Year Five - Thinking in Powers of 10
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About this Big Idea
In this Big Idea students compare very large numbers and very small numbers by visualising the effect of multiplying and dividing by powers of ten.
Understanding Goals:
Students will understand:
- that numbers can be used to represent things which are very big and very small
- the effect of multiplication by powers of 10
Background:
Students need to develop an understanding of place value relationships, such as 10 thousand = 100 hundreds = 1000 tens = 10 000 ones.
Core Content from the Syllabus:
Working Mathematically
Number
- apply an understanding of place value and the role of zero to read and write numbers of any size
- state the place value of digits in numbers of any size
- arrange numbers of any size in ascending and descending order
Multiplication & Division
- use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples
Fractions, Decimals & Percentages
- compare and order unit fractions
- express thousandths as decimals
- recognise the number patterns formed when decimals are multiplied and divided by 10, 100 and 1000
- multiply and divide decimals by 10, 100 and 1000
- Make connections between equivalent fractions, decimals and percentages
Measurement & Geometry
- identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems
Language:
- multiply, multiplied by, product, multiplication, thousands, hundreds, tens, ones, multiple, power, factor, divide, divided by, quotient, division, fraction, decimal, equals, estimate.
Connected to:
Mindset Mathematics Learning Activities
Visualise
Students explore the relationship between powers of 10 from 1/1000 to 1,000 by creating visual references, beginning with a student's height as the unit. Groups present their findings using objects, drawings, and photos, and by marking physical spaces in the classroom and school. - See page 225
Questions for reflection:
- How did you find your values? What strategies did you develop? How did you use tools to support your work?
- How did you think about moving from 1/10 to 1/100 to 1/1000 of the unit? What challenges did you face?
- How did you think about moving from 10 to 100 to 1,000 times the unit? What challenges did you face?
- What relationships did you notice? What surprised you?
- What surprised you about the values you explored? How are these numbers related?
Play
Students play with representing powers of 10 using small everyday objects and comparing the space taken up by 10, 100, 1,000, or more of those objects. They create ways of representing these quantities and of thinking about what 1/10 or 1/100 of a small object might look like. The class compares how these values, from 1/100 to 1,000 and beyond, look when the units are different sizes. - See page 233
Questions for reflection:
- Which units were the most interesting or challenging to work with? Why?
- All of our units were small, but they weren't the same size. How did the size of the unit affect what the values looked like?
- How was exploring space different from exploring with length? How was exploring with a large unit (a person) different from exploring with a small unit? How did it change your thinking about these values?
- What quantity or representation surprised you the most? Why?
Investigate
In this investigation, we name the numbers we have been learning about as “powers of 10” and investigate the meaning of very large and small powers of 10. Small groups choose a power of 10 and construct a museum exhibit to make their number's meaning clear, and the class stages a Museum of the Very Large and Small for visitors. - See page 239
Questions for reflection:
- What did you learn from making your exhibit? What did you learn from the other exhibits?
- Look at what people wrote that surprised them. What patterns do you notice? What did our visitors learn?
- Look at what people were wondering. What kinds of questions were visitors still thinking about? What are the most intriguing questions? What might be worth exploring?
- What did you learn from the museum that you think will be most useful to you in the future? Why?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
