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Course: praxis core math   >   unit 1.

## What are ratios and proportions?

What skills are tested.

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Want to join the conversation.  ## Teaching Ratio and Proportion Problem Solving Using Schema-based Instruction

Teaching Ratio and Proportion Problem Solving Using Schema-based Instruction. Asha K. Jitendra, 1 Jon Star, 2 Kristin Starosta, 3 Sheetal Sood, 3 Grace Caskie, 3 Jayne Leh, 3 Cheyenne Hughes, 3 Toshi Mack, 3 and Sarah Paskman 3 1 University of Minnesota 2 Harvard University ## Presentation Transcript

Teaching Ratio and Proportion Problem Solving Using Schema-based Instruction Asha K. Jitendra,1 Jon Star,2 Kristin Starosta,3 Sheetal Sood,3 Grace Caskie, 3 Jayne Leh, 3 Cheyenne Hughes, 3 Toshi Mack, 3 and Sarah Paskman 3 1University of Minnesota 2Harvard University 3Lehigh University Paper Presented at the 2008 Annual CEC Convention, Boston, MA

Thanks to … • Research supported by Institute of Education Sciences (IES) Grant # R305K060075-06) • All participating teachers and students (Shawnee Middle School, Easton, PA) April 4, 2008

Mathematical word problems • Represent “the most common form of problem solving” (Jonassen, 2003, p. 267) in school mathematics curricula. • Present difficulties for special education students and low achieving students Cummins, Kintsch, Reusser, & Weimer, 1988; Mayer, Lewis, & Hegarty, 1992; Nathan, Long, & Alibali, 2002; Rittle-Johnson & McMullen, 2004). April 4, 2008

Math Wars April 4, 2008

To solve word problems, • Need to be able to recognize the underlying mathematical structure • Schemas • Domain or context specific knowledge structures that organize knowledge and help the learner categorize various problem types to determine the most appropriate actions needed to solve the problem Chen, 1999; Sweller, Chandler, Tierney, & Cooper, 1990 April 4, 2008

Focus on math structure helps … • Allows for the organization of problems and identification of strategies based on the underlying mathematical similarity rather than superficial features • “This is a rate problem” • Rather than “This is a train problem” April 4, 2008

Prior research on SBI has focused on • Schema priming (Chen, 1999; Quilici & Mayer, 1996; Tookey, 1994), • Visual representations such as number line diagrams (e.g., Zawaiza & Gerber, 1993) or schematic diagrams (e.g., Fuson and Willis, 1989); Jitendra, Griffin, McGoey, Gardill, Bhat, & Riley, 1998; Xin, Jitendra, & Deatline-Buchman, 2005; Jitendra, Griffin, Haria, Leh, Adams, & Kaduvettoor, 2007; Willis and Fuson, 1988) • Schema-broadening by focusing on similar problem types (e.g., Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp & Jancek, 2003; Fuchs, Seethaler, Powell, Fuchs, Hamlett, & Fletcher, 2008; ) April 4, 2008

Our Approach • Schema-Based Instruction with Self-Monitoring • Translate problem features into a coherent representation of the problem’s mathematical structure, using schematic diagrams • Apply a problem-solving heuristic which guides both translation and solution processes Marshall (1990); Mayer (1999); Riley, Greeno, & Heller (1983) April 4, 2008

Teaching proportionality is critical … • Challenging topic for many students (National Research Council, 2001) • Current curricula typically do not focus on developing deep understanding of the mathematical problem structure and flexible solution strategies (NCES, 2003; NRC, 2001). April 4, 2008

Purpose of the study • To investigate the effectiveness of SBI-SM instruction on students’ ability to solve ratio and proportion problems. • To evaluate the outcomes for students of varying levels of academic achievement. April 4, 2008

Participants • 148 7th grade students (79 girls), in 8 classrooms, in one urban public middle school • Mean chronological age 153.12 months (range = 137.04 to 174.96; SD = 5.76). • 54% Caucasian, 22% Hispanic, 22% African American • 42% Free/reduced lunch • 15% receiving special education services and 3% ELLs April 4, 2008

Teacher Participants • 6 teachers (3 female) • (All 7th grade teachers in the school) • 8.6 years experience (range 2 to 28 years) • Three teachers had a degree in mathematics • Text: Glencoe Mathematics: Applications and Concepts, Course 2 April 4, 2008

Study Design Pretest-intervention-posttest-delayed posttest with random assignment to condition by class Four “tracks” - Advanced, High, Average, Low* *Referred to in the school as Honors, Academic, Applied, and Essential April 4, 2008

Professional Development SBI-SM teachers received one full day of PD immediately prior to unit and were also provided with on-going support during the study Understanding ratio and proportion problems Introduction to the SBI-SM approach Detailed examination of lessons Control teachers received 1/2 day PD Implementing standard curriculum on ratio/proportion April 4, 2008

Procedure - Both Conditions • Instruction on same topics • Duration: 40 minutes daily, five days per week across 10 school days • Classroom teachers delivered all instruction • Lessons structured as follows: • Students work individually to complete a review problem and teacher reviews it in a whole class format, • Teacher introduces the key concepts/skills using a series of examples • Teacher assigns homework • Students allowed to use calculators. April 4, 2008

SBI-SM Condition • Our intervention unit on ratio and proportion • Lessons scripted • Instructional paradigm: Teacher-mediated instruction - guided learning - independent practice, using schematic diagrams and problem checklists (FOPS) • Teacher and student “think alouds” April 4, 2008

SBI-SM Instructional Sequence April 4, 2008

Problem Checklist (FOPS) • Step 1. Find the problem type • Step 2: Organize the information • Step 3: Plan to solve the problem • Step 4: Solve the problem April 4, 2008

Applying SBI-SM to Solve Ratio Problems Example: The ratio of the number of girls to the total number of children in Ms. Robinson’s class is 2:5. The number of girls in the class is 12. How many children are in the class? April 4, 2008

1. Find the problem type Read and retell problem to understand it Ask self if this is a ratio problem Ask self if problem is similar or different from others that have been seen before The ratio of the number of girls to the total number of children in Ms. Robinson’s class is 2:5. The number of girls in the class is 12. How many children are in the class? April 4, 2008

2. Organize the information April 4, 2008

2. Organize the information Underline the ratio or comparison sentence and write ratio value in diagram Write compared and base quantities in diagram Write an x for what must be solved The ratio of the number of girls to the total number of children in Ms. Robinson’s class is 2:5. The number of girls in the class is 12. How many children are in the class? April 4, 2008

2. Organize the information 12 Girls x Children March 27, 2008 AERA 53.026 23

3. Plan to solve the problem Translate information in the diagram into a math equation Plan how to solve the equation April 4, 2008

4. Solve the problem Solve the math equation and write the complete answer Check to see if the answer makes sense April 4, 2008

Problem solving strategies A. Cross multiplication April 4, 2008

Problem solving strategies B. Equivalent fractions strategy “7 times what is 28? Since the answer is 4 (7 * 4 = 28), we multiply 5 by this same number to get x. So 4 * 5 = 20.” April 4, 2008

Problem solving strategies C. Unit rate strategy “2 multiplied by what is 24? Since the answer is 12 (2 * 12 = 24), you then multiply 3 * 12 to get x. So 3 * 12 = 36.” April 4, 2008

Additional problem types/schemata April 4, 2008

Control condition • Instructional procedures outlined in the district-adopted mathematics textbook April 4, 2008

Outcome Measure Mathematical problem-solving (PS) 18 items from TIMSS, NAEP, and state assessments Cronbach’s alpha 0.73 for the pretest 0.78 for the posttest 0.83 for the delayed posttest April 4, 2008

Figure 1. Sample PS Test Item If there are 300 calories in 100g of a certain food, how many calories are there in a 30g portion of this food? 90 100 900 1000 9000 April 4, 2008

Treatment Fidelity • Treatment fidelity checked for all lessons. • Mean treatment fidelity across lessons for intervention teachers was 79.78% (range = 60% to 99%). April 4, 2008

Results At pretest: SBI-SM and control classes did not differ Scores in each track significantly differed as expected: High > Average > Low No interaction April 4, 2008

Results • At posttest: • Significant main effect for treatment: SBI-SM scored higher than control classes • Low medium effect size of 0.45 • Significant main effect for track as expected • High > Average > Low • No interaction April 4, 2008

Results • At delayed posttest: • Significant main effect for treatment: SBI-SM scored higher than control classes • Medium effect size of 0.56 • Significant main effect for track as expected • High > Average > Low • No interaction April 4, 2008

Figure 1 Mathematics Problem-Solving Performance by Condition April 4, 2008

Figure 2 Mathematics Problem-Solving Performance by Condition and Students’ Ability Level Status April 4, 2008

Summary and Discussion SBI-SM led to significant gains in problem-solving skills. • A low moderate effect size (0.45) at Time 1 • A strong moderate effect (0.56) at Time 2 Developing deep understanding of the mathematical problem structure and fostering flexible solution strategies helped students in the SBI-SM group improve their problem solving performance April 4, 2008

Discussion • Three issues undermined the potential impact of SBI-SM • One high ability control classroom teacher deviated from the textbook presentation • One intervention teacher experienced classroom management difficulties • Variation in implementation fidelity • Intervention was time-based (10 days) rather than criterion-based (mastery of content) April 4, 2008

Thanks! Asha K. Jitendra (ji[email protected]) Jon R. Star ([email protected]) April 4, 2008

SBI References from our Research Team BOOKS AND CURRICULAR MATERIALS • Jitendra, A. K. (2007). Solving math word problems: Teaching students with learning disabilities using schema-based instruction. Austin, TX: Pro-Ed. • Montague, M., & Jitendra, A. K. (Eds.) (2006). Teaching mathematics to middle school students with learning difficulties. New York: The Guilford Press. April 4, 2008

SBI References from our Research Team CHAPTERS Chard, D. J., Ketterlin-Geller, L. R., & Jitendra, A. K. (in press). Systems of instruction and assessment to improve mathematics achievement for students with disabilities: The potential and promise of RTI. In E. L. Grigorenko (Ed.), Educating individuals with disabilities: IDEIA 2004 and beyond. New York, N.Y.: Springer. Xin, Y. P., & Jitendra, A. K. (2006). Teaching problem solving skills to middle school students with mathematics difficulties: Schema-based strategy instruction. In M. Montague & A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning difficulties (pp. 51-71). New York: Guilford Press. April 4, 2008

SBI References from our Research Team Journal Articles • Griffin, C. C. & Jitendra, A. K. (in press). Word problem solving instruction in inclusive third grade mathematics classrooms. Journal of Educational Research. • Jitendra, A. K., Griffin, C., Deatline-Buchman, A., & Sczesniak, E. (2007). Mathematical word problem solving in third grade classrooms. Journal of Educational Research, 100(5), 283-302. • Jitendra, A. K., Griffin, C., Haria, P., Leh, J., Adams, A., & Kaduvetoor, A. (2007). A comparison of single and multiple strategy instruction on third grade students’ mathematical problem solving. Journal of Educational Psychology, 99, 115-127. • Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem solving instruction on students with learning problems. Journal of Special Education, 39(3), 181-192. April 4, 2008

SBI References from our Research Team Journal Articles • Jitendra, A. K. (2005). How design experiments can inform teaching and learning: Teacher-researchers as collaborators in educational research. Learning Disabilities Research & Practice, 20(4), 213-217. • Jitendra, A. K., DiPipi, C. M., & Perron-Jones, N. (2002). An exploratory study of word problem-solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. Journal of Special Education, 36(1), 23-38. • Jitendra, A. K., Hoff, K., & Beck, M. (1999). Teaching middle school students with learning disabilities to solve multistep word problems using a schema-based approach. Remedial and Special Education, 20(1), 50-64. • Jitendra, A. K., Griffin, C., McGoey, K., Gardill, C, Bhat, P., & Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. Journal of Educational Research, 91(6), 345-356. • Jitendra, A. K., & Hoff, K. (1996). The effects of schema-based instruction on mathematical word problem solving performance of students with learning disabilities. Journal of Learning Disabilities, 29(4), 422-431. April 4, 2008

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Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete) Last updated

18 February 2021

• Share through email
• Share through pinterest Lesson objective: To solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.

In this lesson, students will be introduced to ratio and proportion and it will be explained that ratio shows the relative sizes of two or more values and proportion is a part, share, or number in relation to the whole.

Through an engaging powerpoint they will first learn how ratio and proportion are used in real-life contexts and will begin to write the ratio and proportion of shaded parts of shapes/ objects. They will have a go at differentiated questions before moving onto the differentiated activity sheets. 3 levels of challenge and provided along with the answer sheets.

Duration: 1- 2 hours.

This lesson is the first of 4 lessons on ratio and proportion. If you would like to purchase the rest of the BUNDLE, please click here: https://www.tes.com/teaching-resource/maths-ratio-and-proportion-year-6-12306457

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## Get this resource as part of a bundle and save up to 66%

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## Maths Term 2 Year 6 BUNDLE

This term 1 BUNDLE for Year 6 students includes lessons on the following: **Fractions, decimals and percentages:** - Dividing decimals by integers - Multiplying decimals by integers - Fraction & decimal equivalents - Multiplying and dividing decimals by 10,100,1000 - Fractions, decimals and percentages **Measures:** - Converting metric units - Converting imperial units - Problem solving with metric and imperial units - Area and perimeter - Area of triangles and parallelograms - Volume of cubes and cuboids **Ratio & Proportion:** - Ratio and proportion - Ratio and scale factor - Calculating amounts in a given ratio - Problem solving with ratio and proportion **Algebra:** - Finding the rule - Forming expressions - Using simple formulae - Enumerating possibilities of combinations of variables - Finding pairs of numbers in equations All lessons come with an interactive powerpoint presentation and relevant resources which are differentiated. Answers are also provided. These resources have been tried and tested- they are high quality and support effective teaching towards the National Curriculum objectives. If you would like to see more resources from ResourcesForYou then please visit: https://www.tes.com/teaching-resources/shop/ResourcesForYou Leave a review for this resource and send a copy of your receipt to resourcesforyou1[email protected] to receive a FREE single resource of your choice!

This sequence of lessons cover: - solving problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts. -solving problems involving unequal sharing and grouping using knowledge of fractions and multiples. -solving problems involving similar shapes where the scale factor is known or can be found. -Mix of problem solving with ratio and proportion. All lessons include an engaging powerpoint presentation and 3 levels of differentiated worksheets. Answer sheets are also provided. These lessons are aimed at Year 6 students but can easily be modified to suit Year 5 or lower KS3 students. Leave a review for this resource and send a copy of your receipt to resourcesforyou10[email protected] to receieve a FREE single resource of your choice!

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## Not quite what you were looking for? Search by keyword to find the right resource: • Preferences ## Teaching Ratio and Proportion Problem Solving Using Schema-based Instruction - PowerPoint PPT Presentation ## Teaching Ratio and Proportion Problem Solving Using Schema-based Instruction

Students allowed to use calculators. april 4, 2008. 16. sbi-sm condition ... if there are 300 calories in 100g of a certain food, how ... – powerpoint ppt presentation.

• Asha K. Jitendra,1 Jon Star,2
• Kristin Starosta,3 Sheetal Sood,3
• Grace Caskie, 3 Jayne Leh, 3 Cheyenne Hughes, 3 Toshi Mack, 3 and Sarah Paskman 3
• 1University of Minnesota
• 2Harvard University
• 3Lehigh University
• Paper Presented at the 2008 Annual CEC Convention, Boston, MA
• Research supported by Institute of Education Sciences (IES) Grant R305K060075-06)
• All participating teachers and students (Shawnee Middle School, Easton, PA)
• Represent the most common form of problem solving (Jonassen, 2003, p. 267) in school mathematics curricula.
• Present difficulties for special education students and low achieving students
• Need to be able to recognize the underlying mathematical structure
• Domain or context specific knowledge structures that organize knowledge and help the learner categorize various problem types to determine the most appropriate actions needed to solve the problem
• Allows for the organization of problems and identification of strategies based on the underlying mathematical similarity rather than superficial features
• This is a rate problem
• Rather than This is a train problem
• Schema priming (Chen, 1999 Quilici Mayer, 1996 Tookey, 1994),
• Visual representations such as number line diagrams (e.g., Zawaiza Gerber, 1993) or schematic diagrams (e.g., Fuson and Willis, 1989) Jitendra, Griffin, McGoey, Gardill, Bhat, Riley, 1998 Xin, Jitendra, Deatline-Buchman, 2005 Jitendra, Griffin, Haria, Leh, Adams, Kaduvettoor, 2007 Willis and Fuson, 1988)
• Schema-broadening by focusing on similar problem types (e.g., Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp Jancek, 2003 Fuchs, Seethaler, Powell, Fuchs, Hamlett, Fletcher, 2008 )
• Schema-Based Instruction with Self-Monitoring
• Translate problem features into a coherent representation of the problems mathematical structure, using schematic diagrams
• Apply a problem-solving heuristic which guides both translation and solution processes
• Challenging topic for many students (National Research Council, 2001)
• Current curricula typically do not focus on developing deep understanding of the mathematical problem structure and flexible solution strategies (NCES, 2003 NRC, 2001).
• To investigate the effectiveness of SBI-SM instruction on students ability to solve ratio and proportion problems.
• To evaluate the outcomes for students of varying levels of academic achievement.
• 148 7th grade students (79 girls), in 8 classrooms, in one urban public middle school
• Mean chronological age 153.12 months (range 137.04 to 174.96 SD 5.76).
• 54 Caucasian, 22 Hispanic, 22 African American
• 42 Free/reduced lunch
• 15 receiving special education services and 3 ELLs
• 6 teachers (3 female)
• (All 7th grade teachers in the school)
• 8.6 years experience (range 2 to 28 years)
• Three teachers had a degree in mathematics
• Text Glencoe Mathematics Applications and Concepts, Course 2
• Pretest-intervention-posttest-delayed posttest with random assignment to condition by class
• Four tracks - Advanced, High, Average, Low
• SBI-SM teachers received one full day of PD immediately prior to unit and were also provided with on-going support during the study
• Understanding ratio and proportion problems
• Introduction to the SBI-SM approach
• Detailed examination of lessons
• Control teachers received 1/2 day PD
• Implementing standard curriculum on ratio/proportion
• Instruction on same topics
• Duration 40 minutes daily, five days per week across 10 school days
• Classroom teachers delivered all instruction
• Lessons structured as follows
• Students work individually to complete a review problem and teacher reviews it in a whole class format,
• Teacher introduces the key concepts/skills using a series of examples
• Teacher assigns homework
• Students allowed to use calculators.
• Our intervention unit on ratio and proportion
• Lessons scripted
• Instructional paradigm Teacher-mediated instruction - guided learning - independent practice, using schematic diagrams and problem checklists (FOPS)
• Teacher and student think alouds
• Step 1. Find the problem type
• Step 2 Organize the information
• Step 3 Plan to solve the problem
• Step 4 Solve the problem
• The ratio of the number of girls to the total number of children in Ms. Robinsons class is 25. The number of girls in the class is 12. How many children are in the class?
• Read and retell problem to understand it
• Ask self if this is a ratio problem
• Ask self if problem is similar or different from others that have been seen before
• Underline the ratio or comparison sentence and write ratio value in diagram
• Write compared and base quantities in diagram
• Write an x for what must be solved
• Translate information in the diagram into a math equation
• Plan how to solve the equation
• Solve the math equation and write the complete answer
• Check to see if the answer makes sense
• A. Cross multiplication
• B. Equivalent fractions strategy
• C. Unit rate strategy
• Instructional procedures outlined in the district-adopted mathematics textbook
• Mathematical problem-solving (PS)
• 18 items from TIMSS, NAEP, and state assessments
• Cronbachs alpha
• 0.73 for the pretest
• 0.78 for the posttest
• 0.83 for the delayed posttest
• If there are 300 calories in 100g of a certain food, how
• many calories are there in a 30g portion of this food?
• Treatment fidelity checked for all lessons.
• Mean treatment fidelity across lessons for intervention teachers was 79.78 (range 60 to 99).
• SBI-SM and control classes did not differ
• Scores in each track significantly differed as expected
• High gt Average gt Low
• No interaction
• At posttest
• Significant main effect for treatment SBI-SM scored higher than control classes
• Low medium effect size of 0.45
• Significant main effect for track as expected
• At delayed posttest
• Medium effect size of 0.56
• A low moderate effect size (0.45) at Time 1
• A strong moderate effect (0.56) at Time 2
• Three issues undermined the potential impact of SBI-SM
• One high ability control classroom teacher deviated from the textbook presentation
• One intervention teacher experienced classroom management difficulties
• Variation in implementation fidelity
• Intervention was time-based (10 days) rather than criterion-based (mastery of content)
• Asha K. Jitendra (jiten001_at_umn.edu)
• Jon R. Star (jon_star_at_harvard.edu)
• BOOKS AND CURRICULAR MATERIALS
• Jitendra, A. K. (2007). Solving math word problems Teaching students with learning disabilities using schema-based instruction. Austin, TX Pro-Ed.
• Montague, M., Jitendra, A. K. (Eds.) (2006). Teaching mathematics to middle school students with learning difficulties. New York The Guilford Press.
• Chard, D. J., Ketterlin-Geller, L. R., Jitendra, A. K. (in press). Systems of instruction and assessment to improve mathematics achievement for students with disabilities The potential and promise of RTI. In E. L. Grigorenko (Ed.), Educating individuals with disabilities IDEIA 2004 and beyond. New York, N.Y. Springer.
• Xin, Y. P., Jitendra, A. K. (2006). Teaching problem solving skills to middle school students with mathematics difficulties Schema-based strategy instruction. In M. Montague A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning difficulties (pp. 51-71). New York Guilford Press.
• Journal Articles
• Griffin, C. C. Jitendra, A. K. (in press). Word problem solving instruction in inclusive third grade mathematics classrooms. Journal of Educational Research.
• Jitendra, A. K., Griffin, C., Deatline-Buchman, A., Sczesniak, E. (2007). Mathematical word problem solving in third grade classrooms. Journal of Educational Research, 100(5), 283-302.
• Jitendra, A. K., Griffin, C., Haria, P., Leh, J., Adams, A., Kaduvetoor, A. (2007). A comparison of single and multiple strategy instruction on third grade students mathematical problem solving. Journal of Educational Psychology, 99, 115-127.
• Xin, Y. P., Jitendra, A. K., Deatline-Buchman, A. (2005). Effects of mathematical word problem solving instruction on students with learning problems. Journal of Special Education, 39(3), 181-192.
• Jitendra, A. K. (2005). How design experiments can inform teaching and learning Teacher-researchers as collaborators in educational research. Learning Disabilities Research Practice, 20(4), 213-217.
• Jitendra, A. K., DiPipi, C. M., Perron-Jones, N. (2002). An exploratory study of word problem-solving instruction for middle school students with learning disabilities An emphasis on conceptual and procedural understanding. Journal of Special Education, 36(1), 23-38.
• Jitendra, A. K., Hoff, K., Beck, M. (1999). Teaching middle school students with learning disabilities to solve multistep word problems using a schema-based approach. Remedial and Special Education, 20(1), 50-64.
• Jitendra, A. K., Griffin, C., McGoey, K., Gardill, C, Bhat, P., Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. Journal of Educational Research, 91(6), 345-356.
• Jitendra, A. K., Hoff, K. (1996). The effects of schema-based instruction on mathematical word problem solving performance of students with learning disabilities. Journal of Learning Disabilities, 29(4), 422-431.

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2. 4 is to 20 as 15 is to? (Basic Math Problem)

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1. PPT PowerPoint Presentation

PowerPoint Presentation Use ratios and rates to solve real-life problems. Solve proportions. A ratio is the comparison of two numbers written as a fraction. For example: Your school's...

2. PPT PowerPoint Presentation

1. Solve problems involving ratios. 2. Solve for a missing number in a proportion. 3. Solve proportion problems. 4. Use proportions to solve for missing lengths in figures that are similar. You may use calculators in this chapter!! Ratio: A comparison of two quantities using a quotient (fraction).

3. Ratios and proportions

[Example: Part to whole] [Examples: Simplifying ratios] Equivalent ratios are ratios that have the same value. Given a ratio, we can generate equivalent ratios by multiplying both parts of the ratio by the same value. [Example] How do we use proportions?

4. PPTX PowerPoint Presentation

If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example 1: 2 . 6. 3. x. x 3. 2 . 6. 3 x. Hint: To find the value of x, multiply 3 by 3 also. 2 . 6. 3. 9. x 3 = = =

5. PPT PowerPoint Presentation

Ex 1. Ex 2. How can we apply ratios to word problems? Example 1 - The ratio of two supplementary angles is 4:11. Find the measure of each angle. 4x + 11x = 180 15x = 180 x = 12 4x = 4(12) = 11x = 11(12) = 48 132 Check: 48 + 132 = 180 and Steps for completing ratio word problems: 1. Create an equation using the ratio. 2. Solve the equation for ...

6. Ratios And Proportions Ppt Teaching Resources

Sixth Grade Ratios and Proportions Bundle - It is made up of 5 separate Powerpoint lessons on the following topics: 1 - Introduction to Ratios, 2 - Rates and Unit Rates, 3 - Finding Ratios, 4 - Plotting ratios on the coordinate plane, 5 - Solving Proportion Problems. For more information on each lesson click on the individual lessons.

7. 1

Step 1: Set up the proportion. $1.00 =$609.00 3 miles d miles Step 2: Cross multiply. 1d = 1827 Step 3: Divide 1 1 Step 4: Check answer. d = 1827. 1. Justin's car uses 40 gallons of gas to drive 250 miles. At this rate, approximately, how many gallons of gas will he need for a trip of 600 miles. 2.

8. PPT

Ratio And Proportion 1240 Views Download Presentation Ratio And Proportion. How to compare objects?. We can compare two objects by subtraction or division. We can compare these objects with their lengths. Which is big?. Which of the trees is taller?. Which is liked by all?. Uploaded on Jul 20, 2014 Dex Paxton + Follow unskilled workers

9. Proportion

Example: How many minutes are in 5 hours? To solve this problem we need a unit rate that relates minutes to hours. Because there are 60 minutes in an hour, the unit rate we choose is 60 minutes per hour. 5 hours • 60 minutes _____ 1 hour = 300 minutes ; Proportion An equation in which two ratios are equal is called a proportion . A proportion ...

10. 11.1 Problem Solving Using Ratios and Proportions

Ratios and Proportions - Powerpoint tutorial. ratios and proportions. overview…. in this tutorial you will learn about ... 120 miles 20 miles 60 gallons 1 gallon 11.1 Problem Solving Using Ratios and Proportions In a ratio, if the numerator and denominator are measured in different units then the ratio is called a rate. A unit rate is a rate ...

11. KS3: Introduction to Ratio and Proportion [Level 4/5]

Lesson 1: Introduction to Proportion Lesson 2: Introduction to Direction Proportion Lesson 3: Introduction to Ratio Lesson 4: Ratio and Proportion Problems Suitable for lower and middle set year 7's. Mostly worksheet free. Creative Commons "Sharealike" Report this resource to let us know if it violates our terms and conditions.

12. Ratio and Proportion PowerPoint (Teacher-Made)

Check out our Teaching Wiki all about how to do ratio. A brilliant whole-class activity for this subject. If you're looking for more Ratio and Proportion resources, check out this Ratio and Proportion Lesson Pack or this Warm Up PowerPoint. You could even take a look at our KS2 Solving Ratio Word Problems Worksheets.

13. PPT

11.1 Problem Solving Using Ratios and Proportions When ratios are written in this order, a and d are the extremes, or outside values, of the proportion, and b and c are the means, or middle values, of the proportion. abcd Extremes Means 5 11.1 Problem Solving Using Ratios and Proportions To solve problems which require the use of a

14. PPT

Teaching Ratio and Proportion Problem Solving Using Schema-based Instruction. Asha K. Jitendra, 1 Jon Star, 2 Kristin Starosta, 3 Sheetal Sood, 3 Grace Caskie, 3 Jayne Leh, 3 Cheyenne Hughes, 3 Toshi Mack, 3 and Sarah Paskman 3 1 University of Minnesota 2 Harvard University Slideshow 337756 by...

15. Results for solving proportions powerpoint

An introductory 12 page lesson on solving all three types of percent problems using a proportion. The lesson shows how to set up and solve the percentage problems by cross multiplying and creating an equation. 12 additional supporting slides may be used as a student worksheet will follow the 12 page lesson.

16. Ratio and proportion for GCSE

Main PowerPoint covers all aspects of ratio and proportion for GCSE (but not direct and inverse proportion): relationship between fractions and ratios dividing an amount in a ratio - inc finding the total amount and solving problems from the difference between two shares simplifying ratios by converting units expressing as 1:n

17. Maths Ratio & Proportion Year 6

-Mix of problem solving with ratio and proportion. All lessons include an engaging powerpoint presentation and 3 levels of differentiated worksheets. Answer sheets are also provided. These lessons are aimed at Year 6 students but can easily be modified to suit Year 5 or lower KS3 students.

18. Solving Proportions

Solving Proportions Warm Up Problem of the Day Lesson Presentation Pre-Algebra 2 Warm Up Find two ratios that are equivalent to each given ratio. Possible answers 10 12 20 24 3 5 1. 2. 45 30 90 60 24 27

19. PPT

3 4 Ratio word problem solving 5 Rates 6 7 Proportion word problem solving 8 9 Scale drawing word problem solving 10 Fractions and percents April 4, 2008 18 Problem Checklist (FOPS) Step 1. Find the problem type ; Step 2 Organize the information ; Step 3 Plan to solve the problem ; Step 4 Solve the problem; April 4, 2008 19 Applying SBI-SM to ...

20. ratios and proportions introduction powerpoint

Sixth Grade Ratios and Proportions Bundle - It is made up of 5 separate Powerpoint lessons on the following topics: 1 - Introduction to Ratios, 2 - Rates and Unit Rates, 3 - Finding Ratios, 4 - Plotting ratios on the coordinate plane, 5 - Solving Proportion Problems. For more information on each lesson click on the individual lessons.