“What’s My Rule?” - Everyday Math · PDF file1 Teaching the Lesson Math...
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Transcript of “What’s My Rule?” - Everyday Math · PDF file1 Teaching the Lesson Math...
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112 Unit 2 Adding and Subtracting Whole Numbers
Advance Preparation
Teacher’s Reference Manual, Grades 1–3 pp. 18, 19, 209–215
“What’s My Rule?”Objective To provide opportunities to review and solve
“What’s My Rule?” problems.
��������
Key Concepts and Skills• Use basic facts to compute extended facts.
[Operations and Computation Goal 1]
• Describe rules for patterns and use them
to solve problems.
[Patterns, Functions, and Algebra Goal 1]
• Describe rules and patterns in “What’s My
Rule?” tables; use them to solve addition
and subtraction problems.
[Patterns, Functions, and Algebra Goal 1]
Key ActivitiesChildren discuss problems in which one
quantity depends on another. They illustrate
this kind of relationship between pairs of
numbers with a function machine and
“What’s My Rule?” tables. They solve
“What’s My Rule?” problems.
Ongoing Assessment: Informing Instruction See page 114.
Ongoing Assessment: Recognizing Student Achievement Use journal page 34. [Patterns, Functions, and Algebra Goal 1]
Key Vocabularyfunction machine � input � rule � output �
“What’s My Rule?”
MaterialsMath Journal 1, p. 34
Home Link 2�2
transparency of Math Masters, p. 41
(optional)
Playing Fact GamesStudent Reference Book, pp. 278 or
310 and 311
Beat the Calculator
per group: 4 each of number cards
0–9 (from the Everything Math Deck, if
available), calculator
Subtraction Top-It
per group: 4 each of number cards
0–10 and 1 each of number cards
11–20 (from the Everything Math
Deck, if available)
Children maintain and/or practice basic
fact fluency.
Math Boxes 2�3Math Journal 1, p. 35
Children practice and maintain skills
through Math Box problems.
Home Link 2�3Math Masters, p. 42
Children practice and maintain skills
through Home Link activities.
READINESS
Acting Out a Function Machinecardboard box � counters
Children act out a function machine.
ENRICHMENTCreating “What’s My Rule?” TablesMath Masters, p. 41
Children work together to make up their
own “What’s My Rule?” tables.
Teaching the Lesson Ongoing Learning & Practice
132
4
Differentiation Options
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
112_EMCS_T_TLG1_G3_U02_L03_576809.indd 112112_EMCS_T_TLG1_G3_U02_L03_576809.indd 112 2/4/11 9:35 AM2/4/11 9:35 AM
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
Algebraic Thinking Draw or display a function machine and “What’s My Rule?” table. Ask children to imagine that the function machine works like this:
● A number (the input) is dropped into the machine.
● The machine changes the number according to a rule.
● A new number (the output) comes out the other end.
The rule for the Math Message problem is Double the number. Write the word Double in the function machine. Point out the “What’s My Rule?” table that you have displayed. Discuss the 8 in the in column and the 16 in the out column. Explain to children that numbers in the in column represent the number of bacteria now. Corresponding numbers in the out column represent the number of bacteria 20 minutes from now.
Review the answers to the Math Message problem by posing questions in the following manner:
● If 50 is dropped into the function machine, which number will come out? 100 Enter the appropriate numbers in the in and out columns. Repeat with the other numbers in the problem.
Lesson 2�3 113
Getting Started
Math Message Some bacteria double in number every 20 minutes. Use this information to complete the table.
Home Link 2�2 Follow-Up Go over answers as necessary. Review the idea that basic facts can be used to solve problems with larger numbers.
Mental Math and Reflexes Pose “What’s My Rule?” riddles. Ask children to say a number. Apply a secret rule and tell them the new number. For example, a child might say 48. Apply the rule “Add 10” and tell the new number, 58. Continue as above until most children know the secret rule. Then you say a number and ask children to apply the rule and tell you the new number.
Secret rules: Add 10; Subtract 10
Secret rules: Add 5; Subtract 5
Secret rules: Add 8; Subtract 8
Rule
out
in
Double
in out
8 16
50 100
200 400
75 150
150 300
Unit
bacteria
Now 20 min later
8 16
50 100
200 400
75 150
150 300
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114 Unit 2 Adding and Subtracting Whole Numbers
Date Time
Fill in the blanks.
1. 2.
3. 4.
Rule
out
in
Subtract 50
Rule
out
in
Add 8
Rule
out
in
Subtract 30
in out
100 5050 070 20150 100200 150
in out
60 30
80 50
130 100
230 200
30 0
Rule
out
in
Add 9
Answers vary. Answers vary.
Answers vary.
Answers vary. Answers vary.
Answers vary.
in out
14 23
34 43
44 53
64 73
94 103
in out
5 13
15 23
35 43
65 73
85 93
5. 6.
Rule
out
in
Rule
out
in
Add 7
in out
6 13
9 165 124 11
11 18
in out
35 20
60 45
20 550 35
46 31
“What’s My Rule?”LESSON
2�3
Subtract 15
� �
Math Journal 1, p. 34
Student Page
� Reviewing Variations of the WHOLE-CLASS ACTIVITY
“What’s My Rule?” Routine(Math Masters, p. 41)
Algebraic Thinking If you made a transparency of Math Masters, page 41, you can demonstrate each type of “What’s My Rule?” table on the overhead. Otherwise, draw the tables on the board. In the Math Message problem, the rule and sample inputs are known, and the outputs must be determined. (See Type 1 in the margin.)
� In a second type of “What’s My Rule?” problem, the rule and sample outputs are known, but the inputs must be determined. (See Type 2 in the margin.)
� In a third type of “What’s My Rule?” problem, the inputs and outputs are known, and the rule must be determined. (See Type 3 in the margin.)
� In a fourth type of “What’s My Rule?” problem, some inputs and outputs are known; missing numbers and the rule must be determined. (See Type 4 in the margin.) To find the rule in problems like these, children should use the pairs in which both in and out numbers are given. Then, after the rule is discovered, children can use the rule to fill in the missing in and out numbers. Pose problems like the fourth type to the class.
� In a fifth type of “What’s My Rule?’’ problem, rules are often stated as simple commands to perform a specific operation, such as Add 5. However, rules may also be stated in a con-text—“Mark is 4 years younger than his sister, Susie” or as in the Math Message—“Some bacteria double in number every 20 minutes.” (See Type 5 in the margin.) Encourage children to supply both types of rules.
� Completing “What’s My Rule?” PARTNER ACTIVITY
Tables(Math Journal 1, p. 34; Math Masters, p. 41)
Algebraic Thinking Children may work in partnerships or independently to complete the journal page. Note that the last row in each table is left blank. Encourage children
to create difficult problems. Math Masters, page 41 may be used to provide additional practice with “What’s My Rule?” tables.
Ongoing Assessment: Informing Instruction
Watch for children who have difficulty finding the missing in numbers. Have them
check their work by reading the number sentence formed by the in number, the
rule, and the out number.
PROBLEMBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMMOOOOOOOOOOBBBBBBBLBLBLBLBBLBLLLLBLPROPROPROPROPROPROPROPROPROPROPRPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROROROOPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELELEELEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBB ELEELEMMMMMMMMMOOOOOOOOOBLBLBLBLBLBLBLBLBLBLROOOROROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINVINNNVINVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOLOOLOOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOLOLOLOLOLOLOLOOOO VVVVVLLLLLLLLLLVVVVVVVVVOSSOSOSOSOSOSOSOSOSOSOSOSOSOOOOOSOOSOSOSOSOSOSOSOSOSOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING
in out
13 4
10 1
17 8
18 9
in out
7 12
10 15
21 26
45 50
in out
10 20
20 30
30 40
50 60
Rule
Subtract 9
Rule
Add 5
Rule
Add 10
Type 1 Type 2 Type 3
in out
13 9
23 19
43 39
53 49
in out
45 25
30 10
100 80
52 32
RuleMark is 4 years younger than his sister Susie
Rule
Subtract 20
Type 4 Type 5
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Name Date Time
“What’s My Rule?”HOME LINK
2�3
You can find an explanation of function machines and “What’s My Rule?” tables on pages202–204 in the Student Reference Book. Ask your child to explain how they work. Help your child fill in all the missing parts for these problems.
Please return this Home Link to school tomorrow.
FamilyNote
202 204
Practice facts and fact extensions. Complete the “What’s My Rule?”problems. Make up problems of your own for the last table.
1.
3.
2.
4.
Rule
out
in
Subtract 7
in out
14 77 012 515 810 321 14
Rule
out
in
Add 9
in out
7 169 18
37 4677 86
49 58
Rule
out
in
Add 30
in out
70 100
20 5030 60
90 120
50 80
Rule
out
in in out
Answers vary.
Answers vary.
Answers vary.
Math Masters, p. 42
Home Link Master
5. What time is it?
What time willit be in 20minutes?
How many minutes until 5:15?
40 min
4:55
4:35
3. Write the numbers that are 100more and 100 less than each givennumber.
100 more 100 less
614
994
2,462
3,965 3,8654,0652,3622,5628941,094514714
Date Time
2. Fill in the missing numbers.
4. You spent $7.88 at the store. Yougave the cashier a $10 bill. Howmuch change should you receive?
$2.12
6. Measure the line segment to thenearest �
12� inch.
inches2
1. Put these numbers in order fromsmallest to largest.
32,764
8,596
32,199
85,096 85,09632,76432,1998,596
20
143–145
1,072 1,073 1,074 1,0751,082 1,083 1,084
1,0941,104
1,114
1,0851,095
12 12
3
4567
8
9
1011
7 8
Math BoxesLESSON
2�3
18 19
�12�
Math Journal 1, p. 35
Student Page
Lesson 2�3 115
Ongoing Assessment: Journal
Page 34 �Recognizing Student Achievement
Use journal page 34, Problems 1 and 2, to assess children’s ability to write and
use rules for functions involving addition and subtraction. Children are making
adequate progress if they are able to complete Problems 1 and 2. Some children
may be able to complete the remaining problems involving missing rules and
numbers.
[Patterns, Functions, and Algebra Goal 1]
2 Ongoing Learning & Practice
� Playing Fact Games SMALL-GROUP ACTIVITY
(Student Reference Book, pp. 278
or 310 and 311)
Have children play either Beat the Calculator (Addition) or Subtraction Top-It to maintain and/or practice basic fact fluency. Review the rules for these two games in the Student Reference Book (page 278 for Beat the Calculator and pages 310 and 311 for Subtraction Top-It).
Continue to provide children with opportunities to play fact games regularly.
� Math Boxes 2�3 INDEPENDENTACTIVITY
(Math Journal 1, p. 35)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-1. The skill in Problem 6 previews Unit 3 content.
Writing/Reasoning Have children write an answer to the following: Explain your strategy for Problem 4. Sample answer: I counted up $0.12 from $7.88 to get to $8.00. From $8.00 to $10.00 is $2.00. The change is $2.00 + $0.12 or $2.12.
� Home Link 2�3 INDEPENDENTACTIVITY
(Math Masters, p. 42)
Home Connection Children practice facts and fact extensions in the “What’s My Rule?” format. “What’s My Rule?” may not be familiar to parents, so you might want to send home the Student Reference Book.
PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMLEBLELEBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBLBLBLBLBLBLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB ELEELEEMMMMMMMMMMOOOOOOOOOOBBBLBLBLBBLBBBBLROOORORORORORORORORORORORO LELELLEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNVINVINVINNVINVINVINVINV GGGGGGGGGGGGOLOOOLOOOLOOLOO VVINVINLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINGGGGGGGGGGGOOLOLOLOLOLLOOOOLVVVVVLLLLLLLLLLVVVVVVVVVOOSOSOSOOSOSOSOSOSOSOOSOSOSOOOSOOOOSOSOSOSOSOSOSOSOOSOSOOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLLLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
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116 Unit 2 Adding and Subtracting Whole Numbers
3 Differentiation Options
READINESS SMALL-GROUP ACTIVITY
� Acting Out a Function Machine 5–15 Min
Algebraic Thinking To explore function machines using a concrete model, use a cardboard box without a lid to demonstrate how a function machine works.
Draw a picture of an Everyday Mathematics function machine on one side of the box. Place 15 counters inside the box. To begin the demonstration, put 3 counters into the machine. Take 6 counters out of the machine. Repeat with additional numbers of counters (4 and 8, 5 and 10). Then ask children how the machine is changing the number of counters each time. Children should try to state the rule the machine is using. (In the example, the machine doubles the number.) Repeat with other rules (for example, +4, –2). As children understand the process, have them serve as the rule makers.
ENRICHMENT
PARTNER ACTIVITY
� Creating “What’s My Rule?” 15–30 Min
Tables(Math Masters, p. 41)
To provide further exploration of “What’s My Rule?” problems, have children create their own “What’s My Rule?” tables. Encourage them to use negative numbers,
larger numbers, or rules stated in a context (such as Type 5 in the margin on page 114.) To support English language learners, have children read their rules. Consider having them state their rules in different ways. For example, “My rule is to add 2. Plus 2 is another way to say my rule.”
ELL
Math Masters, p. 41
Teaching Master
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