Graphical Approach to solve multi-step problems Cindy and George have equal number of pencils. After...
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![Page 1: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/1.jpg)
Graphical Approach to solve multi-stepproblems
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)
![Page 2: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/2.jpg)
Graphical Approach to solve multi-stepproblems
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)
![Page 3: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/3.jpg)
Graphical Approach to solve multi-stepproblems
1): They both have equal number of pencils.
CindyGeorge
![Page 4: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/4.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge
2): George gives Cindy 30 pencils.
![Page 5: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/5.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge ?
2): George gives Cindy 30 pencils.
30
Pencils kept
Given away
![Page 6: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/6.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge ?
2): George gives Cindy 30 pencils.
30
Pencils kept
Given away
![Page 7: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/7.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge ?
2): George gives Cindy 30 pencils. Before Cindy gets more pencils, she has the same number as George.
30
![Page 8: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/8.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge
2): George gives Cindy 30 pencils.
? 30
? 30
![Page 9: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/9.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge
2): George gives Cindy 30 pencils.
? 30
? 30
![Page 10: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/10.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge ?
30? 30
2): George gives Cindy 30 pencils.
![Page 11: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/11.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge ?
30? 30
? ? ? ?
3): Now Cindy has 4 more pencils than George.
![Page 12: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/12.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge ?
? 60
? ? ? ?
3): Now Cindy has 4 more pencils than George.
![Page 13: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/13.jpg)
Graphical Approach to solve multi-stepproblems
CindyGeorge 20
20 60
20 20 20 20
3): Now Cindy has 4 more pencils than George.
Total number of pencils: 100
![Page 14: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/14.jpg)
Graphical Approach to solve multi-stepproblems
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
![Page 15: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/15.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
Pencils with Cindy: PPencils with George: P
![Page 16: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/16.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
Pencils with Cindy: PPencils with George: P
George gives Cindy 30 pencils
![Page 17: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/17.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
Pencils with Cindy: P + 30Pencils with George: P – 30
George gives Cindy 30 pencils
![Page 18: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/18.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
Cindy’s Pencil George’s Pencil
Cindy has 4 more pencils than George
=P + 30P - 30
= 4
![Page 19: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/19.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
Cindy’s Pencil George’s Pencil
=P + 30P - 30
= 4
P+30 = 4 (P-30) = 4P –120
![Page 20: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/20.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
Cindy’s Pencil George’s Pencil
=P + 30P - 30
= 4
P+30 = 4 (P-30) = 4P –120
P+30 = 4P - 120
150 = 3P
![Page 21: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/21.jpg)
Graphical Approach to solve multi-stepproblems
Algebraic Approach
150 = 3P
P = 50
The total number of pencils betweenCindy and George: 100
![Page 22: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051819/551ab87355034656628b542f/html5/thumbnails/22.jpg)
Graphical Approach to solve multi-stepproblems
Graphicalapproach
Algebraicapproach
• See Algebra steps visually.• Accessible in 4th grade
• Requires the knowledge in fractions & Ratios, and Pre- Algebra