a pattern-block toss experiment - everyday math · pdf filea pattern-block toss experiment ......

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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.


• Predict the outcome of a probability

experiment and conduct a probability

experiment.


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

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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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● 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.

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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


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]

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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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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.

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Name Date Time

Grid

Math Masters, p. 414

Teaching Aid Master


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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a pattern-block toss experiment - everyday math · pdf filea pattern-block toss experiment ......

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