Curriculum Map by James Tanton

STAGE 1 ( ~ grades 3, 4, 5)

tanton_math — 2022-11-24 14:07:23 UTC

A BRIEF HISTORY NUMBERS

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* First evidence of counting
* The counting numbers and zero
* Addition and "take away" -- mentions
* Mention even and odd numbers.
* (* Jo Boaler's number play can be good meta-messaging here)

Place Value System - base 10

tanton_math — 2022-11-24 14:15:37 UTC

* The decimal system
* Multiplication and Division
* Subtraction
* Order of operations (vinculum/parentheses)

Multi-Digit Work

tanton_math — 2022-11-24 14:16:30 UTC

* Exploding Dots (actually ... for stage 2)
* Rounding
* Estimation

The Geometry of Numbers

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* Square and Triangular Numbers
* Mathematical Expressions - seeds for algebraic expressions
* Prime and Composite numbers --> clever multiplying
* Even/Odd numbers: Parity

Area Model

tanton_math — 2022-11-24 14:20:31 UTC

* Multiplication (and division?)
* Chopping up rectangles (distributive rule)

Intuitions for Fractions

tanton_math — 2022-11-24 14:22:46 UTC

* First models
* addition, subtraction, "of", equivalence, comparison
* mixed numbers
* Basic division: 1/2 ÷ 3
* Hints of the number line

Decimals

tanton_math — 2022-11-24 14:23:36 UTC

* Introduction
* Rounding

Geometry

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* Shapes and their characteristics
* Area. Perimeter
* Volume
* Angles
* Symmetry

Measurement, Estimation, Data

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* units, metric system
* basic unit conversion
* time
* Data collection and display

OTHER TYPES OF NUMBERS

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* A focus on troublesome zero
* Opposite numbers (negative numbers)
* Might fractions actually be numbers? (Review of the models and what they hint at)
* The number line

Garden Paths

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* Fun with fractional thinking
* Seeds of probability theory

tanton_math — 2022-11-24 14:38:29 UTC

tanton_math — 2022-11-24 14:39:17 UTC

THE STORY OF NUMBERS

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STAGE 2 ( ~ grades 6, 7, 8)

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WHAT WE CHOOSE TO BELIEVE

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THE STORY SO FAR

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* Review what we "know" about the system 0, 1, 2, 3, 4, ....
* Identify basic properties of numbers that feel fundamental and "right."
* Do we want the opposite numbers to follow the same rules?
Logical consequences. (e.g. negve x negve = posve)
* Area model extended

Expressions

tanton_math — 2022-11-24 14:47:11 UTC

* Practice writing, creating, evaluating mathematical expressions
* Identifying equivalent expressions

Fractions as Numbers

tanton_math — 2022-11-24 14:52:11 UTC

* Focus on unit fractions 1/2, 1/3, /14, ... and their key property: n x 1/n = 1
* Define a/b to be a copies of 1/b: a/b = a * 1/b.
* a/b is the answer to the division problem a ÷b. so "deserve" number status.
* Defining ÷, x, +, - for fractions
* All the usual fraction content to be covered
* Recognizing (-a)/b and a/(-b) and - a/b as equivalent.
* Placing fractions on the number line.
* Distance on the number line (aka absolute value)

tanton_math — 2022-11-24 14:53:16 UTC

Math is a Language

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* For us, that language is English!
* Writing mathematical sentences (with punctuation!)
* =, > , < , and so on.
* Meaning of these in terms of balance scales:
- intuition for basic properties

What does it mean to solve an Equation?

tanton_math — 2022-11-24 14:57:04 UTC

* Deep understanding of this
* The art of solving equations

From 1 dimension to 2: Coordinate Systems

tanton_math — 2022-11-24 14:59:49 UTC

* The power of two number lines
* Scatter plots for display of data

What does it mean to Graph an Equation?

tanton_math — 2022-11-24 15:01:01 UTC

* Deep understanding
* Simultaneous equations solved graphically

Linear Equations

tanton_math — 2022-11-24 15:02:18 UTC

* Usual horrors of understanding, graphing, solving
* Pairs of linear equations
* Connect with linear regression when time comes

Fractions as Decimals

tanton_math — 2022-11-24 15:03:15 UTC

* All the usual
* Existence of irrational numbers

Proportional Reasoning

tanton_math — 2022-11-24 15:04:49 UTC

* Radically decluttered version of all this!

Exponents

tanton_math — 2022-11-24 15:06:34 UTC

* Positive integer exponents
* What are we choosing to believe?
* zeroth powers, negative powers
* square roots as powers
* Scientific Notation

Geometry

tanton_math — 2022-11-24 15:09:38 UTC

* Square roots
* Pythagorean Theorem
* More on the coordinate plane.
* Distance in 2 dimensions. (Connect to distance in 1 dimension)
* Circles and pi
* Parallelism
* Rigid motions
* Dilations
* similarity and congruence
* What we choose to believe about area and volume

Probability

tanton_math — 2022-11-24 15:12:31 UTC

* Review of garden paths
* Believing certain scenarios come with inherent probability values. (Coin: p = 1/2. Die: p = 1/6, etc.)
* Using data to estimate p

DATA continued

tanton_math — 2022-11-24 15:13:38 UTC

* Central tendency
* variation
* distributions
* sampling
* inference
* linear regression (Connect with equations of lines)

Introduction to Functions?

tanton_math — 2022-11-24 15:16:32 UTC

* Need to mull on this.
Even though many curricula do this early on, I am not sure what problem the notion of a function is solving for the student right now. (I fear this is another "Do this now because you will need to know it later on" thing.)

tanton_math — 2022-11-24 15:17:43 UTC

To do: OUTLINE PRE-KNOWLEDGE

tanton_math — 2022-11-25 18:26:27 UTC

Specify what we are presuming as pre-existing understanding and skill sets.

To do: Meld in/Place Current Strands

tanton_math — 2022-11-25 18:33:41 UTC

Place Value (PNS)
Multiplication (Aaron and Loretta)
Fractions (Hannah and Joan)
Subtraction

To Do: Flesh all this out!

tanton_math — 2022-11-25 18:35:42 UTC

* Develop topic strands
* Not every strand need begin at grade 3. Sort out progressions here.

WIDGETS +

tanton_math — 2022-11-28 20:59:18 UTC

1. Tally
2. Symbols
OTHER: Some first figurate numbers
How we count: Feynman reading story
James' Horse Counting?

WIDGET +

tanton_math — 2022-11-28 21:03:30 UTC

1. Positional notation
2. Piles and Holes