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194 Unit 3 Linear Measures and Area
Advance PreparationFor Part 1, tape two square pattern blocks together to form a double-thick block; do the same with two triangle
and two trapezoid pattern blocks. For the Line Plot activity in Part 2, draw a line plot on the board and add
stick-on notes as shown in Part 2.
For the optional Enrichment activity in Part 3, make 10 copies of Math Masters, page 414. Tape them together
to form a grid scroll. Number the rows 2 through 12. Display this scroll on the board or a wall where children
can reach it.
For the optional Extra Practice activity in Part 3, obtain a copy of Probably Pistachio by Stuart J. Murphy
(HarperCollins Publisher, 2001).
Teacher’s Reference Manual, Grades 1–3 pp. 118 –128
Key Concepts and Skills• Collect and organize data in a tally chart.
[Data and Chance Goal 1]
• Use probability terms to describe the
likelihood of an event.
[Data and Chance Goal 3]
• Predict the outcome of a probability
experiment and conduct a probability
experiment.
[Data and Chance Goal 4]
Key ActivitiesChildren perform an experiment in which they
determine the likelihood that a block will land
on an edge when tossed. They determine
whether doubling the thickness of a block
changes the likelihood.
MaterialsMath Masters, p. 70
Home Link 3 �4
pattern blocks: triangles, squares, and
trapezoids � tape � slate � Class Data Pad
(optional)
Displaying Shoe Lengths on a Line PlotMath Journal 1, p. 64
Student Reference Book, pp. 89A
and 89B
stick-on notes
Children create a class line plot for
shoe lengths.
Math Boxes 3 � 5Math Journal 1, p. 66
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 5. [Patterns, Functions, and Algebra Goal 4]
Home Link 3 � 5Math Masters, p. 69
Children practice and maintain skills
through Home Link activities.
ENRICHMENTPredicting the Results of Rolling 2 DiceMath Masters, p. 414 (See Advance
Preparation.)
per partnership: 2 dice, paper � tape �
colored markers
Children predict the results of rolling two dice
and then test their predictions.
EXTRA PRACTICE
Using Probability Terms Children read Probably Pistachio and
discuss probability.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
A Pattern-Block TossExperiment
Objective To guide children as they collect, tabulate, and
interpret experimental data.
�������
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
194_EMCS_T_TLG1_G3_U03_L05_576809.indd 194194_EMCS_T_TLG1_G3_U03_L05_576809.indd 194 2/11/11 1:41 PM2/11/11 1:41 PM
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASS ACTIVITY
NOTE The authors of Everyday Mathematics feel it is important to use correct
terminology. Sometimes, however, it is necessary to simplify language to prevent
confusion. For this reason, the authors choose to refer to the narrow side (or
narrow face) of a pattern block in this lesson as an edge.
Have children vote for the shape they believe is most likely to land on an edge. Tally their votes. Save the tally chart to compare to children’s experimental results.
� Performing a Pattern-Block SMALL-GROUP ACTIVITY
Toss Experiment(Math Masters, p. 70)
Children conduct an experiment to determine which of three pattern-block shapes is most likely to land on an edge (narrow side) after being tossed into the air. They toss a block of each shape a sufficient number of times (at least 50) to obtain reliable results.
As part of the experiment, children also toss a double-thick block of each shape. They determine whether doubling the thickness changes the chance of the block landing on an edge.
Show children the six blocks that will be used in the experiment: the three single blocks and the three taped, double-thick blocks. Ask children to help you plan this experiment. In order to compare results easily, each of the six blocks should be tossed the same number of times.
Lesson 3�5 195
Getting Started
Math Message Suppose you toss three pattern blocks into the air—a triangle , a square , and a trapezoid . Which one has the best chance of landing on one of its edges?
Home Link 3�4 Follow-Up Briefly go over the answers. Ask children if the areas of the polygons in Exercise 1 are the same. no Have a few children explain their thinking.
Mental Math and ReflexesOn your slate, write sure, not sure, or impossible for each event.
Tomorrow will be cold at the North Pole. sure Tomorrow it will be cloudy outside your school. Not sure
A dolphin will sit in your chair tomorrow. impossible Scientists will find water on Mars. Not sure
If there are 2 white socks and 2 black socks in a drawer and you close your eyes and pick 3, you will pick 2 socks of the same color. sure
Single blocks
Double-thick blocks;
the 6 blocks used in the experiment
Name Date Time
Block:
LESSON
3�5 Group Tally Chart
Result Tallies Total
on an edge
not on an edge
Total number
of tosses
Name Date Time
Block:
LESSON
3�5 Group Tally Chart
Result Tallies Total
on an edge
not on an edge
Total number
of tosses
Math Masters, p. 70
Teaching Master
Result Most likely to land on an edge
Tally children’s guesses.
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196 Unit 3 Linear Measures and Area
● How many times should we toss each block? At least 50 times is best. Point out that by increasing the number of tosses, they are increasing the reliability of the results.
● How will you divide the work? One possibility: Divide the class into six groups and assign one of the blocks to each group. For example, assign the single triangle to group 1, the double triangle to group 2, and so on. Then decide how many times each group member should toss the block to get a total of 50 or more tosses per block.
When the class has a plan, distribute the blocks and agree on how to toss a block. (For best results, all children should use the same technique.) A good way is to shake the block in cupped hands and release it about 2 feet above a surface. A dense carpet is best. Blotters will also reduce sound and bounce.
Each group fills in the type of block they have on the top line of the tally chart on Math Masters, page 70. Then, they keep track of the number of tosses and the number of times the block lands on one of its edges. Children count their tallies to obtain group totals.
Compile the results in a table on the board or Class Data Pad. Make sure that each group reports the same total number of tosses. Use language such as “The double-thick square block landed on an edge 21 times out of 50 tosses.”
� Discussing the Experimental WHOLE-CLASSDISCUSSION
ResultsHave children rank the three single-block shapes according to the number of times that each one landed on an edge.
● How well did you predict this ranking?
Review the tally chart with class responses to the Math Message. Results may vary greatly from class to class. It is likely that the single triangle will land on an edge more often than the single square or the single trapezoid.
● Does doubling the thickness of a block change its chance of landing on an edge? Yes, each double block has a better chance of landing on an edge than a single block of the same shape.
● Why should doubling the thickness of a block give it a better chance of landing on an edge? Sample answer: When you put two blocks together, you get twice as much edge part (area), but the pattern-block parts (areas) stay just the same. The extra edge part gives a double block a better chance of landing on an edge.
PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBLBLBLBLBLLLLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELELELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB ELEELELEMMMMMMMMMOOOOOOOOOBBBLBLBLBBBLBBLOOROROROORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINNNNVINVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOOLOOLOLOLOO VVINVINLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLOLOLLO VVVLLLLLLLLLLVVVVVVVVOSOSOSOOSOSOSOSOSOSOOSOSOSOSOSOOOSOOSOSOSOSOSOSOSOSOOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVLLLLLLLLVVVVVVVVVLLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
Sample group tally sheet for a double-thick
square block
Result Tallies Totalon an edge ////\ ////\ ////\ ////\ / 21
not on an ////\ ////\ ////\ ////\ 29edge ////\ ////
Total number of tosses 50
Block: double □
Sample results for one class;
each block was tossed 50 times.
Number of times Block landed on an edge
15
3
6
double 36
double 21
double 16
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Links to the Future
2 Ongoing Learning & Practice
� Displaying Shoe Lengths WHOLE-CLASS ACTIVITY
on a Line Plot(Math Journal 1, p. 64; Student Reference Book,
pp. 89A and 89B)
Use pages 89A and 89B in the Student Reference Book to review line plots. On a stick-on note, have children record their shoe length measures from journal page 64. Have children share their measures while you record them on the board. Ask them to identify the shortest (minimum) and longest (maximum) lengths. Draw a line plot on the board or class data pad and label the axes “Number of Children” and “Shoe Length in Inches.” Write the horizontal scale in 1 _ 2 -inch increments beginning with the shortest shoe length and ending with the longest. Ask children why the line plot can begin with a number other than zero. Sample answers: No one has a shoe that is zero inches long; no one in the class has a shoe shorter than the shortest shoe length. Invite children to place their stick-on notes above the number on the line plot corresponding to their shoe length. Have the class calculate the difference between the minimum and maximum shoe length (the range) and identify the shoe length that occurs the most (the mode). Next have children find the middle (median) class shoe length by removing one stick-on note from each end of the line plot one after another until only one or two remain.
Finding the maximum, minimum, mode, range, and median of a data set is a
Grade 3 Goal. To provide practice with this skill, exercises such as this will be
repeated several times throughout the year.
� Math Boxes 3�5 INDEPENDENTACTIVITY
(Math Journal 1, p. 66)
Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 3-7 and 3-9. Problem 6 previews Unit 4 content.
Ongoing Assessment: Math Boxes
Problem 5 �Recognizing Student Achievement
Use Math Boxes, Problem 5 to assess children’s ability to apply and describe
the Commutative and Associative Properties of Addition. Children are making
adequate progress if they are able to complete the 3- and 4-addend problems
correctly. Some children may be able to combine the addends to make easier
numbers.
[Patterns, Functions, and Algebra Goal 4]
PROBLEMBBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBBBLBLBLLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELELELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB EEELELEMMMMMMMMMOOOOOOOOOBBBLBLBLBLBBLBBOOROROROORORORORORORORORO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINVINNNNVINVINVINVINVINVINVINGGGGGGGGGGGOLOLOOLOLOLOLOOLOO VINVINVLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLLOO VVVLLLLLLLLLLVVVVVVVVSOSOSOSOOSOSOSOSOSOSOOSOSOSOOSOOOOSOSOSOSOSOSOSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLVVVVVVVVLLLLLLLVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
Lesson 3�5 197
Line plot with stick-on notes
The median is 9 1/2 inches.
3 cm
2 cm
4 cm3.5 cm
2 cm
4 cm
5. Solve.
9 + 1 + 4 = 14
20 = 3 + 7 + 8 + 2
3 + 15 + 7 + 4 = 29
3. Write <, >, or =. Use a tape
measure to help.
1 1 _ 2 feet > 16 inches
3 feet < 2 yards
5 feet = 60 inches
55 inches > 1 yard
Date Time
2. What is the perimeter?
18.5 cm
4. Add. Show your work.
Ballpark estimate:
550 + 200 = 750
6. Solve.
3 × 0 = 0
0 = 5 × 0
0 × 7 = 0
9 × 0 = 0
Math BoxesLESSON
3 �5
143 144
57–59 192
150
50 51
13, 146
56
1. Measure to the nearest 1 __
2 inch. Fill
in the oval next to the best answer.
1 in.
1 1 _ 2 in.
2 in.
2 1 _ 2 in.
(unit)
555+ 192
747
�
Unit
Unit
Sample answer:
EM3MJ1_G3_U03_55-78.indd 66 1/14/11 1:52 PM
Math Journal 1, p. 66
Student Page
9 10 11
Class Shoe Lengths (Inches)
Numberof
Children
9 12 10 1
2
9 10 11
Class Shoe Lengths (Inches)
Numberof
Children
9 12 10 1
2
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198 Unit 3 Linear Measures and Area
Name Date Time
Describing DataHOME LINK
3 5
You can find information about minimum, maximum, range, median, and mode for a set ofdata on pages 79–82 in the Student Reference Book.
Please return this Home Link to school tomorrow.
FamilyNote
79–82
Children in the Science Club collected pill bugs. The tally chart shows howmany they collected. Use the data from the tally chart to complete a line plot.
Use the data to answer the questions.
1. What is the maximum (greatest) number of pill bugs found? pill bugs
2. What is the minimum (least) number of pill bugs found? pill bugs
3. What is the range for the data? pill bugs
4. What is the median for the data? pill bugs
5. What is the mode for the data? pill bugs33
42
6
Number of Number ofPill Bugs Collectors
012 ///3 ////\45 //6 //
0 1 2 3 4 5 6
XXX
XXXXX
XX
XX
Number of Pill Bugs
Numberof
Children
UnitMake ballpark estimates. Solve on the back of this paper. Show your work.
6. 67 28
7. 33 29 62; 30 30 6095; 70 30 100
Practice
Math Masters, p. 69
Home Link Master
� Home Link 3�5 INDEPENDENTACTIVITY
(Math Masters, p. 69)
Home Connection Children create a line plot and use the data to find the maximum, minimum, range, median, and mode.
3 Differentiation Options
ENRICHMENT PARTNER ACTIVITY
� Predicting the Results 15–30 Min
of Rolling 2 Dice(Math Masters, p. 414)
To further explore the concept of probability, have children predict the results of rolling 2 dice. Post the scroll described in Advance Preparation on page 194. Children work in partnerships. Each partnership needs two dice and a sheet of paper.
First, ask children to predict which total from 2 to 12 will come up most often when two dice are rolled. Ask them to make one prediction per partnership. They record their predictions on a sheet of paper.
Next, children draw a frequency table on the same sheet of paper and record the results of rolling the dice 30 times.
As children finish their 30 rolls, have them come up to the scroll and make Xs with a marker to record the number of rolls for each sum.
The class graph should look something like a bell curve, although individual results may not. With enough rolls, 7 is usually the most frequent sum. Children discuss their predictions and individual results, and then compare them to the class graph.
NOTE There are 36 possible combinations of two dice. Six of these have 7 as the
sum: 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1. Five combinations have 6 as
the sum, five have 8 as the sum, and so on. So 7 is the most likely sum.
Children may continue and predict the results of rolling one die. Repeat the above experiment for one die. The scroll should be numbered from 1 to 6. Discuss why and how the results are different from those for two dice. Each number on the single die has an equal chance of being rolled, so the bars of the graph should be about the same length.
PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEEMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBLBBLBLBLLLLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBB ELEELEEMMMMMMMMMMOOOOOOOOOBBBLBBLBLBLBBBBLOOORORORORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNVINVINVINNVINVINVINVINV GGGGGGGGGGGGOLOOOLOOOLOOOO VVINVINLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVIVINVINGGGGGGGGGGOOLOLOLOLOLLOOOOLVVVVVLLLLLLLLLLLVVVVVVVVVOOSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOOOOSOSOSOSOSOSOSOSOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
Name Date Time
Grid
Math Masters, p. 414
Teaching Aid Master
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Lesson 3�5 199
EXTRA PRACTICE SMALL-GROUP ACTIVITY
� Using Probability Terms 5–15 Min
Read Probably Pistachio by Stuart J. Murphy in class or have children read the book themselves.
Summary: Probability terms are used to describe events as Jack lives through an unlucky day. Children can use probability terms to describe events in their day.
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