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Using Bar Models to Make Math Visual

Using Bar Models to Make Math Visual. GRADES 3-5 January 13, 2015. 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

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Using Bar Models to Make Math Visual

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  1. Using Bar Models to Make Math Visual GRADES 3-5 January 13, 2015 Coweta Committed to Student Success

  2. 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

  3. A picture is worth a thousand words … Coweta Committed to Student Success

  4. Consider these problems … • Julie has three more apples than Lucy. 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

  5. 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

  6. 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

  7. Making connections 9 + 6 = 15 Coweta Committed to Student Success

  8. 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

  9. Developing conceptual understandingConcrete → Pictorial → Visualization → Abstract Coweta Committed to Student Success

  10. Bar model types Coweta Committed to Student Success

  11. Addition and subtraction Part-whole Comparison larger quantity – smaller quantity = difference smaller quantity + difference = larger quantity part part part + part = whole whole – part = part whole Coweta Committed to Student Success

  12. 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

  13. Part-whole model Another way to draw the model: 62 29 ? Jorge Trevor Coweta Committed to Student Success

  14. Part-whole model Ways to draw the model: . . Coweta Committed to Student Success

  15. 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 134 ? Boys 15 Coweta Committed to Student Success

  16. Multiplication and division Part-whole Comparison one part × number of parts = whole whole ÷number of parts = one part whole ÷ one part = number of parts larger quantity ÷ smaller quantity = multiple smaller quantity × multiple = larger quantity larger quantity ÷ multiple = smaller quantity Coweta Committed to Student Success

  17. Part-whole model • Devi saved $8 a week for 5 weeks. How much did she save altogether? $8 $8 $8 $8 $8 ? Coweta Committed to Student Success

  18. 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? 21 White flowers Red flowers 21 21 21 ? = 63 Coweta Committed to Student Success

  19. 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 8 8 8 8 Carla ? Abby 15 Coweta Committed to Student Success

  20. Modeling fraction problems Part-whole Comparison Coweta Committed to Student Success

  21. Part-whole model • Kelly buys 24 flowers. Two-thirds of them are pink. How many pink flowers did Kelly buy? 24 ? ? ? 24 Coweta Committed to Student Success

  22. Part-whole model ? 12 12 12 12 12 12 12 48 Coweta Committed to Student Success

  23. Comparison model 75 15 15 15 Girls 15 15 Boys 15 15 15 Coweta Committed to Student Success

  24. Summary • Part-Whole Model • Also known as the ‘part-part-whole’ 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

  25. 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

  26. 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

  27. 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

  28. “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

  29. 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

  30. Coweta Committed to Student Success

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