application – applies knowledge making as few errors as possible. | | | | |

| |1 |2 |3 |4 |

|Mark: |4=D |6=C- |10=B- |14=A- |

| |5=D+ |7-8=C |11-12=B |15=A |

| | |9=C+ |13=B+ |16=A+ |

Notes:

Problem solving assessment sheet Name: __________________

Problem: Double Bar Graph.

| |With limited |With some |With |With high |

| |effectiveness |effectiveness |considerable |degree of |

| | | |effectiveness |effectiveness |

|Knowledge and Understanding – demonstrates considerable knowledge of| | | | |

|how to create and interpret a double-bar graph. |1 |2 |3 |4 |

|Thinking – makes and carried out a plan (making a bar graph). All | | | | |

|the parts of a bar graph were included (title, labels, good scale) |1 |2 |3 |4 |

|Communication – expresses mathematical thinking using conventions | | | | |

|and vocabulary. |1 |2 |3 |4 |

|Application – applies knowledge making as few errors as possible. | | | | |

| |1 |2 |3 |4 |

|Mark: |4=D |6=C- |10=B- |14=A- |

| |5=D+ |7-8=C |11-12=B |15=A |

| | |9=C+ |13=B+ |16=A+ |

Notes:

|Name: __________________ |[pic] |

|Date: __________________ | |

| | |

|How Much? | |

The Question:

Does the amount of time spent doing (the activity you chose) increase, decrease, or stay the same when comparing adults and students

Or…

Is the amount of time spent doing an activity different when comparing girls to boys, women to men?

Your job:

Use the data we have collected to answer the question. Your assignment MUST HAVE THESE 4 PARTS. Be clear. Use math vocabulary.

1. Display or Compare the data:

• calculate the median, mode, and mean of the data

• decide how it would be best to display or compare the data

• think about if or how to use: bar graphs,

line graphs,

stem-and-leaf plots,

mean, median, mode,

double-bar graphs

2. Explain why you think the graph/table you chose to display the data is the most effective.

3. Analyse the data:

• answer The Question and make some predictions/conclusions

• think about:

- Who did it the most and who did it the least?

- What information does the mean, median and mode give us?

- What are the factors that may influence the amount of time students or adults do this activity?

- What are the positive and negative effects of this activity can have on health, knowledge, family, homework, the things you buy, etc… ?

- Why the survey we did may be flawed?

4. Make a connection:

• explain how you could use the information collected from this survey to promote something positive (like physical activity) amongst your classmates.

Assessment sheet for “How Much?” assignment

|Assessment Category |With limited |With some |With considerable |With a high degree|

| |effectiveness |effectiveness |effectiveness |of effectiveness |

|Knowledge and Understanding | | | | |

|• represented data (graphs and tables) (question 1) | | | | |

| |1 |2 |3 |4 |

|• calculated median, mode (& mean) | | | | |

| |1 |2 |3 |4 |

|Thinking | | | | |

|• explained effectiveness of data display choice | | | | |

|(question 2) |1 |2 |3 |4 |

|• analysed the data making logical conclusions (question| | | | |

|3) |1 |2 |3 |4 |

|Communication | | | | |

|• explained mathematical thinking (detailed, appropriate| | | | |

|vocabulary) |1 |2 |3 |4 |

|• communicated clearly | | | | |

| |1 |2 |3 |4 |

|Application | | | | |

|• made connections among concepts (question 4) | | | | |

| |1 |2 |3 |4 |

|• Overall impression | | | | |

| |1 |2 |3 |4 |

| Marks: |D= 8-9 |C-= 13-14 |B-= 21-23 |A-= 28-29 |

| |D+= 10-12 |C= 15-17 |B= 24-25 |A= 30-32 |

| | |C+= 18-20 |B+26-27 |A+= 32 |

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