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Why Counting Numbers Are Not Enough for Subtraction

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The World of Numbers · Counting and the origins of numbers · 3:22

You'll learn: Test closure under addition and subtraction and motivate larger number systems.

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Why Counting Numbers Are Not Enough for Subtraction

3:22

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Why Counting Numbers Are Not Enough for Subtraction

You'll learn: Test closure under addition and subtraction and motivate larger number systems.

Now playing

Same topic

Counting and the origins of numbers

4

Counting Before Numerals: Match One Object to Another
3:26
Counting Before Numerals: Match One Object to Another
You'll learn: Explain one-to-one correspondence and why counting numbers were needed.
Tally Marks, Grouping and the History of Counting
3:36
Tally Marks, Grouping and the History of Counting
You'll learn: Explore the chapter’s bone-tally examples and the need for larger-number notation.
Trade Ratios and Prime-Number Groups
3:26
Trade Ratios and Prime-Number Groups
You'll learn: Apply counting to a trade ratio and identify the property of a numerical group.
Count to Twelve on One Hand
3:30
Count to Twelve on One Hand
You'll learn: Explain the finger-joint counting method and its connection with base twelve.

Next topic

Zero and integers

6

Zero as a Placeholder and as a Number
3:35
Zero as a Placeholder and as a Number
You'll learn: Distinguish an empty place in numeral notation from zero as a quantity used in arithmetic.
What Happens When We Calculate with Zero?
3:22
What Happens When We Calculate with Zero?
You'll learn: Explain a−a=0, a+0=a, a−0=a and a×0=0.
Debts and Fortunes: Why We Need Negative Numbers
3:21
Debts and Fortunes: Why We Need Negative Numbers
You'll learn: Introduce negative values, zero and positive integers on one number line.
Add and Subtract Integers with Meaning
3:33
Add and Subtract Integers with Meaning
You'll learn: Interpret signed changes and subtraction of a negative amount.
Why Does a Negative Times a Negative Become Positive?
3:40
Why Does a Negative Times a Negative Become Positive?
You'll learn: Explain the chapter’s signed multiplication rules, then apply integer division.
Track Temperature Changes and a Trader’s Balance
3:40
Track Temperature Changes and a Trader’s Balance
You'll learn: Translate a sequence of changes into an integer calculation.

Next topic

Rational numbers and arithmetic

5

From Parts of a Whole to Rational Numbers
3:24
From Parts of a Whole to Rational Numbers
You'll learn: Define p/q with integer numerator and non-zero integer denominator. Include negative fractions and integers.
Different Fractions Can Name the Same Number
3:32
Different Fractions Can Name the Same Number
You'll learn: Generate equivalent signed fractions and reduce to lowest terms.
Check Fraction Equality with Cross Products
3:12
Check Fraction Equality with Cross Products
You'll learn: Use ad=bc to check equality when denominators are non-zero.
Add and Subtract Rational Numbers
3:36
Add and Subtract Rational Numbers
You'll learn: Find a common denominator, combine signed numerators and simplify.
Multiply and Divide Rational Numbers
3:31
Multiply and Divide Rational Numbers
You'll learn: Multiply numerators and denominators and divide by a non-zero fraction using its reciprocal.