# [algebra] Lessons.

Some of my best lessons and ideas have been inspired by what I've seen from teachers that have shared what they've done. Maybe you'll find something useful here.

**Real Numbers**

- ๐ฎ Bojagi
- Square puzzle
- Locker Problem [Locker problem spreadsheet]
- Desmos: Approximating roots using square areas
- ๐ป Evaluating squares and square roots
- Open Middle: Decimal approximations of roots
- Line Town (spreadsheet)
- Open Middle: Rational and Irrational Roots
- ๐ป Electronic review of classifying numbers
- Four-Square: Pythagorean Intro

Notice and Wonder: Pythagorean puzzle

Desmos: Right triangles to make a square

Spreadsheet: Pythagorean Theorem Notes

3 act: Taco cart

Open middle: Pythagorean theorem

๐ป Pythagorean Theorem and solving right triangles

Open middle: Triangle Inequality [geogebra]

Find exact perimeter and area for the given figure

**Functions**

- Desmos: Function Carnival
- Lesson: Function carnival lesson (followup)
- Open Middle: Table of values function
- Desmos: Independent vs Dependent card sort
- Desmos: Function carnival part deux
- Shifting Times Tables (Nrich Maths) (Desmos version)
- ๐ฎ Make 23.
- Find a strategy that will help you win every time.
- Once you figure it out, change the game settings by making a new target number and change per turn value and create a new strategy.
- What if the target number was 625? Is your strategy the most efficient way of knowing how to win?

- Desmos: Multiple respentations of functions
- Desmos: Graphing stories

**Solving equations**

*Building equations lesson*- Open Middle: Two step equations
- solveMe Mobiles (explorer level)
- ๐ป Solving Two Step Equations
- Lesson: Counting dots
- Open Middle: Distributive property with max/min solution
- Desmos: Identifying properties used in simplifying equations
- ๐ป Solving distributive property equations (integer solutions)
- Open Middle: Like terms equation
- Lesson: Solving with variables on both sides (introducing no solution and infinite solutions as possibilities)
- ๐ป Solving multi step equations
- Extension: Make a spreadsheet that allows you to change coefficient numbers for an equation and it calculates the new solution.

**Writing equations of lines**

- Open middle:
- Desmos: Land the plane
- Lesson: All about that base
- Open middle: Maximum y-intercept and slope steepness
- Desmos: Match my line
- What can you tell me about my time at the gas station from the information below? [Slow gas pump video and receipt]
- Point-Slope Form Number Talk
- Desmos: Applications of Linear Equations
- Desmos: Marble Slide
- Lesson: Standard form equations using intercepts
- Open middle: Standard form and intercepts
- Desmos: Extended marble slide
- Open Middle: Equivalent equations
- Line of best fit exploration
- Desmos: Line of Best Fit Exploration
- Desmos: Peninsulas of Blaine

**Geometry of lines**

- Desmos graph: Overhead demo of perpendicular lines using right triangles
- Desmos: Introduction to parallel and perpendicular line equations
- Desmos: Parallel, Perpendicular or Neither Card Sort
- Open middle: Coordinates for parallel/perpendicular lines
- Open middle: Perpendicular equations through a given point
- Desmos: Writing equations to complete given quadrilaterals
- ๐ป Writing equations of a line that are parallel or perpendicular to a line through a given point
- ๐ป Parallelograms and rectangles in a coordinate grid
- Extensions:

**Systems of linear equations **

I start with an application problem focus to give students an incentive for learning faster or more efficient strategies. Students start with guess and check but we move toward a table for organizing our thinking. We look at the rate of change for each quantity that can change and the effect on the overall output values we are trying to hit. I'll ask students to guess the effect lowering the value of one variable and increasing the value of the other will have. We begin to use proportions to determine how much to lower one variable and increase the other by making the connection between the difference between each of their rates. Students will also begin to recognize which variable has to be the one to increase or decrease.

- Here is the learning progression I'd use for these related activities:
- Example Application situations related to systems of equations and students using a table method to solve systems of equations.
- Desmos: Systems of Linear Equations: Discoveries
- solveMe Mobiles and lesson
- Substitution method examples
- Work analysis
- Jerry's Furniture
- Dan Meyer's 3-Act Intro
- Fact #1: The cash is worth $62.00
- Fact #2: There are 1,400 coins
- Summary Lesson for after students are done with the 3-Act

- ๐ป Systems of equations with integer solution values.
- Open Middle: Create a system with infinite solutions
- Extension option: Digital Desmos

**Inequalities and Absolute Value**

- Desmos: Inequalities bundle
- Lesson: Inequalities and equations
- Lesson: Real world applications to introduce inequalities
- ๐ป Solving two step inequalities
- Open Middle: Create an inequality given a solution set
- ๐ป Solving inequalities with variables on both sides
- Desmos & Open Middle:
*Inequalities with variables on both sides* - Extensions:
- Desmos: Locating numbers using absolute value [Day 1 follow-up]
- Desmos: Building understanding for absolute value inequalities
- Lesson: Investigating absolute value expressions
- ๐ป Absolute Value Equations and Inequalities
- Long Jumping Activity for writing equations

**Exponents and nonlinear functions**

- Exponent Card Game
- Desmos: Avi and Benitaโs repair shop
- Desmos: Game, set flat
- Open Middle: System of arithmetic and geometric functions
- ๐ป Working with geometric sequences
- Paper folding investigation
- Desmos: Marble slide exponentials
- Open Middle: Simplifying Exponents
- Paper folding followup and exponential relationships
- ๐ป Multiplication and Division Property
*Open Middle & Desmos:*- ๐ปZero and Negative Exponents
- Connecting rules of exponents to operations w/scientific notation