Solving for a Variable Wednesday 9/21/11 - Thursday 9/22/11

Objective: Today you will learn to solve equations using concrete models and the properties of equality, select a method, and solve the equations. 


Vocabulary: formula, literal equation


After today you will know:
1. How to identify the variable to isolate.
2. How to identify the operations on this variable and the order in which they are applied.
3. How to use inverse operations to undo operations and isolate the variable.


First you will watch a video and practice
1. Solving for a Variable
2. Practice Literal Equations

Then you will watch another video and practice
1. Video
2. Practice work in station


Conversation: What is the difference between solving an equation with numbers and only one variable and a literal equation with several variables?


Evaluation: How could you check the solution to a literal equation for accuracy?

Solving Equations Monday 9/19/11 - Tuesday 9/20/11

Objective: Today you will solve linear equations using concrete models, graphs, and the properties of equality, select a method, and solve the equations.


Vocabulary: Simplify, inverse operations, solution of an equation, 


After today you will know:
1. How to simplify to solve multi-step equations (including distributive property).
2. How to combine like terms.
3. Which operation to 'undo' first.
4. How to solve multi-step equations using inverse operations.


First you will watch a video and practice
1. Equations With Variables on Both Sides
2. Algebra Balance
3. Algebra Balance with Negatives




Then you will watch a second video and practice
1. Multi-Step Equations
2. Algebra Balance
3. Algebra Balance with Negatives
4. Solving Equations with Balancing Strategy

Closure:  What is the product of any number and its reciprocal? How does that help you solve equations?

Table, Graph, Equation, and Situation Tuesday 9/20/11 - Thursday 9/22/11

Objective:You will use graphs, tables, and algebraic representations to make predictions and solve problems


Vocabulary: input, output, equation, variable


After today you will know:
1. That an equation describes the relationship between input and output values in a table, or x and y coordinates on a graphs.
2. How to relate the values in an equation to a situation.
3. How to generate a graph, table, or equation, given any of the three.

First you will explore how tables and graphs are related completing the Block Patterns activities


Then you will practice the concept at mangahigh by 
1. Complete Mangahigh Lesson Point on A Line
2. Play Save our Dumb Planet


Extension
3. Play Algebra Meltdown


Evaluation: Juan says the point (-1.5, 0) is in quadrant II. Jessica says it is in quadrant III. Who is right? Explain your thinking.

Graphing on the Coordinate Plane Monday 9/19/11

Objective: Today you will locate and name points on a coordinate plane using ordered pairs of rational numbers.


Vocabulary: coordinate plane, origin, x & y axes, quadrant, x & y coordinate, ordered pair


After today you will know:
1. How to identify the x and y axis.
2. Which value in the ordered pair is the x and y coordinate.
3. That a positive x or y value is to the right or above the origin and a negative x or y value is to the left or below the origin.
4. The quadrants I, II, III, IV.


First you will watch a Brain Pop Video

Next you will practice the concepts at the following web sites.
1. Coordinate Plane Game
2. Point Plotter
3. Stock the Shelves


Extension
4. Locate the Aliens
5. Catch the Fly
6. Co-ordinates

Academic Conversation: Why do you think the point (0, 0) is called the origin?

Compare and Order Integers

Objective: Today you will learn to compare and order integers.


You will compare and order integers.

At the end of the lesson you will be able to say "I Know":
1. That numbers to the right on a number line are always larger than numbers to the left.
2. That integers to the left of zero are the opposite values of their mirror images on the right side of zero and fall in the reverse order.


In stations you will watch a video and play a game at the following web sites:
Opposite of a Given Number
Points on a Number Line

Number Balls
Mission 2110 Negative Numbers - ascending order is least to greatest / descending order is greatest to least
Compare and Order Jeopardy
Pearl Diver

Closure: How do you compare and order positive and negative numbers?


Discussion: Do you think that there is a greatest negative number? Explain your thinking.

Integer Operations 3

Objective: Today you will select and use appropriate operations to solve problems and justify solutions with integers.


You will learn and review integer operations and solve problems.


After the lesson you will be able to say "I Know":
1. How to add and subtract integers.
2. How to multiply and divide integers.
3. Solve problems containing integers.


In this station you will explore integer multiplication with the coordinate plane.
Rectangle Multiplication

In this station you will play a game to apply integer multiplication.
Connect 4

In this station you will review all that you have learned this week.
Integer Jeopardy

Discussion: The product of two integers is -48. List the integers that might work in this situation and discuss with your partner what patterns you observe. Write what you find on the closure sheet.

Closure: Explain why the product of a negative integer and a positive integer is a negative, but the product of two negative integers is a positive.

Extension
In stations you will work through the following web sites:
Negative Numbers Activity
Tic Tac Go Integers
Algebra Meltdown

Solving Equations

Objective: Today you will use models, graphs, and the properties of equality to solve linear equations.


Vocabulary: simplify, inverse operations, solution of an equation


You will be able to say "I Know":
1. How to solve one step equations using inverse operations.
2. How to simplify to solve multi-step equations.
3. How to identify which operation to 'undo' first.
4. How to solve multi-step equations using inverse operations.


In Stations you will watch videos and work examples at the following web sites:
Linear Equations 1
1 Step Equations Matching Game


Linear Equations 2
Solving Multi Step Equations Activity 1


Linear Equations 3
Solving Multi Step Equations Activity 2- Variables on Both Sides

Synthesis: Create a multi step equation. Describe the solution steps and explain why each step is performed.

Integer Operations 2

Objective: Today you will select and use appropriate operations to solve problems and justify solutions with integers.


Vocabulary: integer, positive, negative, opposite, zero pairs or canceling


You will learn integer operations and solve problems.

After the lesson you will be able to say "I Know": 
1. The multiple meanings of the subtraction sign, including "opposite of?"
2. How to use integer chips or a number line to find the solution to an integer subtraction problem.
3. How to use a vertical number line (thermometer) to find integer differences in problem situations?


Watch this video first
Brain Pop


In stations you will work on problems at the following web sites:
Integer Number Line
Integer Number Line #2
Closure: Describe how you use a number line to find the solution to an integer subtraction problem


Integer Chips
Integer Chips #2
Closure: Describe how you use integer chips to find the solution to an integer subtraction problem


Differences in Temperatures on a Thermometer
Differences in Temperatures on a Thermometer
Closure: Describe how you use a thermometer to find the differences in temperatures

Discussion: When working with integers, how is subtraction like addition? When?
Write in your own words the rule for subtracting integers. Explain how to check your answer.

Extension:
In stations you will watch a video and work on problems at the following web sites: 
Adding Integers with Different Signs
Circle Zero
Number Line Bounce
Integer Operations Matching
Integer Expressions Activity
Challenge

Simplifying Expressions

Objective: Today you will use the commutative, associative, and distributive properties to simplify algebraic expressions.


Vocabulary: term, like terms, coefficient, constant, commutative, associative, and distributive properties


You will be able to say "I know"
1. How to use the commutative, associative, and distributive properties to simplify algebraic expressions.
2. How to apply simplifying expressions to perimeter problems.
3. How to write algebraic expressions and equations from words


In stations you will watch videos and work examples at the following sites:
Simplifying Algebraic Expressions
Simplifying Algebraic Expressions #2

Simplifying Expressions 1
Simplifying Example 2
Simplifying Example 3
Simplifying Example 4

Writing Algebraic Equations
Translate from words to algebra "5 less than twice a number"

Discussion: Consider -(a + b - c + d)
What is the effect of distributing the -1?


Application: The length of a rectangle is 4 units less than the width, w.  Write an expression for the length of the rectangle.

Integer Operations

Objective: Today you will select and use appropriate operations to solve problems and justify solutions with integers.

Vocabulary: integer, positive, negative, opposite, zero pairs or canceling

You will learn integer operations and solve problems.

After the lesson you will be able to say "I Know": 
1. That the sum of one and a negative one is zero (a zero pair)?
2. How to use integer chips or a number line to find the solution to an integer addition problem?
3. How to use a vertical number line, like a thermometer, to find integer sums in a problem situation?


In stations you will work problems at the following web sites:
Using a Number Line
Using a Number Line #2
Using a Number Line Closure answer the question on the closure sheet

Using Integer Chips 
Using Integer Chips #2
Using Integer Chips Closure answer the question on the closure sheet

Discussion: When is it possible to add two negatives and get a negative answer?


Closure: Explain in complete sentences how to add integers using a number line?


Think: How many yards must be gained after a loss of 3 yards for a total gain of 10 yards?


Is addition the same as subtraction? When? Can you write a rule describing when addition behaves like subtraction?