# Research Ideas

Mathematics (funded by SSHRC + Fields)

1. Infinity in my hand (gr. 3: fractions, infinity, limit)
2. Making sums of 10 (gr. 3-4: patterning, linear functions)
3. How to fence a pen (gr. 2-4: area, perimeter, optimization)
4. Where parallel lines meet (gr. 2: geometry of a sphere)
5. Probability race (gr. 2-4: probability with dice)
6. Odds and evens (gr. 2, 7: growth patterns, odds, evens)
7. Low floor, high ceiling (big ideas for young mathematicians)
8. I don't like math anymore (I love it now! - math-for-teachers)
9. Math performance (what did you do in math today?)
10. Research performance (arts-informed research dissemination)
Mathematics(funded by KNAER)
1. How much is a billion? (gr. 3: Fermi questions, social justice)
2. Math pattern trains (gr. 1-4: growth patterns, slope, linear functions)
3. Math waves around us (gr. 3-4: patterning, trigonometry)
Science
1. Cough, cough (gr. 4: pollution, social justice)
2. Eating plastic (gr. 3-4: the great plastic dump, social justice)
3. Refraction action (gr. 2-3: refraction)
4. Will it float, will it sink? (gr. 2-3: density, buoyancy)
5. Gravity's pull (gr. 2-3: gravity, density)
Peter Jaffe on violence & abuse
1. Never met a happy bully (bullying and breaking the silence)
2. The lizard in your brain (violence in the media)

# How much is a Billion?

In this activity grade 3 students explore big numbers in the contexts of:

• physical models
• Fermi questions
• children's literature
• How much is a million?
• How big is a billion?
• A chance to shine
• social justice

Their ideas, as well as feedback from parents, are used to create and perform two songs that celebrate their learning. Click on the links below to listen to their songs. See Part 11 below for the music video and lyrics.

#### Resources to support this activity

 Lesson plan Get the lesson plan (pdf) Materials cubic metre litre cubes (to model that 10 litre cubes fit along each edge of the cubic metre) chart paper, markers(for students to record and share/present ideas) Children's literature Counting on Frank (Fermi questions) - use before this activity for a playful introduction to Fermi questions such as, "How long a line can a pen draw before running out of ink?" How much is a million? (exploring the "size" of numbers) - used in Part 4 below How big is a billion? (big numbers around us; poverty; social justice) - used in Part 8 below A chance to shine (poverty; social justice) - read anytime before, during or after this activity

#### "How big is a Billion?" in Grade 3

1 - How many children fit in a cubic metre?

 Grade 3 students estimate then check how many children fit in a cubic metre. This hands-on experience helps students develop a robust mental image of a cubic metre.

2 - How many litres of milk fit in a cubic metre?

 Grade 3 students estimate then check how many litres of milk fit in a cubic metre. They discover that 1000 litres of milk fit in a cubic metre. This makes sense as a litre is defined as a cube with a side length of 10 cm. Hence, 10 litres fit along each edge of the cubic metre, and 10x10x10 = 1000. This hands-on experience helps them develop a robust mental image of (a) the size of a litre, (b) the size of a cubic metre, and (c) the number 1000.

3 - How many ping pong balls fit in a cubic metre?

 Grade 3 students estimate then check how many ping pong balls fit in a cubic metre. They discover the strategy of first estimating how many ping pong balls fit in a litre (about 18). Then they use their knowledge of the number of litres in a cubic metre (1000) to arrive at an estimate of the number of ping pong balls that might fit in a cubic metre (18 000). This hands-on experience helps them develop strategies and measurement benchmarks for estimating what might at first appear impossible measurements.

4 - Children's literature: "How much is a million?"

5 - Fermi questions

 Grade 3 students create and estimate solutions to their own Fermi questions. Fermi questions come from a physicist named Enrico Fermi who developed the quantum theory.  Fermi questions emphasize trying different approaches to solving mathematical puzzles instead of focusing on finding “the answer”.   A classic Fermi question is solved through a process of estimation, numerical reasoning, and problem-solving by multiplying a series of estimates that equal “the answer,” assuming the estimates are correct.
 The song "Help me Fermi" illustrates the nature of Fermi questions.

6 - Patterns in big numbers

 Grade 3 students compare and look for patterns in numbers that are multiples of 10, from 1 to 1 billion.

7 - Working a minimum wage

 Grade 3 students explore how long it would take to make \$1000, \$1 000 000 and \$1 000 000 000 while working at minimum wage. Did you know that it would take 50 000 years to make 1 billion dollars while working at minimum wage (assuming you saved every penny)?

8 - Issues of social justice in children's literature: "How big is a billion?"

 Grade 3 students read the story How big is a billion and explore issues of poverty and social justice.

9 - If I had a billion dollars

 Grade 3 students sing along to the song "If I had a million dollars" and write their own lyrics to the song "If I had a billion dollars" to help children living in poverty.

10 - Cross-curricular connections