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When Do We Need an Exact Number?

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Large Numbers Around Us · Exact and approximate values · 3:13

You'll learn: Some situations need an exact number and others only a sensible approximation; the purpose decides.

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When Do We Need an Exact Number?

3:13

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When Do We Need an Exact Number?

You'll learn: Some situations need an exact number and others only a sensible approximation; the purpose decides.

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Exact and approximate values

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Use Nearest Place-Value Neighbours to Round a Number
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Use Nearest Place-Value Neighbours to Round a Number
You'll learn: Round by finding the nearest place-value neighbours and choosing the closer one.

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Estimating and comparing quantities

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Estimate a Population Change with Sums and Differences
3:19
Estimate a Population Change with Sums and Differences
You'll learn: Estimate sums and differences of large numbers to judge a change such as population growth.
Compare Large Quantities Using How Many Times
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Compare Large Quantities Using How Many Times
You'll learn: Compare large quantities by asking 'how many times as much?', not only 'how much more?'.

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Multiplication shortcuts

2

Multiply by 5, 25 or 125 Using 10, 100 or 1000
3:10
Multiply by 5, 25 or 125 Using 10, 100 or 1000
You'll learn: 5 = 10 ÷ 2, 25 = 100 ÷ 4 and 125 = 1000 ÷ 8, so multiply by a power of ten and divide: one shortcut, three cases.
Regroup Factors to Make a Large Product Easier
3:15
Regroup Factors to Make a Large Product Easier
You'll learn: Reorder and regroup factors so that pairs like 4 × 25 or 8 × 125 make a long product easy.

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Predicting product length

2

What Patterns Appear in Repeated-Digit Products?
3:14
What Patterns Appear in Repeated-Digit Products?
You'll learn: Products of repeated-digit numbers such as 11 × 11 or 111 × 111 form patterns worth predicting.
Predict a Product's Digit Count Using Smallest and Largest Cases
3:21
Predict a Product's Digit Count Using Smallest and Largest Cases
You'll learn: Bound a product between the smallest and largest numbers with the given digit counts to predict its number of digits.

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Calculations revealing large-number facts

1

What Does a Large Calculation Tell Us About a Real Quantity?
3:17
What Does a Large Calculation Tell Us About a Real Quantity?
You'll learn: Turn the result of a large calculation back into a real quantity with sensible units and judge its size.

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Estimation thought-experiments

2

Could a Lakh Buses Hold a City's Population?
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Could a Lakh Buses Hold a City's Population?
You'll learn: Use stated assumptions about bus capacity to estimate whether a lakh buses could carry a city's population.
Could You Reach the Moon in Ten Years?
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Could You Reach the Moon in Ten Years?
You'll learn: Estimate in stages, distance then speed then time, to test whether the Moon is reachable in ten years.

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Toothpick-digit exploration

1

Make the Largest and Smallest Numbers with Fixed Toothpicks
3:10
Make the Largest and Smallest Numbers with Fixed Toothpicks
You'll learn: Moving a fixed number of toothpicks changes digits; plan moves to make the largest and smallest numbers.

Next topic

Expressions and their values

2

Turn a Calculation Story into an Arithmetic Expression
3:28
Turn a Calculation Story into an Arithmetic Expression
You'll learn: Write a story's calculation as an arithmetic expression and read what each operation means.
Find the Value of an Arithmetic Expression
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Find the Value of an Arithmetic Expression
You'll learn: Evaluate an expression term by term to find its value.

Next topic

Comparing expressions through reasoning

2

Compare Two Expressions Without Calculating Everything
3:16
Compare Two Expressions Without Calculating Everything
You'll learn: Compare two expressions by tracking how their parts differ, without calculating everything.
Change an Expression While Keeping Its Value
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Change an Expression While Keeping Its Value
You'll learn: Change parts of an expression in balancing ways so its value stays the same.