Using Bar Models to Make Math Visual GRADES

Using Bar Models to Make Math Visual GRADES 3 -5 January 13, 2015 COWETA COMMITTED TO STUDENT SUCCESS

Session goal and agenda Session Goal: Explore the visual representation of bar models as a tool to solve word problems and support student learning. Session Agenda: Introduction to bar models Modeling addition and subtraction Modeling multiplication and division Modeling 2 -step problems Modeling fraction problems COWETA COMMITTED TO STUDENT SUCCESS

A picture is worth a thousand words … COWETA COMMITTED TO STUDENT SUCCESS

Consider these problems … Julie has three more apples than Lucy has two apples. How many apples does Julie have? Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have? A student who attacked these problems using key words would think that the same operation is appropriate for both problems. COWETA COMMITTED TO STUDENT SUCCESS

Introduction to bar models Model drawing is a tool for representing relationships in problem situations. Model drawing is often called … Bar models Bar diagrams Strip models Tape method Tape diagrams Singapore method COWETA COMMITTED TO STUDENT SUCCESS

Why use a bar model? Pictures are worth a thousand words. Children find equations and abstract calculations difficult to understand. Bar models help to convert the numbers in a problem into pictorial images. Use of bar models helps bridge students’ learning from elementary to secondary – from arithmetic to algebra. COWETA COMMITTED TO STUDENT SUCCESS

Making connections 9 + 6 = 15 Abstract Pictorial Concrete COWETA COMMITTED TO STUDENT SUCCESS

Benefits to bar models Allows students to focus on comprehension of the problem’s situation rather than just finding numbers to crunch or just looking for a “key” word or phrase Explicitly shows the problem structure along with the known and unknown quantities Is a visual tool to help students determine the operation needed to solve the problem COWETA COMMITTED TO STUDENT SUCCESS

Developing conceptual understanding Concrete → Pictorial → Visualization → Abstract COWETA COMMITTED TO STUDENT SUCCESS

Bar model types COWETA COMMITTED TO STUDENT SUCCESS

Addition and subtraction Part-whole Comparison part whole part + part = whole – part = part larger quantity – smaller quantity = difference smaller quantity + difference = larger quantity COWETA COMMITTED TO STUDENT SUCCESS

Part-whole model Jorge and Trevor collect baseball cards. Together they have 62 cards. If Jorge has 29 cards, how many cards does Trevor have? 62 29 ? Jorge Trevor COWETA COMMITTED TO STUDENT SUCCESS

Part-whole model Another way to draw the model: 62 29 ? Jorge Trevor COWETA COMMITTED TO STUDENT SUCCESS

Part-whole model Ways to draw the model: 1. . 2. . COWETA COMMITTED TO STUDENT SUCCESS

Comparison model In the school’s art showcase, 134 girls entered their work which was 15 more than the number of boys. How many boys participated? Girls Boys 134 ? 15 COWETA COMMITTED TO STUDENT SUCCESS

Multiplication and division Part-whole one part × number of parts = whole ÷number of parts = one part whole ÷ one part = number of parts Comparison larger quantity ÷ smaller quantity = multiple smaller quantity × multiple = larger quantity ÷ multiple = smaller quantity COWETA COMMITTED TO STUDENT SUCCESS

Part-whole model Devi saved $8 a week for 5 weeks. How much did she save altogether? $8 $8 $8 ? COWETA COMMITTED TO STUDENT SUCCESS

Comparison model Mrs. Plant’s garden has 21 white flowers. Her garden has three times as many red flowers. How many red flowers are there? White flowers 21 Red flowers 21 21 21 ? = 63 COWETA COMMITTED TO STUDENT SUCCESS

Two-step problems Carla has 4 packages of silly bands. Each package has 8 silly bands in it. Abby is supposed to get 15 fewer silly bands than Carla. How many silly bands should Abby get? 32 Carla Abby 8 8 ? 8 8 15 COWETA COMMITTED TO STUDENT SUCCESS

Modeling fraction problems Part-whole Comparison COWETA COMMITTED TO STUDENT SUCCESS

Part-whole model Kelly buys 24 flowers. Two-thirds of them are pink. How many pink flowers did Kelly buy? ? 24 COWETA COMMITTED TO STUDENT SUCCESS

Part-whole model 12 12 12 ? 12 12 48 COWETA COMMITTED TO STUDENT SUCCESS

Comparison model 75 Girls 15 15 15 Boys 15 15 15 COWETA COMMITTED TO STUDENT SUCCESS

Summary Part-Whole - Model Also known as the ‘part-partwhole’ model, shows the various parts which make up a whole Comparison - Model Shows the relationship between two quantities when they are compared COWETA COMMITTED TO STUDENT SUCCESS

Solving word problems • Read the problem. • What are we trying to find? A total? A part? Are we comparing? • Draw a sketch representing the problem. • Use your diagram to solve the problem. • Write an answer sentence. • Check the answer to be sure it makes sense. COWETA COMMITTED TO STUDENT SUCCESS

Key points When building proficiency with bar model skills, start with simple accessible situations and add complexities one at a time. Develop habits of mind in students: Continue to ask, “Is there anything else I can see in my model? ” before moving on to the next sentence in the problem. Reflect on the size of bars relative to one another by asking, “Who has more? ” questions. COWETA COMMITTED TO STUDENT SUCCESS

Review … Part-whole models are more helpful when modeling situations where you are given information relative to a whole. Compare to models are best when comparing quantities. COWETA COMMITTED TO STUDENT SUCCESS

“Next step” ideas Give the children a well-labeled bar model drawing and have them work in groups to write a story problem that goes with it. Give the children a story problem, but without the question. Have the kids work with a partner to represent the situation and then write a question that could be answered. COWETA COMMITTED TO STUDENT SUCCESS

Create 2 -3 story problems that involve the same names and numbers, but different situations and a bar model drawing of each. Cut them apart and have children work in groups to match each problem with its representation, explaining why it is a match. COWETA COMMITTED TO STUDENT SUCCESS

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