Bar Modeling

Todd SmithMonroe #1 BOCEShttp://thinkmath.blog.monroe.edu/

Role of Model Drawing Strategy that can be taught and used to help students understand and solve word

problems (Provide mental models) It is the pictorial stage in the learning sequence of concrete – pictorial – abstract It develops students’ visual-thinking capabilities and algebraic thinking It integrates and reinforces higher-level thinking, computation, and mental math

strategies in a meaningful working context Bridges the gap to algebra Provides the tools students need to attack multi-step problems in a systematic approach

Connect to previous work with fractions

If 2/3 of a number is 8, what is the number?

If 4/7 of the boys in a school play sports and 32 boys play sports, how many total boys are there in the school?

Kelley buys 24 flowers. 2/3 of them are white. How many white flowers are there?

Ratio and RatesThree types Sometimes the quantities have the same units and can be represented as points on the same number line (e.g., 3 cups of apple juice and 2 cups of grape juice);- Same Units:

Part to Part Part to Whole

Other times they do not (e.g., 3 meters and 2 seconds) and have to be represented as points on different number lines- Different Units - Rates

What are Tape Diagrams and when do I use them?

Tape diagrams are best used to model ratios when the two quantities have the same units.

B a s ic R a t i o s

1. David and Jason have marbles in a ratio of 2:3. Together, they have a total of 35 marbles. How many marbles does each boy have?

2. The ratio of boys to girls in the class is 5:7. There are 36 children in the class. How many more girls than boys are there in the class?

Comparing Ratios of 3 Items

3. Lisa, Megan and Mary were paid $120 for babysitting in a ratio of 2: 3: 5. How much less did Lisa make than Mary?

Comparing 2 Different Ratios

4. The ratio of Patrick’s M & M’s to Evan’s is 2: 1 and the ratio of Evan’s M & M’s to Michael’s is 4: 5. Find the ratio of Patrick’s M & M’s to Michael’s.

Changing Ratios

5. The ratio of Abby’s money to Daniel’s is 2: 9. Daniel has $45. If Daniel gives Abby $15, what will be the new ratio of Abby’s money to Daniel’s?

6. The ratio of Jim's money to Peter's money was 4:7 at first. After Jim spent 1/2 of his money and Peter spent $60, Peter had twice as much money as Jim. How much money did Jim have at first?

Danny poured 78 liters of water into containers X,Y, and Z. The ratio of the volume of water in container X to the volume of water in container Y is 5 : 2. The ratio of the volume of water in container Y to the volume of water in container Z is 8:11.

a) How much water was poured into container X?

b)How much more water was poured into container X than container Z?

When and how do I use a double number line diagram?Double number line diagrams are best used when the quantities have different units.

Finding average rate1. It took Megan 2 hours to complete 3 pages of math homework. Assuming she works at a constant rate, if she works for 8 hours, how many pages of math homework will she complete? What is the average rate at which she works?

2. I use 3 cups of flour for 9 batches of cookies. If I have 6 cups of flour how many batches of cookies can I make? What if I have 7 cups of flour?

Two kindergarteners participated in a fund raiser event “Walk Backwards for Hunger” last weekend. John walked 2/3 of a mile and Mary walked ¾ of a mile. Together, they raised $93.50. Please find out how much money John and Mary each raised. To be fair, the amount raised is proportional to the distance walked.

A clothing store offers a 30% discount on all items in the store. Part A: If the original price of a sweater is $40, how much will it cost after the discount? Show your work.

Answer: ____________________

Part B: A shopper bought three of the same shirt and paid $63 after the 30% discount. What was the original price of one of the shirts? Show your work.

Answer: ____________________

Part C: Every store employee gets an additional 10% off the already discounted price. If an employee buys an item with an original price of $40, how much will the employee pay? Show your work.

Adding Fractions

What is 25+ 15?

Add 13+ 12

AlgebraNancy had n baseball cards she wants to give away. She gave 12 baseball cards to her brother and divided the rest of them equally among her 4 friends. How many cards did each friend receive?

There are n apples in a box but 5 apples are too green to eat. Aaron and Barry share the ripe apples in a ratio of 2:3. How many ripe apples does Barry get?

Inez and Emma collected stamps. Inez had 3 times as many stamps as Emma. Together, they had 40 stamps. How many stamps did Inez have?

Eddie had 4 times as much money as Fred. Tina had twice as much money as Fred. If Tina had $60, how much money did Eddie have?

One number is one third of another number. If the difference between the numbers is 26, find the two numbers.

Mr. King has a total of 22 animals on his farm. He has geese, chickens, and ducks. He has 3 more chickens than geese. He has 2 fewer ducks than geese. How many ducks does he have?

88 children were in swimming camp. One-third of the boys and three-sevenths of the girls wore goggles. If 34 students wore goggles, how many girls wore goggles?

Maria baked cookies. One-third of the cookies were chocolate chip, and 2/3 of the remaining cookies were peanut butter. The rest were oatmeal cookies. If she made 12 oatmeal cookies, how many total cookies did she make?