Download Foundations of Mathematical Reasoning Assignment 3.6.A

Foundations of Mathematical Reasoning
Assignment 3.6.A
Assignment for Lesson 3.6 Part A
Questions
Question 1: The table below gives dimensions of different rectangles.
Width
Length
Rectangle 1
18
120.6
Rectangle 2
23.4
156.8
Rectangle 3
33
221.1
Rectangle 4
52.2
349.7
1) Part A: Choose Proportional or Not Proportional to correctly describe the relationship
between the rectangles.
Part B: If the rectangles are proportional, give the ratio of width to length, simplified to a unit
rate. Round to the thousandths place if necessary. The ratio
width
= . If the rectangles are
length 1
not proportional, insert NP into blank.
Question 2: The table below gives dimensions of different rectangles.
Width
Length
Rectangle 1
7.4
16.2
Rectangle 2
17
45
Rectangle 3
23.4
64.2
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Foundations of Mathematical Reasoning
Assignment 3.6.A
Rectangle 4
36.2
102.6
2) Part A: Choose Proportional or Not Proportional to correctly describe the relationship
between the rectangles.
Part B: If the rectangles are proportional, give the ratio of width to length, simplified to a unit
rate. Round to the thousandths place if necessary. The ratio
width
= . If the rectangles are
length 1
not proportional, insert NP into blank.
Question 3: The table below gives dimensions of different rectangles.
Width
Length
Rectangle 1
2
12
Rectangle 2
6.7
16.7
Rectangle 3
13.5
23.5
Rectangle 4
21
31
3) Part A: Choose Proportional or Not Proportional to correctly describe the relationship
between the rectangles.
Part B: If the rectangles are proportional, give the ratio of width to length, simplified to a unit
rate. Round to the thousandths place if necessary. The ratio
width
= . If the rectangles are
length 1
not proportional, insert NP into blank.
4) In his book, Ratio: The Simple Codes Behind the Craft of Everyday Cooking, Michael
Ruhlman writes,
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Foundations of Mathematical Reasoning
Assignment 3.6.A
A culinary ratio is a fixed proportion of one ingredient or ingredients relative to another. These
proportions form the backbone of the craft of cooking. When you know a culinary ratio, it’s not
like knowing a single recipe, it’s instantly knowing a thousand. (p. xi)
One of the ratios Ruhlman gives in his book is for biscuits. The ratio of flour to fat to liquid is
3:1:2. To make enough biscuits for a family dinner, James decides he needs to use 5 cups of
flour. How much fat and liquid should he use based on Ruhlman’s ratio?
5) Nutritionists help people plan diets to improve their health. Some diets are based on a ratio of
different types of nutrients. The ratio depends on the goal of the diet. One diet uses a ratio of
9:6:5 for carbohydrates, protein and fat.
A nutritionist is developing a diet that provides 450 calories from protein per day. Find the
number of calories that should come from carbohydrates and fat.
6) In Unit 1, you learned that a statement such as 30% of voters support Candidate A can be
interpreted as 30 out of 100.
Part A: How many voters out of 1,000 support Candidate A?
Part B: How many voters out of 1,500 support Candidate A?
Part C: Is this a proportional relationship? Be prepared to explain your reasoning.
7) A staircase is made up of individual steps that should be consistent in height and
width. The height of each step is called the rise, and the width of the step is called the
run.
Part A: The staircase below is made up of four steps. Each step has a rise of 6.5" and a
run of 8.25". Find the height (H) and depth (D) of the entire staircase.
H
D
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Foundations of Mathematical Reasoning
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Part B: Builders have to follow guidelines on the rise and run of stairs when building a staircase
to meet a code. One acceptable ratio is a rise of 7-3/4 inches for a run of 9-3/4 inches. If a
builder is using this ratio to build a staircase that is 15 feet high, how deep will the staircase
need to be (d in the drawing below)? Note that the drawing does not show the correct number of
steps. Round to the nearest tenth.
15’
d
Question 8: Now, you will once again return to graphing on a coordinate plane. You
may have noticed that the two axes split the coordinate plane into four sections. These
are called quadrants and are numbered using Roman numerals as shown below.
The vertical and horizontal lines that cover the coordinate place are called gridlines.
Often short marks are often placed on the axis to show where the numbers on the scale
are placed. These are called tick marks.
For practical reasons, only a small part of the coordinate plane can be shown, but
understand that the axes can go on into infinity in all four directions. The scale of the
grid tells you which numbers are included in the portion of the plane that is shown. You
can change the scale to make graphs with very large or very small numbers.
The scale on a single axis must be consistent. In other words, if the distance between
the gridlines represents 5 units on one part of the horizontal axis, then that same
distance must always represent 5 units on that axis. However, the vertical and
horizontal axes can have different scales as in the example below. As you have seen
with other types of graphs, it is important to pay close attention to the scale.
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Foundations of Mathematical Reasoning
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Quadrant I
Quadrant II
Quadrant III
Quadrant IV
8) Indicate if each statement is true or false.
Part A: The point (–7, –5) is in Quadrant II.
Part B: The point (0, 5) lies on the vertical axis.
Part C: All the points in Quadrant IV have a positive horizontal coordinate and a
negative vertical coordinate.
Part D: The points (20, 12) and (20, 200) lie on the same horizontal line.
Part E: The distance between the tick marks on the vertical axis represents 20
units.
Hints (Not all questions will have a hint)
Hint #1: Refer to Resource Ratios and Fractions, if needed.
Hint #2: Refer to Resource Ratios and Fractions, if needed.
Hint # 3: Refer to Resource Ratios and Fractions, if needed.
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Foundations of Mathematical Reasoning
Assignment 3.6.A
Hint # 4: Refer to Resource Ratios and Fractions, if needed.
# 5: Refer to Resource Ratios and Fractions, if needed.
Hint # 6: Refer to Resource Fractions, Decimals, and Percentages, if needed.
Hint # 7: Refer to Resource Ratios and Fractions, if needed.
Hint # 8: Refer to Resource Coordinate Plane, if needed.
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