D. Data · Data and LikelihoodOrdering Data and Drawing Conclusions
D1.4 D1.5About 35 minutes
Learning goals- I can order categories from greatest to least.
- I can ask and answer questions about data in graphs, tables, logbooks and diagrams.
- I can use data to make a decision and explain why.
Words to know
frequency
How many times something happens or how many chose it. If 7 children chose moose, the frequency of moose is 7.
greatest
The most.
least
The fewest.
conclusion
Something we figure out or decide by looking at the data.
logbook
A list where you write down data day by day, like a weather log.
diagram
A drawing that shows how data is sorted, like two circles that overlap.
Let's get started!
Your class is voting for a class mascot: a Canadian animal! 20 children voted. Which animal won? Which came second? How do you know?
Today you will learn to put data in order and to read data like a detective, so you can make good decisions.
Ordering from greatest to least
The frequency of a category is how many are in it. To order from greatest to least:
- Find the category with the most. Write it first.
- Find the next most. Write it next.
- Keep going until you write the one with the least.
On a bar graph, the tallest bar is the greatest. On a pictograph or tally table, look for the longest row.
Worked examplePut the animals in order
Order the animals from greatest to least votes.
- Read each bar: beaver 4, moose 7, loon 3, polar bear 6.
- The most is 7: moose. Write moose first.
- Next is 6: polar bear. Then 4: beaver.
- The least is 3: loon. It goes last.
- Check: 7, 6, 4, 3 goes down each time. Yes!
Moose (7), polar bear (6), beaver (4), loon (3). Moose is our mascot!
The same data with the bars ordered from greatest to least. Now it is easy to see the winner and the order.Asking and answering questions about data
Good data detectives ask questions like:
- Which category has the most? The least?
- How many chose ___?
- How many more chose ___ than ___?
- How many fewer?
- How many altogether?
- Are any categories the same?
- What surprised you?
Worked exampleHow many more?
How many more children voted for moose than for beaver?
- Moose has 7 votes. Beaver has 4 votes.
- Count up from 4 to 7: 5, 6, 7. That is 3 jumps.
- Or subtract: 7 − 4 = 3.
3 more children voted for moose.
Counting up from 4 (beaver) to 7 (moose) takes 3 jumps.Data in a logbook
A logbook is data written down over time. Ella kept a weather log for one week in October.
| Day | Weather |
|---|
| Monday | ☀️ Sunny |
| Tuesday | 🌧️ Rainy |
| Wednesday | ☁️ Cloudy |
| Thursday | 🌧️ Rainy |
| Friday | ☀️ Sunny |
| Saturday | ☀️ Sunny |
| Sunday | ☁️ Cloudy |
Worked exampleReading the logbook
What kind of weather happened most often? Can you order the kinds of weather?
- Count each kind. Sunny: Monday, Friday, Saturday = 3.
- Rainy: Tuesday, Thursday = 2. Cloudy: Wednesday, Sunday = 2.
- Order from greatest to least: sunny 3, then rainy 2 and cloudy 2. Rainy and cloudy are tied (the same), so they share second place.
- Check: 3 + 2 + 2 = 7 days in a week. Yes!
Sunny happened most often (3 days). Rainy and cloudy were tied with 2 days each.
Data in a diagram
This diagram has two circles. Children wrote their names in the circle that fits them. If both are true, the name goes in the middle where the circles overlap. If neither is true, the name goes outside the circles.
Worked exampleReading the diagram
How many children have a pet?
- Look at everything inside the Has a pet circle, including the middle part.
- Ava, Sam, and Leo (Leo is in the middle, but he is still inside the pet circle).
- Count: 1, 2, 3.
Drawing conclusions and making decisions
A conclusion is what the data tells us. We use data to make informed decisions: smart choices based on facts.
The class asked "Which snack should we have at our Family Day party?" Apple slices: 9. Crackers: 5. Cheese: 4. (18 children)
Decision: The class should get the most apple slices, because 9 is the greatest number. Some crackers and cheese too, so everyone gets something they like!
A convincing argument uses the numbers: "We should pick apple slices because 9 children chose it, and that is more than any other snack."
Just for funFun fact: Canada's one-dollar coin has a loon on it. That is why people call it the loonie!
Hands-on activityData detective at home
- Keep a weather logbook for one week. Each day, draw or write the weather.
- At the end of the week, make a tally table and order the kinds of weather from greatest to least.
- Ask a grown-up 3 questions about your data ("Which was the most? How many more sunny days than rainy days?").
- Make a decision: "Next week, I think we should keep our umbrella by the door because..."
Your turn
1A tally table shows: Red 5, Green 8, Blue 2, Yellow 6. Order from greatest to least.
Green (8), yellow (6), red (5), blue (2).
2Use the mascot graph. How many children voted altogether?
4 + 7 + 3 + 6 = 20 children.
3Use the mascot graph. How many more votes did polar bear get than loon?
4Use the logbook. How many days were NOT sunny?
7 − 3 = 4 days (2 rainy + 2 cloudy).
5Use the diagram. How many children have a sibling?
Mia, Noor, Ben and Leo = 4 children.
6Use the diagram. Who has neither a pet nor a sibling? How do you know?
Kai. His name is outside both circles.
7A pizza survey says: cheese 10, pepperoni 6, veggie 2. Which pizza should the class order the most of? Explain.
Cheese, because 10 is the greatest frequency. More children chose it than any other kind.
Math talk
When you make a decision, explain it with the word because and a number from the data. "I think... because..."
More practice: warm-up
1Votes: Cats 4, Dogs 9, Fish 6. Which pet has the greatest frequency?
2Use the mascot graph (beaver 4, moose 7, loon 3, polar bear 6). Which animal got the fewest votes?
3Fill in the blank: A list where you write down the weather every day is a ___.
4Use Ella's weather logbook. What was the weather on Tuesday?
5Use the two-circle diagram. Where is Leo's name? Why?
In the middle, where the circles overlap, because Leo has a pet and a sibling.
More practice: on your own
1Favourite breakfast: Muffins 5, Bagels 2, Pancakes 8, Toast 4. Order from greatest to least.
Pancakes (8), muffins (5), toast (4), bagels (2). Check: 8, 5, 4, 2 gets smaller each time.
2Use the mascot graph. How many children voted for beaver or loon altogether?
3Use Ella's logbook. How many more sunny days than cloudy days were there?
Sunny 3, cloudy 2. 3 − 2 = 1 more sunny day.
4Use the two-circle diagram. How many children are in the diagram altogether? (Don't forget anyone!)
7 children: Ava, Sam, Leo, Mia, Noor, Ben, and Kai (outside the circles).
5Recess vote: Tag 6, Skipping 6, Soccer 3. Order from greatest to least. Is there a tie?
Tag and skipping are tied with 6, so they share first place. Soccer (3) is last. Order: tag and skipping (6), then soccer (3).
Challenge
1Find the mistake! Ravi ordered the mascot votes from greatest to least like this: Moose 7, Beaver 4, Polar bear 6, Loon 3. What is wrong?
Polar bear (6) has more votes than beaver (4), so it should come before beaver. Correct order: moose 7, polar bear 6, beaver 4, loon 3.
2Snack vote for a class hike: Granola bars 8, Apples 5, Trail mix 3. That is 16 children. Which snack should the class bring the most of? How many children did not pick granola bars?
Bring the most granola bars, because 8 is the greatest number. Children who did not pick granola bars: 5 + 3 = 8. (Or 16 − 8 = 8.)
3Ben kept a weather logbook for 10 days: sunny 5, rainy 3, snowy 2. His friend says, "Rain happened the most." Is that true? How do you know?
Not true. Sunny happened 5 times and rainy only 3 times. 5 is more than 3, so sunny happened the most.
Quiz
1. Bars show: Soccer 5, Hockey 8, Swimming 3. What is the order from greatest to least?
2. What does frequency mean?
3. Hockey has 8 votes. Swimming has 3 votes. How many more chose hockey?
4. A class voted for a field trip: Zoo 12, Farm 4, Museum 6. What is the best decision?
5. On a bar graph, how do you find the least?
6. Votes: Pizza 6, Tacos 9, Soup 2. How many children voted altogether?
7. In a two-circle diagram, where does a name go if both things are true?
What your child is learning: to order categories from greatest to least frequency (D1.4) and to read data in graphs, tables, logbooks and diagrams, ask and answer questions, draw conclusions, and make decisions they can justify (D1.5).
Common mistakes:
- Ordering categories in the order they appear, not by size. Have your child cross off each category as it is placed.
- Confusing how many more with how many altogether. Model with towers of blocks: put the two towers side by side and count the extra blocks on top.
- In the two-circle diagram, forgetting names in the overlap. Ask: "Is Leo inside the pet circle?"
- Ties (two categories with the same number) can confuse children; tell them tied categories can go side by side.
How to help: Look at graphs in flyers, sports standings, or a weather app together. Ask "What do you notice? What do you wonder?" Always ask your child to explain decisions with "because" and a number.