Research Ideas
- News (home page)
- Random Acts of Math
Mathematics (funded by SSHRC + Fields)
- Infinity in my hand (gr. 3: fractions, infinity, limit)
- Making sums of 10 (gr. 3-4: patterning, linear functions)
- How to fence a pen (gr. 2-4: area, perimeter, optimization)
- Where parallel lines meet (gr. 2: geometry of a sphere)
- Probability race (gr. 2-4: probability with dice)
- Odds and evens (gr. 2, 7: growth patterns, odds, evens)
- Low floor, high ceiling (big ideas for young mathematicians)
- I don't like math anymore (I love it now! - math-for-teachers)
- Math performance (what did you do in math today?)
- Research performance (arts-informed research dissemination)
- How much is a billion? (gr. 3: Fermi questions, social justice)
- Math pattern trains (gr. 1-4: growth patterns, slope, linear functions)
- Math waves around us (gr. 3-4: patterning, trigonometry)
- Cough, cough (gr. 4: pollution, social justice)
- Eating plastic (gr. 3-4: the great plastic dump, social justice)
- Refraction action (gr. 2-3: refraction)
- Will it float, will it sink? (gr. 2-3: density, buoyancy)
- Gravity's pull (gr. 2-3: gravity, density)
- Never met a happy bully (bullying and breaking the silence)
- 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
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"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?"
| Grade 3 students read the story 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
| Grade 3 teacher discusses how she links this activity to media literacy and to adolescent poverty. |
11 - Students sharing their learning through song
If I had a billion dollars How much is a billion How much is a billion If I had a billion dollars I would buy them clothes They need a house for shelter |
If I had a billion dollars They need a dentist I don't like to see If I had a billion dollars |
Animation of Grade 3 students' song "If I had a billion dollars." Their math performance was also shared at the Math Performance Festival. Download the professional recording (mp3). |
A little goes a long way Save just a little every day By doing this at home It's possible to explain She learned what it means She became pretty passionate |
Save just a little every day He said how good it was Too often we are wrapped up It's never too late It's important that our kids Save just a little every day |
Grades 3 students perform the song "A little goes a long way." Song lyrics are statements made by parents after students shared with them what they learned in math. Students' song performance was also shared at the Math Performance Festival. Download the professional recording (mp3). |
12 - Let's paint a math story!
Below is an artistic representation of "How Much is a Billion?" Artistically rendered by Jin Lee Ye (Faculty of Education, UWO). Designed by George Gadanidis. Download the poster for printing.
