MATH 2160 2nd Exam Review

Problem Solving and Proportional Reasoning

Problem Solving+Polya’s 4 Steps Understand the problem

What does this mean? How do you understand?

Devise a plan What goes into this step? Why is it important?

Carry out the plan What happens here? What belongs in this step?

Look back What does this step imply? How do you show you did this?

Problem Solving+Strategies for Problem Solving

Make a chart Make a table Draw a picture Draw a diagram Guess, test, and revise Form an algebraic model Look for a pattern Try a simpler version of the problem Work backward Restate the problem differently Eliminate impossible situations Use reasoning

Proportional Reasoning+Piaget Concrete

A manipulative Something I can move around and

investigate things with Semi-concrete

A picture of the things I have been moving around

If I have never moved it around before this becomes semi-abstract for me

Proportional Reasoning +Piaget

Semi-abstract Symbols or alternate representations

for my semi-concrete models Good time to use algebraic thinking

with students Abstract

Using numbers to represent all parts of the original concrete model

Proportional Reasoning+Equivalent Representations

Percents Decimals Ratios Fractions 25% = 0.25 = 25/100 = ¼ Need to be able to fill in missing

equivalent values on a table

Proportional Reasoning+ Circle Graph Representations

5/3

12.5%

1.25

All circles contain exactly 100%

Proportional Reasoning+Integer Rods

White 1 cm x 1 cm W Red 2 cm x 1 cm R Lime 3 cm x 1 cm L Purple 4 cm x 1 cm P Yellow 5 cm x 1 cm Y Green 6 cm x 1 cm G Black 7 cm x 1 cm K Brown 8 cm x 1 cm N Blue 9 cm x 1 cm B Orange 10 cm x 1 cm O

Proportional Reasoning +Integer Rods

Equivalents / Combinations

Number of Equivalents = 2n-

1

Proportional Reasoning +Integer Rods

Equivalent Fractions ½ 1/3

¼ Etc.

Proportional Reasoning +Scale Factors

Enlargement >100%Reduction <100%Original = 100%Percent = per 100

Proportional Reasoning +Types of Percent Problems A% x B = C

What is 27.37% of 123.4 to the nearest thousandth?

0.2737 x 123.4 = C C = 33.775

What percent of 785.46 is 800.03 to the nearest thousandth?

A x 785.46 = 800.03 A = 1.019 A% = 101.9%

Proportional Reasoning +Types of Percent Problems

A% x B = C 237.9% of what number is 48.37 to

the nearest thousandth? 2.379 x B = 48.37 B = 20.332

Proportional Reasoning + Bar Graphs

ALLALL graphs must have the following Title Scales Labels

Proportional Reasoning + Bar Graphs

A survey was taken and the following results were obtained from a group of 25 people: Hats = 5; Glasses = 10; Neither = ?

Proportional Reasoning + Circle Graphs

A survey was taken and the following results were obtained from a group of 25 people: Hats = 5; Glasses = 10; Neither = ?

Proportional Reasoning +Additive Models

A factory builds 500 widgets a week. They want to increase productivity by 25 widgets a week over the next 3 months. What is the factories production rate per week for any given week?

500 + 25W = P where P = Production rate and W = the number of weeks

Proportional Reasoning +Multiplicative Models

A factory builds 500 widgets a week. They want to increase productivity by 2.5% widgets a week over the next 3 months. What is the factories production rate per week for any given week?

500∙1.025W = P where P = Production rate and W = the number of weeks

Proportional Reasoning +Tangrams

Recognizing piecesWhole to partPart to wholeConservation of area

Proportional Reasoning +Tangrams Recognizing pieces

1 whole square or large square composed of 7 pieces

2 large triangles2 small triangles1 medium triangle1 small square1 parallelogram

Proportional Reasoning +Tangrams

Whole to partIf the whole tangram has an area of 36 units2, what is the area of the parallelogram?

Proportional Reasoning +Tangrams

Part to wholeIf the parallelogram and a small triangle have an area of 3/8 units2, what is the area of the whole large square?

Test Taking Tips Get a good nights rest before the exam Prepare materials for exam in advance

(scratch paper, pencil, and calculator) Read questions carefully and ask if you

have a question DURING the exam Remember: If you are prepared, you

need not fear