# materials Teaching the Lesson

```Objectives
To review counting by 2s, 5s, and 10s; to extend this
to counting by any number n; and to provide experiences with
describing patterns that result from counting.
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materials
Teaching the Lesson
Key Activities
Children count by 2s, 5s, 10s, and by any number n from an arbitrary starting number, orally
and with a calculator. They record and describe counting patterns on a number grid.
Key Concepts and Skills
• Count up and back by 2s, 5s, and 10s.
[Number and Numeration Goal 1]
• Skip count on a calculator.
[Number and Numeration Goal 1]
ⵧ Math Journal 2, p. 161
ⵧ Teaching Master (Math Masters,
p. 195)
ⵧ Teaching Aid Master (Math
Masters, p. 415)
ⵧ Transparency (Math Masters,
p. 195; optional)
ⵧ calculator
ⵧ crayons
• Record and discuss skip-counting patterns on a number grid.
[Patterns, Functions, and Algebra Goal 1]
Key Vocabulary
multiple of 10
Ongoing Assessment: Recognizing Student Achievement Use the Math Message.
[Number and Numeration Goal 1]
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materials
Ongoing Learning & Practice
Children practice addition and subtraction facts using Fact Triangles.
Children practice and maintain skills through Math Boxes and Home Link activities.
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materials
Differentiation Options
Children correlate
rhythmic counting
by 2s, 5s, and 10s
with different
movements.
ENRICHMENT
EXTRA PRACTICE
ELL SUPPORT
Children find
patterns on a
five-column
number chart.
Children make
patterns by coloring
square and
triangular grids.
Children find
multiples of 2,
5, and 10 on a
five-column
number chart.
Advance Preparation For the Part 1 activity Using a Calculator to Find Patterns on a Number
Grid, make extra copies of Math Masters, page 195. You may also want to make an overhead
544
Unit 7 Patterns and Rules
ⵧ Math Journal 2, p. 162
ⵧ Home Link Master (Math Masters,
p. 196)
ⵧ , Fact Triangles
ⵧ Teaching Master (Math Masters,
p. 197)
ⵧ Teaching Aid Master (Math
Masters, p. 439)
ⵧ crayons
ⵧ counters (transparent preferred)
ⵧ yellow and blue markers
Technology
Assessment Management System
Math Message
See the iTLG.
Getting Started
Mental Math and Reflexes
Math Message

Pose problems involving multiplication of equal groups. Suggestions:
Isabel has 7 packages of cupcakes. There are 2 cupcakes per package.
How many cupcakes in all? 14 cupcakes
Jerome has 5 sheets of stickers. There are 8 stickers per sheet. How many
stickers in all? 40 stickers
Each lollipop costs 10 cents. Andrea bought 9. How much did she pay? \$0.90
Start at 80 and count by 2s.
Count as far as you can.
Write your counts on an Exit Slip ( Math
Masters, page 415).
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Masters, p. 415)
Ongoing Assessment:
Recognizing Student Achievement
Math Message

Use the Math Message to assess children’s ability to count by 2s. Children are
making adequate progress if they are able to count by 2s to 100. Some children
may be able to count by 2s to numbers greater than 100.
[Number and Numeration Goal 1]
Have small groups or the whole class count by 2s from several
2-digit even numbers. Extend to counts from 3-digit numbers if
children do well. Keep oral counting brisk and rhythmic. Ask
volunteers to describe the pattern in counts by 2s. All counts are
even numbers; the pattern of the ones digits repeats:
0, 2, 4, 6, 8, 0, 2, ....
0
8
2
6
4
When counting by 2s, the pattern of the
ones digits repeats—0, 2, 4, 6, 8, 0, 2, ....
Repeat with counts by 5s and 10s. For counts by 5s, begin with
numbers that end in 0 or 5. For counts by 10s, begin with
numbers that end in 0. Point out that when a number ends in 0 it
is a multiple of 10. Each of the numbers in this 10 count is a
multiple of 10. To support English language learners, discuss the
meaning of multiple in this context. Encourage children to
describe the patterns in these counts. Counts by 5s from numbers
ending in 0 or 5 end in 0 and 5. Counts by 10s from numbers
ending in 0 end in 0. Children may notice that numbers that end
in 0 are also multiples of 2 and 5.
Ask children to count back, as well
as up. In addition, have children discuss the
pattern of counts by 10s starting from any
number. As you count from one number to the
next, the ones digit remains the same and the
tens digit is increased by 1: 303, 313, 323,
333, .... If the tens digit is 9, then the tens
digit becomes 0 and the hundreds digit is
increased by 1: 393, 403, ....
AUDITORY
䉬
KINESTHETIC
䉬
TACTILE
䉬
VISUAL
Lesson 7 1
䉬
545
NOTE For skip counting on most calculators,
number by which you want to count) = + n
= + n = .... Remember that different
calculators are “programmed” differently to
handle skip counting. For example, for the first
suggestion on the right:
Press 22
+
=
=
3
WHOLE-CLASS
ACTIVITY
Calculator
press s (the starting number) + n (the
=
䉴 Skip Counting on the
for the TI-108;
Have a volunteer recall how to program calculators to count up by
2s, starting at 0, as the class follows along. (See margin note.)
After children have programmed their calculators, have them
press
repeatedly, and slowly, while counting together by 2s.
Try group counts by numbers other than 2, 5, and 10. Use such
numbers as 3, 4, and 9. Children press the appropriate keys on
their calculators as they count in unison. Suggestions:
䉯 Count from 22 by 3s. 25, 28, 31 ...
Press 3
22
䉯 Count from 22 by 4s. 26, 30, 34 ...
for the
Casio SL-450. See Lesson 1-9 for
䉯 Count from 80 by 6s. 86, 92, 98 ...
programming instructions for these two
䉯 Count from 180 by 9s. 189, 198, 207 ...
calculator models.
Extend the range of numbers.
A U D I T O R Y
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
V I S U A L
Have volunteers record some of the counts on the board so the
class can observe the patterns in the ones digits. You might find
it helpful to circle the ones digits.
䉴 Using a Calculator to Find
PARTNER
ACTIVITY
Patterns on a Number Grid
(Math Journal 2, p. 161; Math Masters, p. 195)
Student Page
Date
LESSON
7 1
䉬
Time
Using a Calculator to Find Patterns
1. Use a calculator to count by 5s starting with the number 102.
Color the counts on the grid with a crayon. Look for a pattern.
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Have children use their calculators to solve Problem 1 on the
journal page. Children count by 5s from the starting number 102.
107, 112, 117, 122, .... As children count with their calculators,
they color the numbers on their number grids. You might choose
to model this on an overhead transparency of Math Masters, page
195. Ask children to share any patterns they see. All numbers fall
in two columns of the grid. The ones digit alternates between 2
and 7.
2. Pick a number to count by. Start with a number less than 310.
Use your calculator to count. Record your counts on the grid with
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Sample
The ones
Here is a pattern that I found:
digits are always even numbers.
I counted by
6s
starting with the number
Math Journal 2, p. 161
546
Unit 7 Patterns and Rules
Have children complete the journal page with a partner. Partners
must first decide on a number to count by and then a starting
number. Suggestions:
䉯 Children can select any number to count by, but encourage
them to count by some number other than 2, 5, and 10.
䉯 Children can select any starting number less than 310.
Student Page
Partners write in their journals about any number patterns they
observe for their count. When most of the children have completed
the journal page, bring the class together to share and discuss the
different patterns they found.
Date
Time
LESSON
Math Boxes
71
䉬
1. Which one is certain to happen?
2. Solve.
17 9 A. A spaceship will land at
27 9 school.
NOTE Math Masters, page 195 is the same as journal page 161. Make extra
copies of this page for children who finish early and want to repeat Problem 2
using different numbers. Extra copies are also useful for children who make an
error and need to start again.
57 9 B. Your favorite sports team
68
88
will win every time.
Unit
8
18
48
77 9
97 9
D. You will be a movie star.
3. Make a 7-by-7 array with dots.
How many in all?
49
4. Arrange the allowances in order
from the minimum (smallest) to
the maximum (largest).
dots
\$10, \$3, \$7, \$1, \$4
\$1 , \$3 , \$4 , \$7 , \$10
The minimum is \$1 .
The maximum is \$10 .
2 Ongoing Learning & Practice
45
5. Match each person with the
䉴 Practicing with
ⴙ, ⴚ Fact Triangles
6. How many boxes are on this
correct weight.
PARTNER
ACTIVITY
newborn
Math Boxes page?
6
144 pounds
63 pounds
boxes
1
How many boxes are on of
2
3
boxes
Partners practice addition and subtraction facts.
Math Journal 2, p. 162
䉴 Math Boxes 7 1
䉬
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 162)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 7-3. The skill in Problem 6
previews Unit 8 content.
Writing/Reasoning Have children draw, write, or verbalize
their answers to the following: Describe any patterns you see
in Problem 2. Sample answer: The ones digit is 8 in all the
answers, and the tens digit is one less than the tens digit in the
first number.
䉬
INDEPENDENT
ACTIVITY
(Math Masters, p. 196)
Home Connection Children count up from 3-digit
numbers. They record some of their counts and look for
Name
Date
71
䉬
Family
Note
Time
Count by 2s, 5s, and 10s
In this lesson, your child has been counting by 2s, 5s, and 10s. After your child has completed
these problems, help him or her look for patterns in the ones digits of the answers. In the
example, the ones digits repeat: 0, 2, 4, 6, 8, 0, 2, 4, and so on. If your child is successful
with these problems, ask him or her to count backward by 2s, 5s, or 10s. Start from a
number that is a multiple of 10, such as 200.
96
Example:
Count by 2s. Begin at 100. Write your first 10 counts below.
100 , 102 , 104 , 106 , 108 , 110 , 112 , 114 , 116 , 118
1. Count by 2s. Begin at 200. Write your first 10 counts below.
200 , 202 , 204 , 206 , 208 , 210 , 212 , 214 , 216 , 218
2. Count by 5s. Begin at 500. Write your first 10 counts below.
500 , 505 , 510 , 515 , 520 , 525 , 530 , 535 , 540 , 545
3. Count by 10s. Begin at 550. Write your first 10 counts below.
550 , 560 , 570 , 580 , 590 , 600 , 610 , 620 , 630 , 640
the counts.
In Problem 1, the ones digits repeat: 0, 2, 4, 6, 8, 0, 2, 4, ….
In Problem 2, the ones digits repeat: 0, 5, 0, 5, ….
In Problem 3, all the ones digits are 0.
Math Masters, p. 196
Lesson 7 1
䉬
547
Teaching Master
Name
LESSON
71
䉬
Date
Time
3 Differentiation Options
Patterns on a Number Chart
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䉴 Counting by 2s, 5s, and 10s
SMALL-GROUP
ACTIVITY
5–15 Min
To provide experience with counting, have children correlate
rhythmic counting with a physical motion. For example:
䉯 1, 2 (clap), 3, 4 (clap), ...
䉯 1, 2, 3, 4, 5 (touch toes), 6, 7, 8, 9, 10 (touch toes), ...
䉯 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (jumping jack), ...
ENRICHMENT
䉴 Exploring Patterns on a
INDEPENDENT
ACTIVITY
15–30 Min
Number Chart
Math Masters, p. 197
(Math Masters, p. 197)
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To further explore patterns, have children use a five-column
number chart. Children decide on a skip-count pattern, such as
counting by 4s. They color the skip-count pattern on the number
chart or use transparent counters to mark the numbers. They
record the patterns they find. Have children describe their
patterns using words like row, column, diagonal, left, right, skip,
and so on. Sample answers: When counting by 4s, a diagonal
pattern forms. Each time I go down a row I am counting by 5s.
EXTRA PRACTICE
Teaching Aid Master
Name
Date
Time
LESSON
Making0 0Patterns
Page Title
䉴 Making Patterns by
INDEPENDENT
ACTIVITY
15–30 Min
Coloring Grids
䉬
Make designs by coloring the grids. Use more than one color
in each design.
(Math Masters, p. 439)
Art Link Using at least two colors, children color a design
on the square grid on Math Masters, page 439. They color a
second design on the triangular grid.
ELL SUPPORT
䉴 Finding Patterns in Multiples
SMALL-GROUP
ACTIVITY
5–15 Min
of 2, 5, and 10
(Math Masters, p. 197)
Math Masters, p. 439
548
Unit 7 Patterns and Rules
To provide language support for multiples, have children use
markers to color multiples of 2 in yellow and multiples of 5 in
blue on a five-column number chart. Children should notice that
multiples of 10 will appear green. Ask children to write lists of
the first ten multiples of 2, 5, and 10. Have children write about
the patterns they see.
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