Core Connections 1 (6th Grade Mathematics)
Chapter 2: Arithmetic Strategies and Area
Learning
Example Problems:
ANSWER KEY
Targets
We are
2-6, 2-49, 2-37, and 2-79
learning to
use the
appropriate
display to
represent
data and to
be able to
read a data
display.
2-37. What is the best way to display the data below? Why? Display the data using the
method you chose.
Daily high temperature for Honolulu, Hawaii in December of 2009:
83, 83, 81, 82, 80, 83, 81, 82, 79, 83, 84, 82, 81, 81, 80, 81, 84, 80, 80, 81, 81, 82, 80,
79, 78, 80, 84, 82, 82, 81, 83
[ See dot plot below. The data is numeric, discrete, and has order to it. ]
2-49. Given the data in the table below, copy and complete the histogram below to
represent families of various sizes. Remember that data falling on a tick mark (3, 6, 9,
…) goes in the bin to the right of that mark. What range do most families fall between?
Do you see any families that are much larger or much smaller than other families?
[Descriptions will vary. Most families have between 3 and 9 members. No outliers
are apparent. ]
2-79. COMPARING WAYS TO REPRESENT DATA
Use the golf-tournament data below to complete parts (a) through (e).
Ages of golfers participating in a golf tournament:
44, 48, 40, 25, 28, 37, 29, 34, 45, 51, 43, 35, 38, 57, 50,
35, 47, 30, 63, 43, 44, 60, 46, 43, 33, 45, 42, 34, 32
a. Use the data to create a dot plot.
[ Students should notice that a dot plot is difficult to create for the given data. ]
b. Why is a dot plot not the best choice for graphing this data?
[ There are too many different values. ]
c. Create a stem-and-leaf plot for the data.
[ See plot below. ]
d. Use the stem-and-leaf plot to create a histogram for the data.
[ See histogram below. ]
d. What range of ages do most golfers fall between? Do you see any ages that are
much larger or smaller than other ages?
[ The golfers are between 30 and 50 old. There are no obvious outliers. ]
We are
2-34, 2-43, 2-46, 2-47, 2-76, and CL 2-98
learning to
calculate
the area
and
perimeter
of
rectangles
and shapes
made up of
rectangles
and
understand
reasonable
units of
each.
2-34. Assume that the shaded tiles in the large square below each have an area of one
square foot. Use this information to answer the following questions.
a. What is the total area of the shaded squares?
[ 20 square ft ]
b. What is the total area of the un-shaded squares?
[ 29 square ft ]
c. Find the total number of square feet of area in the figure in two different ways.
[ 49 squares, methods vary, but could include adding the answers from parts
(a) and (b) or multiplying the dimensions of 7 ft and 7 ft. ]
2-43 Find the area of each figure below in at least two ways. (Note that in each figure,
all of the angles are right angles.) Explain how you get your answers.
a. [ 30 square inches ] b. [ 90 square inches ]
2-46. Find the area and perimeter of the figure below. All angles are right angles. Show
all of your work.
[ The area is 59 sq cm and the perimeter is 44 cm. ]
2-47. Draw and label two different rectangles, each with perimeters of 20 units. Do the
rectangles have the same area? Explain thinking.
[ Answers vary. Typical answers: 5 5 , 4 6 , 3 7 , 2 8 ,1 9 , the rectangles will
not have the same area. ]
2-30. NATHANIEL’S PATIO
Nathaniel decided to tile his rectangular patio with square tiles. He had 14 blue square
tiles and wanted to lay them throughout the area to make a design. He set the tiles
inside the patio border as shown in the diagram below. Now he needs your help to
figure out how many white tiles (of the same size) he needs to finish the job.
a. What is the total area of Nathaniel’s patio as measured in patio tiles? With a
diagram, explain how you arrived at your answer. [ The entire patio will
require 36 patio tiles. The rectangle is 4 squares by 9 squares. ]
b. How many white tiles does he need to finish the job? You can assume that the
white tiles are the same size and shape as the blue tiles. [ 36 14 22 tiles ]
c. If the sides of the square tiles are 1 foot long, what are the dimensions (the
length and width) of Nathaniel’s patio? What is the area of the patio (using
correct units)? [ 9 feet by 4 feet, the area is 36 square feet. ]
Core Connections 1 (6th Grade Mathematics)
Chapter 2: Arithmetic Strategies and Area
Learning
Example Problems:
Targets
We are
2-55, 2-65, 2-86, and CL 2-99
learning
to
multiply
two and
three digit
numbers
using
multiple
methods
and to
interpret
products
and sums
shown in
rectangles.
2-65. Draw a generic rectangle to help you calculate each product. For each part, write:
(total dimension)(total dimension) = sum of individual area parts = total area. For
example, the diagram below shows that (12)(27) 200 40 70 14 324 .
[ See diagrams below. a: (73)(42) 2800 120 140 6 3066 ,
b: 125 81 8000 1600 400 100 20 5 10,125 ]
We are
learning
to add and
subtract
numbers
with
decimals.
2-10, 2-28, 2-59, and 2-90
2-10. Add or subtract. Remember to line up the decimal point.
a. 53.199 – 27.61 [ 25.589 ]
b. 155.96 + 56.232 [ 212.192 ]
c. 83.617 – 36.518 [ 47.099 ]
2-28. Add or subtract.
a. 9.67 49.7 5.22 [ 64.59 ]
b. 4.2 1.903 [ 6.103 ]
c. 97.135.04 [ 62.06 ]
2-59. Add or subtract.
a. 34.62 74.8 [ 109.42 ]
b. 213.09 37.2 [ 175.89 ]
c. 3.15 36.8 7 [ 46.95 ]
2-90. Add or subtract the following decimals.
a. 2.95 18.3 11 [ 32.25 ]
b. 9.2 0.375 [ 8.825 ]
c. 0.275 27.5 [ 27.775 ]
d. 90 0.903 [ 89.097 ]