Understanding equations
Pre - Requisite / Translate expressions (consecutive, sum)Tape diagrams
Evaluate
Standard / 7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole number, fractions, and decimals) using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
7.EE.4: Use variables to represent quantities in real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
CC Lesson / 7.3.7
Student Learning Goal /
- Students understand that an equation is a statement of equality between two expressions.
- Students build an algebraic expression using the context of a word problem and use that expression to write an equation that can be used to solve the word problem.
Media
HW / #32
Spiral Review #9
WKSP
Find the unknown variable:
1. x – 4 = 82. 8y = 243. 9 + d = -2
Three Sisters
The ages of three sistersare consecutive integers. The sum of their ages is 4. Find their ages.
- Use a tape diagram to find their ages.
- If the youngest sister is x years old, describe the ages of the other two sisters in terms of x, write an expression for the sum of their ages in terms of x, and use that expression to write an equation that can be used to find their ages.
- Determine if your answer from part (a) is a solution to the equation you wrote in part (b).
Online Music Store
Sophia pays a membership fee for an online music store.
- If she also buys two songs from a new album at a price of each, what is the total cost?
- If Sophia purchases n songs for each, write an expression for the total cost.
c. Sophia’s friend has saved but isn’t sure how many songs she can afford if she buys the membership and some songs. Use the expression in part (b) to write an equation that can be used to determine how many songs Sophia’s friend can buy.
- Using the equation written in part (c), can Sophia’s friend buy 99 or 98songs?
Pens & Pencils
The total cost of four pens and seven mechanical pencils is . The cost of each pencil is cents.
- Let the cost of a pen be dollars. Write an expression for the total cost of four pens and seven mechanical pencils in terms of
- Write an equation that could be used to find the cost of a pen.
- Determine a value for for which the equation you wrote in part (b) is true.
- Determine a value for for which the equation you wrote in part (b) is false.
Sum it Up
What is the process you used to create an equation? What did you build first?
Describe how to determine if a number is a solution to an equation.
Name: ______Date: ______
Pre-AlgebraExit Ticket
Andrew is trying to create a number puzzle for his younger sister to solve. He challenges his sister to find the mystery number. ‘When 4 is subtracted from half of a number, the result is 5.’1. Write an equation to represent the mystery number: ______
2. Andrew’s sister’s first guess is 30. Is she correct? Why or why not?
3. What is the mystery number?
Name: ______Date: _____
Pre-AlgebraHW #32
- Find the smallest integer using a tape diagram.
- Let represent the smallest integer. Write an equation that can be used to find the smallest integer.
- Determine if each value of below is a solution to the equation in part (b).
2. / Circle all the equations below:
1 + xx + x5(x + 1) = 22.1
1 + x = 3x = 73(x + 2)
over
Review: Write the following in standard form.
3. / 2(3x – 4) / 4. / 2 + (3x – 4)5. / 2 – (3x – 4) / 6. /
Factor the following expressions.
7. / 3a + 18 / 8. / 4a + (b + a) + 9b