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What Patterns Appear in Repeated-Digit Products?

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Large Numbers Around Us · Predicting product length · 3:14

You'll learn: Products of repeated-digit numbers such as 11 × 11 or 111 × 111 form patterns worth predicting.

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What Patterns Appear in Repeated-Digit Products?

3:14

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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.

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Predicting product length

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Predict a Product's Digit Count Using Smallest and Largest Cases
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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

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What Does a Large Calculation Tell Us About a Real Quantity?
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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

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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

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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.

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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
3:11
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
3:17
Change an Expression While Keeping Its Value
You'll learn: Change parts of an expression in balancing ways so its value stays the same.

Next topic

Brackets and meaning

2

How Do Brackets Change a Calculation's Meaning?
3:09
How Do Brackets Change a Calculation's Meaning?
You'll learn: Brackets group quantities, so the same numbers with different brackets can mean different calculations.
Evaluate a Bracketed Expression One Group at a Time
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Evaluate a Bracketed Expression One Group at a Time
You'll learn: Evaluate the bracketed groups first, then combine the results.

Next topic

Identifying terms

2

Rewrite Subtraction as Addition of an Opposite
3:25
Rewrite Subtraction as Addition of an Opposite
You'll learn: Subtracting a number is the same as adding its opposite, which turns expressions into sums of terms.
Identify Whole Terms Before Evaluating an Expression
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Identify Whole Terms Before Evaluating an Expression
You'll learn: Products and quotients form single terms; identify the terms first, then add them.

Next topic

Swapping and grouping terms

2

Reorder Signed Terms Without Changing Their Value
3:29
Reorder Signed Terms Without Changing Their Value
You'll learn: Signed terms can be added in any order and grouping without changing the value.
When Does Swapping Numbers Change an Expression?
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When Does Swapping Numbers Change an Expression?
You'll learn: Swapping numbers inside a subtraction or division changes the value; swapping whole signed terms does not.