Systems of Linear Equations

Lesson 7

Math

Unit 6

8th Grade

Lesson 7 of 11

Objective


 Solve real-world and mathematical problems using linear systems and substitution.

Common Core Standards


Core Standards

  • 8.EE.C.8.C — Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Foundational Standards

  • 8.EE.C.7
  • 8.F.B.4

Criteria for Success


  1. Use two equations in two variables to represent real-world situations.
  2. Solve a system of equations using substitution.
  3. Interpret a solution to a system in context of a situation. 

Tips for Teachers


  • This is the third of three lessons on substitution. In Lesson 7, students apply the substitution strategy to model and solve real-world applications of linear systems (MP.4).
  • A common application that can be solved with systems of equations involves situations with more than one total. Anchor Problem #1 describes a total number of legs and heads, and Anchor Problem #2 can be solved by using the total number of coins and the total amount of money. 
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Anchor Problems


Problem 1

Farmer Joe has cows and chickens on his farm. He poses a riddle to his neighbor, saying, "On all the cows and chickens on my farm, I counts 76 legs and 24 heads. How many cows and how many chickens do I have on my farm?"

Answer the farmer's riddle using a system of equations. 

Guiding Questions

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Problem 2

a.   Watch the Act 1 video from Coin Counting by Dan Meyer. For each question below, write an answer that is wrong and write your best guess. 

  1. How much cash do you think that is?
  2. How many coins do you think there are? 

b.   Your teacher will provide you with some additional information about the situation. Use the information to determine how many of each coin there is.

c.   Watch the video answer.

Was your answer reasonable? 
 

Guiding Questions

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References

101Questions Coin Counting

Coin Counting by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed March 10, 2017, 4:26 p.m..

Problem Set

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Target Task


Maya buys greeting cards to give to her friends at school. She buys some greeting cards that cost $2.50 each and some greeting cards that cost $4 each. She buys 12 cards in all for a total of $40.50. How many greeting cards that cost $2.50 did Maya buy?

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 6

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Lesson 8

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Analyze & Solve Systems of Equations Graphically

Topic B: Analyze & Solve Systems of Equations Algebraically

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