good grief, ratios?!?! lisa herron – cypress bay high school josh cross – west broward high...

Good Grief, Ratios?!?!Lisa Herron – Cypress Bay High SchoolJosh Cross – West Broward High School

Jessica Flint – West Broward High SchoolVenessa Smith – Blanche Ely High School

What is a Ratio?A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities.

3

2

Example: What is the ratio of students to pizza slices?

The Ratio Is:

2:3 or or

€

2

3

€

0.6

Two students TO three slices of pizza.

Or there is 1 student to 1 ½ pizza slices?

Is 2:3 the same as 1:1.5?

Take another look…

€

2

3

?

= 1

1.5

€

Students

Pizza

€

= 2

3

€

= 2

3⋅1 2

1 2

€

= 1

3 2

€

= 1

1.5

It is often easiest to solve problems when the unit ratio is known.

This is called the unit ratio.

€

2

3 =

1

1.5

Which row will give the students the most pizza?

Students : Pizza

€

2 : 3

€

2 : 2

€

3 : 2

€

3 : 4

€

4 : 3

€

1:1.5

€

=

€

1:1

€

=

€

1: 0.6

€

=

€

1:1.3

€

=

€

1: 0.75

€

=

€

4 : 6

€

1:1.5

€

=

ANSWER: A & F

Same Ratio?

€

2

3

€

4

6If two ratios are equal then we have a

proportion.

€

= 2

3

Proportions & Algebra

How many ice cream cones should be in row B to have same ratio as row A?

Solution

The ratio of students to ice cream is 1:2.

In row B there are 3 students:

Proportions & Algebra

So, we need 6 ice cream cones to have the same ratio in A and B.

x

3

4

2

Algebraically

x

3

2

1

x

111

2

1

6

3

2

1

6x

222

111

2

1

Ratios in the Classroom

M&M Activity

1. Place M&M candies along the diameter and circumference of each circle. You may have to bite an M&M to get an exact fit.

2. Count the number of M&M’s and fill in the table below. Write the ratio as a decimal.

3. Calculate the average ratio of the 4 circles.

Ratios in the Classroom

M&M Activity

4. What can be said about the ratio between the circumference and diameter of a circle?

M&M Activity

5. If the circumference of the Earth is 40,075.02 KM, and the diameter is 12,756.2 KM, how many M&Ms would be needed to go around the Equator?

What is Scaling?

Applications of Ratios

- Scaling is a linear transformation that enlarges or diminishes objects.

- For similar figures, a scale factor is used to make this transformation.

- A scale factor is the number by which each dimension of the original object is multiplied to find the corresponding dimension of the model.

The scale factor for HO scale trains is 1:87.

Disney’s Haunted Mansion.

The map on the right shows boththe unit ratio and the scale used.

Scaling is used…

Scaling Activity

1. Measure the length and width of the picture.

2. Find the side length of one square in the picture.

3. Measure the length and width of the graph paper.

4. What scale is needed to completely fill the graph paper with the Snoopy picture?

Scaling Activity

5. At the top of the Snoopy picture page label the boxes alphabetically A-H. On the left side of the page, label the boxes vertically from 1-11.

6. On the graph paper label the boxes in the same manner.

7. On the graph paper, enlarge the Snoopy Picture by reproducing each corresponding box.

8. After you sketch the entire drawing, use a pen to outline your drawing. You may also wish to color your drawing.

Geogebra Activity

Sunshine State Standards

Grade 6 Grade 7 Grades 9 - 12

Big Idea 1

Big Idea 2Big Idea 2

Big Idea 1 Strand 2: Polygons

Strand 4: Triangles

Strand 6: Circles

Big Idea1: Develop an understanding of and fluency with multiplication and division of fractions and decimals.

SSS – Grade 6

Code Benchmark

MA.6.A.1.1

Explain and justify procedures for multiplying and dividing fractions and decimals.

SSS – Grade 6

Big Idea2: Connect ratio and rates to multiplication and division.

Code Benchmark

MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems.

MA.6.A.2.2 Interpret and compare ratios and rates.

SSS – Grade 7Big Idea1: Develop an understanding of and apply proportionality, including similarity.

Code Benchmark

MA.7.A.1.1Distinguish between situations that are proportional or not proportional and use proportions to solve problems.

MA.7.A.1.6Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed.

SSS – Grade 7

Code Benchmark

MA.7.A.5.1Express rational numbers as terminating or repeating decimals.

Supporting Idea 5: Numbers and Operations

SSS – Geometry 9-12

Code Benchmark

MA.912.G.2.4

Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry

Standard 2: Polygons

SSS – Geometry 9-12

Standard 4: Triangles

Code Benchmark

MA.912.G.4.4Use properties of congruent and similar triangles to solve problems involving lengths and areas.

MA.912.G.4.5 Apply theorems involving segments divided proportionally.

MA.912.G.4.8Use coordinate geometry to prove properties of congruent, regular, and similar triangles.

SSS – Geometry 9-12

Standard 6: Circles

Code Benchmark

MA.912.G.6.2

Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

MA.912.G.6.5

Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.