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Graphical Approach to solve multi-step problems Cindy and George have equal number of pencils. After George gives 30 pencils to Cindy, she has 4 times as many pencils as George. How many pencils do they have altogether? Based on 70 Must Know Word Problems, Level 4 (Singapore: Singapore Asian Ltd., 2009)

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Graphical Approach to solve multi-step problems Cindy and George have equal number of pencils. After George gives 30 pencils to Cindy, she has 4 times as many pencils as George. How many pencils do they have altogether? Based on 70 Must Know Word Problems, Level 4 (Singapore: Singapore Asian Ltd., 2009)

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Graphical Approach to solve multi-step problems 1): They both have equal number of pencils. Cindy George

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Graphical Approach to solve multi-step problems Cindy George 2): George gives Cindy 30 pencils.

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Graphical Approach to solve multi-step problems Cindy George ? 2): George gives Cindy 30 pencils. 30 Pencils kept Given away

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Graphical Approach to solve multi-step problems Cindy George ? 2): George gives Cindy 30 pencils. 30 Pencils kept Given away

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Graphical Approach to solve multi-step problems Cindy George ? 2): George gives Cindy 30 pencils. Before Cindy gets more pencils, she has the same number as George. 30

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Graphical Approach to solve multi-step problems Cindy George 2): George gives Cindy 30 pencils. ?30?

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Graphical Approach to solve multi-step problems Cindy George 2): George gives Cindy 30 pencils. ?30 ?

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Graphical Approach to solve multi-step problems Cindy George ? 30 ? 2): George gives Cindy 30 pencils.

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Graphical Approach to solve multi-step problems Cindy George ? 30 ? ???? 3): Now Cindy has 4 more pencils than George.

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Graphical Approach to solve multi-step problems Cindy George ? ?60 ???? 3): Now Cindy has 4 more pencils than George.

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Graphical Approach to solve multi-step problems Cindy George 20 60 20 3): Now Cindy has 4 more pencils than George. Total number of pencils: 100

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Graphical Approach to solve multi-step problems Cindy and George have equal number of pencils. After George gives 30 pencils to Cindy, she has 4 times as many pencils as George. How many pencils do they have altogether? Algebraic Approach

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Graphical Approach to solve multi-step problems Algebraic Approach Pencils with Cindy: P Pencils with George: P

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Graphical Approach to solve multi-step problems Algebraic Approach Pencils with Cindy: P Pencils with George: P George gives Cindy 30 pencils

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Graphical Approach to solve multi-step problems Algebraic Approach Pencils with Cindy: P + 30 Pencils with George: P – 30 George gives Cindy 30 pencils

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Graphical Approach to solve multi-step problems Algebraic Approach Cindy’s Pencil George’s Pencil Cindy has 4 more pencils than George = P + 30 P - 30 = 4

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Graphical Approach to solve multi-step problems Algebraic Approach Cindy’s Pencil George’s Pencil = P + 30 P - 30 = 4 P+30 = 4 (P-30) = 4P –120

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Graphical Approach to solve multi-step problems Algebraic Approach Cindy’s Pencil George’s Pencil = P + 30 P - 30 = 4 P+30 = 4 (P-30) = 4P –120 P+30 = 4P - 120 150 = 3P

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Graphical Approach to solve multi-step problems Algebraic Approach 150 = 3P P = 50 The total number of pencils between Cindy and George: 100

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Graphical Approach to solve multi-step problems Graphical approach Algebraic approach See Algebra steps visually. Accessible in 4 th grade Requires the knowledge in fractions & Ratios, and Pre- Algebra

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