Transcript Lesson 1 PPT
Name:________________________________________________________________________________Date:_____/_____/__________ Division Space: Unit 1 Spiral Back: 1. Convert 3 8 into a decimal ( set up a division problem ):______ Place a greater-than or less-than sign in the following blanks: 2.
0.4 _____ 3 8 Evaluate: 3. 3 8 _____ 3.75% 4.
144 = _____ 5. If a square has an area of 36 un 2 , what would its square root be? _________ What part of the square does the square root represent? __________________ 6.
What perfect square # does the square pictured represent? ______ What is its square root? _____ 7. Write 10 -2 as repeated multiplication:___________________________________, as a fraction:__________ and as a decimal:__________ .
Unit 2 Spiral Back (evaluate the following): 8. -25 + 5 = ___ -14 + (-6) = ___ -4 – 16 = ___ (-6)(-4) = ___ -1 – (-9) = ___ 50 −10 = ___
Unit 3 Spiral Back: 9. Evaluate the following when x = -3 and y = 4 : 2y – x + (8 + x) 2 10. Sequence 95, 80, 65, 50 . . .
1000, 200, 40, 8 . . .
Arithmetic or Geometric Common Diff. or Ratio Variable Expression
Today’s Lesson:
What: Modeling one-step addition/subtraction equations Why: To explore the meaning of an equation through an equation modeling lab.
Brainstorm . . .
What is an equation ??
Is this a true equation?
3 + 5 4 + 4
YES! Both sides equal 8 so they are balanced!
Is this a true equation?
3 + 2 1 + 3
NO! 5 is “heavier” than 4!
What does “x” have to equal in order for scale to stay balanced?
8 + x
because 8 + 2 = 10!
5 + 5
Modeling Equations Lab In this lab, we will use algebra tiles in order to model the process of solving equations! Here are the tile pieces we will use . . .
Example: x + (-2) = 3
To solve the above equation, we will isolate “x”. To do this, we need to get rid of the 2 negative tiles that are with “x”. How can we get rid of the 2 negatives?
By making zero pairs!
What is the inverse (opposite) of -2? +2 So, we will add two positives to BOTH sides of the equation because it needs to STAY BALANCED!! Watch . . .
Once the zero pairs are removed, the tiles left are the answer . . .
Let’s do #1 together . . .
1. Solve: x + 3 = 5
Step 1: Model the problem on the scale below.
What do you need to do to isolate the variable?
Add 3 negatives.
Step 2: Place the negative tiles on the mat. Remember– whatever you add to one side, you MUST add to the other side! How many zero pairs do you have on each side?
Left: 3 & Right: 3
Step 3:Take away the zero pairs (indicate this by circling them). What’s left?
2
Step 4: Check your answer by substituting answer back into original problem:
2 + 3 = 5
Your Turn . . .
You will have approximately 20 minutes to finish lab on your own. Ask questions if you have them! We will go over discussion questions together (but answer on your own first). Last, you will take an Exit Ticket, so try your best!! Tip: Use KCC for ALL subtraction equations in the lab! Good Luck! Get to work!
Let’s discuss
(after most have finished) . . .
Discussion Questions:
1. Why did we use a picture of a balance in our model?
Because both sides of equation must be equal or balanced.
2. What is the main goal when solving an equation?
Finding out what x is by isolating it.
3. Identify the main math property that we used while solving our equations.
Inverse Property of Addition (zero pairs)
4. Why are zero pairs (Inverse Property) necessary to solve an equation?
Zero pairs are necessary in order to isolate the variable.
5. Write a rule that you can use to solve an equation like x + 3 = 2 without using models.
Add the inverse of the number with x. Whatever you add to one side, must be added to the other!
Homework/ practice Due by next class!
IXL: 7
th
Grade, T.3
Exit ticket time!
The next slides are student copies of the handouts and/or supporting materials for this lesson. These were handed out in class and filled-in as the lesson progressed.
Name________________________________________________ Date: ___/___/_____
Modeling Equations Lab
( . . . to be completed AFTER initial introduction of equations!)
Objective: The purpose of this lab is to practice MODELING the process of solving an equation. The concept of “balancing” will be emphasized.
Directions
: Model each problem on your equation mats with the tiles. Then, record your work on this paper.
1. Solve: x + 3 = 5
Step 1: Model the problem on the scale below.
Golden Rule of Algebra:
Whatever you do to one side of an equation, you MUST do to the other side!!
What do you need to do to isolate the variable? ______________________
Step 2:
Place the negative tiles on the mat. Remember– whatever you add to one side, you MUST add to the other side! How many zero pairs do you have on each side? _____________
Step 3:
Take away the zero pairs (indicate this by circling them). What’s left?
x = _____ Step 4:
Check your answer by substituting answer back into original problem:
2. Solve: x – 2 = 5
Model the problem on the scale below: What do you need to do to isolate the variable? _____________________________ Place the appropriate tiles on the mat to make zero pairs. How many zero pairs do you have on each side? __________________________________________________ Take away the zero pairs (indicate this by circling them).
Write your final answer:
_____
Check your answer:
3. Solve: x – 4 = -3
Model the problem on the scale below: What do you need to do to isolate the variable? _____________________________ Place the appropriate tiles on the mat to make zero pairs. How many zero pairs do you have on each side? __________________________________________________ Take away the zero pairs (indicate this by circling them).
Write your final answer:
_____
Check your answer:
4. Solve: x + -4 = -2
Model the problem on the scale below: What do you need to do to isolate the variable? _____________________________ Place the appropriate tiles on the mat to make zero pairs. How many zero pairs do you have on each side? __________________________________________________ Take away the zero pairs (indicate this by circling them).
Write your final answer:
_____
Check your answer:
5. Solve: x + 3 = -1
Model the problem on the scale below: What do you need to do to isolate the variable? _____________________________ Place the appropriate tiles on the mat to make zero pairs. How many zero pairs do you have on each side? __________________________________________________ Take away the zero pairs (indicate this by circling them).
Write your final answer: _____ Check your answer:
6. Solve: x + 10 = -2
Model the problem on the scale below: What do you need to do to isolate the variable? _____________________________ Place the appropriate tiles on the mat to make zero pairs. How many zero pairs do you have on each side? __________________________________________________ Take away the zero pairs (indicate this by circling them).
Write your final answer:
_____
Check your answer:
7. Solve: x – (-3) = -1
Model the problem on the scale below: What do you need to do to isolate the variable? _____________________________ Place the appropriate tiles on the mat to make zero pairs. How many zero pairs do you have on each side? __________________________________________________ Take away the zero pairs (indicate this by circling them).
Write your final answer:
_____
Check your answer:
Discussion Questions:
1. Why did we use a picture of a balance in our model?
2. What is the main goal when solving an equation?
3. Identify the main math property that we used while solving our equations.
4. Why are zero pairs (Inverse Property) necessary to solve an equation?
5. Write a rule that you can use to solve an equation like x + 3 = 2 without using models. IXL: 7 th Grade, T.3
Name:__________________________________________________________ Date:____/____/_______
EXIT TICKET
1. Model the below equation on the given mat. Show the entire process, circling any zero pairs needed.
x + (-4) = -2 x = _____
2. How is the
Inverse Property of Addition
used when solving an equation?
3. In your own words, describe the
Golden Rule of Algebra.
4. Identify one thing that you learned during today’s lab/ class discussion– about the process of solving an equation.
NAME:___________________________________________________________________________ DATE: _____/_____/__________
individual practice
Draw tiles onto the below balance scales in order to model the following: 1.
x + -3 = 4 2. 3 + x = 1 3.
x = _____ x + (-2) = 2 4.
x = _____ x – 4 = -2 5.
x = _____ x – (-2) = 5 7.
x = _____ 4 + x = 3 x = _____ 6.
x = _____ x – (-5) = 3 8. x = _____ x + (-1) = -1 x = _____