Bar Model/Tape Diagrams Raising Student Achievement Conference Monday, Dec. 5, 2016 Turquoise Room A 10:15-11:15 a.m. Donna Potaczek Geneva CUSD #304 dpotaczek@geneva304.org

Does this drive you crazy??

What are tape diagrams? A “thinking tool” that allows students to visually represent a mathematical problem and transform the words into an appropriate numerical operation A tool that spans different grade levels

Background Information Diagnostic tests on basic mathematics skills were administered to a sample of more than 17,000 Primary 1 – 4 students These tests revealed: that more than 50% of Primary 3 and 4 students performed poorly on items that tested division 87% of the Primary 2 – 4 students could solve problems when key words (“altogether” or “left”) were given, but only 46% could solve problems without key words Singapore made revisions in the 1980’s and 1990’s to combat this problem – The Mathematics Framework and the Model Method The Singapore Model Method, Ministry of Education, Singapore, 2009 2nd bullet: -indicated that primary school students had not been able to master the basic skills of math -raised concern over low attainment scores and called for a major review/revamping of teaching approaches and instructional materials What resulted was the Math Framework & Model Method, otherwise known as “Singapore Math” These instructional techniques are thought of as an innovation in learning and teaching math…this ain’t your mama’s math class, folks Purpose of the Model Method: Students learn to solve not only basic word problems, but also open-ended and real-world problems These problems facilitate both the acquisition and application of basic mathematical skills and concepts as well as the development of mathematical thinking Distinguishing features of Singapore Math are: -students draw pictoral representations of math qualities (both known & unknown) their relationships to one another (part vs whole) In order to visualize and solve problems for general operations, as well as fractions, ratios, and percents The framework for drawing diagrams has recently been integrated into algebraic thinking

Why use tape diagrams? Modeling vs. Conventional Methods A picture (or diagram) is worth a thousand words Convert the numbers in a problem into pictorial images Convert problem situations into relevant mathematical expressions (number sentences) Bridges the learning from arithmetic method to algebraic method

Connect to Number Bonds 10 253 ? 8 2 134

Practice #1

119 students took part in an art competition 119 students took part in an art competition. If 19 more girls attended the competition than boys, how many boys attended the art competition? ? 19 119

Practice #2 Together, Anthony and Sarah have 36 baseball cards. Sarah has 6 more cards than Anthony. How many baseball cards does Anthony have?

5 x 8.

Practice #3

9 is ¾ of what number?

Practice #4

Ratio and Proportions

One unit: 48 ÷ 6 = 8 Five units: 5 x 8 = 40 The ratio of the height of a rectangle to its width is 6:5. If the height of the rectangle is 48 centimeters, what is its width? One unit: 48 ÷ 6 = 8 Five units: 5 x 8 = 40 The width is 40 units.

The ratio of boys to girls at the school play was 3:2 The ratio of boys to girls at the school play was 3:2. Lexi counted 14 girls. How many children were at the school play altogether? One unit: 14 ÷ 2 = 7 All units: 5 x 7 = 35 There were 35 children at the school play.

Practice #5 Derek and Grace shared some comic books in the ratio 2:3. Grace had 36 comic books. How many more comic books did Grace have than Derek?

Resources: Math Playground website

Resources: books

Would this drive you crazy??

Step One All Tarts

Step Two All Tarts

Step Three All Tarts

Step Four All Tarts

Step Five

Step Six

Bar Model/Tape Diagrams Raising Student Achievement Conference Donna Potaczek Geneva CUSD #304 dpotaczek@geneva304.org