Lesson Topic: Two- and Multi-Step Problems (All Operations) Lesson Objective: I can… Calculate solutions of one-step and multi-step equations by using tape diagrams, tables, and my knowledge of simplifying expressions, order of operations, and properties of equality for addition, subtraction, multiplication, and division. Check to determine if solutions make equations true. 1:47 It’s important in the real world: Remind students of behavior goal

Preview of Exit Ticket Solve the problem using tables and equations and then check your answer with the word problem: A pet store owner, Byron, needs to determine how much food he needs to feed the animals. Byron knows that he needs to order the same amount of bird food as hamster food. He needs four times as much dog food as bird food, and needs half the amount of cat food as dog food. If Byron orders 600 packages of animal food, how much dog food does he buy? Let b represent the amount of bird food. 1:50

Example 1 Juan has gained 20 lb. since last year. He now weights 120 lb. Rashod is 15 lb. heavier than Diego. If Rashod and Juan weighed the same amount last year, how much does Diego weight? Allow j to be Juan’s weight last year (in lb.) and d to be Diego’s weight (in lb.). Does your answer make sense? 1:50 Yes, if Diego weighs 85 lb., and Rashod weight 15 lb. more than Diego, then Rashod weights 100 lb., which is what Juan weighed before he gained 20 lb.

Example 2 Marissa has twice as much money as Frank. Christina has $20 more than Marissa. If Christina has $100, how much money does Frank have? Let f represent the amount of money Frank has in dollars and m represent the amount of money Marissa has in dollars. Does your answer make sense? 1:50 Yes, because if Frank has $40, then Marissa has twice this, which is $80. Then, Christina has $100 because she has $20 more than Marissa, which is what the problem stated.

Example 3 The school librarian, Mr. Marker, knows the library has 1,400 books, but wants to reorganize how the books are displayed on the shelves. Mr. Marker needs to know how many fiction, nonfiction, and resource books are in the library. He knows that the library has four times as many fiction books as resource books and half as many nonfiction books as fiction books. If these are the only types of books in the library, how many of each type of book are in the library? … 1:50

Example 3, Continued… Let’s double-check: Does the library have half as many nonfiction books as fiction books? Yes, because half of 800 is 400. 1:50 Does the library have 1400 books? Yes, because 800 + 400 + 200 = 1,400

Lesson Summary Try choosing a variable to represent the smallest number in the problem to avoid creating fractions throughout problems. Remember that using tables to solve multi-step problems is just like ratio tables – you have to multiply every column by the same number to get to the next row.

Evaluate Your Learning 4 3 2 1 How will you “Sharpen Your Saw”? 2:17

*When you’re done, turn it in and get a homework worksheet. Exit Ticket *When you’re done, turn it in and get a homework worksheet. 2:17

Exercises - Use tape diagrams to solve the problems: 2:17

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