Instructional Sequence

M-GLAnCE Project Directors
Debbie Ferry
Macomb ISD
Mathematics Consultant / Carol Nowakowski
Retired
Mathematics Consultant
K-4 Project Coordinator / Marie Copeland
Warren Consolidated
Macomb MSTC
5-8 Project Coordinator
2004 Project Contributors
David Andrews
Chippewa Valley Schools / William Ashton
FraserPublic Schools / Lynn Bieszki
Chippewa Valley Schools
Sharon Chriss
Romeo Schools / Kimberly DeShon
AnchorBaySchool District / Barbara Diliegghio
Retired, Math Consultant
Kimberly Dolan
AnchorBaySchool District / Jodi Giraud
L’Anse Creuse Schools / Julie Hessell
Romeo Schools
Amy Holloway
Clintondale Schools / Barbara Lipinski
AnchorBaySchool District / Linda Mayle
Romeo Schools
Therese Miekstyn
Chippewa Valley Schools / James Navetta
Chippewa Valley Schools / Gene Ogden
AnchorBaySchool District
Rebecca Phillion
Richmond Comm. Schools / Charlene Pitrucelle
AnchorBaySchool District / Shirley Starman
Van Dyke Public Schools
Ronald Studley
AnchorBaySchool District
2005 and 2006 Session/Module Developers
Carol Nowakowski
Retired, Math Consultant / Deb Barnett
Lake Shore Public Schools / Luann Murray
Genesee ISD
Kathy Albrecht
Retired, Math Consultant / Jo-Anne Schimmelpfenneg
Retired, Math Consultant / Marie Copeland
Warren Consolidated
Terri Faitel
Trenton Public Schools / Debbie Ferry
Macomb ISD

Grade 3: Fluency with Operations and Estimation
N.FL.03.06 / N.FL.03.07 / N.FL.03.08 / N.FL.03.15
Add and subtract fluently two numbers up to and including two-digit numbers with regrouping and up to four-digit numbers without regrouping. / Estimate the sum and difference of two numbers with three digits (sums up to 1,000) and judge reasonableness of estimates. / Use mental strategies to fluently add and subtract two-digit numbers. / Given problems for addition and subtraction, represent with objects, words, and mathematical statements; solve.

Instructional Sequence

Important Tips: / Common Misconceptions:

Student who simply learns procedures, will have only procedural knowledge.
Have students view number statements such as 16-7 as subtraction problems and not just “a flash card fact” to be memorized.
Have students decompose numbers in many ways. (i.e. 5+7 as 5 + 5 +2 or 2 + 3 + 7 for example).
Partial understanding of a concept by students is to be expected as they are learning; children grasp bits and pieces.
Kids see concepts in different ways – no one sequence of teaching is best for all students.

Student may view the digits of a number as “two separate numbers” when misled with explanations such as “borrowing from your neighbor next door.”
Students may consistently subtract the smaller digit from the larger, even though that digit may be on top (i.e. 53 – 27 = 34.) These students need much more work with decomposing numbers and being proficient in seeing,for example, 56 as 50 + 6 or 40 + 16, or 50 + 3 + 3, etc.
Left-to-right addition may be a more viable alternative for some children who struggle with right-to-left algorithms.

Grade 3: Understand and use number notation and place value

N.ME.03.01 / M.ME.03.02 / M.ME.03.03
Read and write numbers to 10,000 in both numerals and words, relate them to the quantities they represent, e.g. relate numeral or written word to a display of dots or objects. / Recognize and use expanded notation for numbers using place value to 10,000’s place, e.g. 2,517 is 2 thousands, 5 hundreds, 1 ten and 7 ones; 4 hundreds and 2 ones is 402. Identify the place value of a digit in a number, e.g. 3,241, 2 is in the hundreds place. / Compare and order numbers up to 10,000.

Instructional Sequence:

Concept of Zero Concept of ten Compose and decompose numbers to 10 Compose and decompose numbers to 20

(10 ones, 1 ten) (Place Value, Expanded Notation)

Compose and decompose numbers to 100 Compose and decompose numbers beyond 100

Important Tips Common Misconceptions
▪use variety of manipulatives ▪Use of 0 placement
-base 10 blocks -students mistake 704 for 74
-playing cards -recording 4,008 as 408
-numbered index cards
-dice Common Errors
▪hang place value chart
▪check frequently for understanding ▪Reversing numbers-reading 18 as 81
▪use and display place value language ▪Realization that 5 tens has the same value as 50
▪use real world examples as reinforcement
▪numbers tell quantity/position of digit designates place value

Grade 3: Understand and use number notation and place value

Sample Activities

I
Foldables*
provide students with 2 sheets of 81/2 x 11 sheets of paper
position lengthwise and fold up 2” from bottom
fold into thirds
help students staple on folds to form pockets
label pockets
using index cards label with digits 0-9
(can use playing cards in place of index cards)
Units
hundreds / tens / ones
Thousands
hundreds / tens / ones
/ II
Expanded Notation Code Sheet
use pattern blocks and give a value to each
reach into a bag, grab a handful of pieces\
write the number in expanded notation and standard form.
e.g.
Hexagon = 1,000
Trapezoid = 100
Parallelogram = 10
Triangle = 1
Place Value Stackers
make or distribute expanded notation cards
use word strip cards
whole strip = 1,000’s
0 / 0 / 0
3/4 of strip = 100’s
0 / 0
1/2 of strip = 10’s
0
1/4 of strip = 1’s
/ III
Write a number
provide each student with an index card
direct students at each table group to choose and write numbers between specific values
“Table 1 students write a number on your card between 1-1,000. Table 2 students write a number on your card between 1,001 and 2,000. etc.”
in table groups have students compare and order numbers from greatest to least or least to greatest.
have students self correct their group
as a whole class, have students place themselves in order from greatest to least/least to greatest
have students orally read their numbers
Spinner Game
refer to Spinner Game (in ISample Activities)
after last round, have students compare and order their numbers
*Adapted from MacMillian/McGraw Hill Mathematics-Grade 3
Activities using Foldables:
1. Guess My Digit*
Devise word problems e.g.
I am thinking of a 4 digit number. The ones digit of the number is 2. The hundreds digit of the number is 6. There are 0 tens. The thousands digit is one less than the hundreds digit. What is my number?
(5,602)
2. Spinner Game*
Give directions regarding building greatest or least number
Working in groups, students take turns spinning a number.
They decide where to place the number in their pockets to build the greatest or the least number.
As they place the number they tell the group, “I am placing the 6 in the thousands place. It is worth 6,000.”
After all pockets are filled, students read their numbers to the group to determine who built the greatest or least number.
*Adapted from MacMillian/McGraw Hill Mathematics-Grade 3 / II
Place Value Stackers
to build 3,409, lay down thousands strip, place the 3 in the thousands place.
lay the hundreds strip on top of the thousands strip and place the 4 in the hundreds place.
lay the tens strip on top of the hundreds strip and place the 0 in the tens place
finally, lay the ones strip on top of the tens strip and place the 9 in the ones place.
take apart the number to form expanded notation with addition signs3,000+400+0+9=3,409
Real World Examples-Spiraling*
Use stories to find value of digits (e.g. “John scored 4,376 points playing a video game. What is the value of the 3 in his score?”)
*Adapted from MacMillian/McGraw Hill Mathematics-Grade 3 / III
Place Value Models
have pairs of students choose a handful of base ten materials from a bag
each partner builds a number using the pieces they picked
partners compare their numbers
write number sentences using < or >.
*Adapted from MacMillian/McGraw Hill Mathematics-Grade 3
Use a number line
using adding machine tape, create a number line-e.g., from 500-1,000
mark in increments of 50
give each student a post-it
have each student write a number on the post-it and place in the correct spot on the number line
Extension:
teacher places a post-it with a question mark on the number line
students estimate what the number could be
10,000 Items Display
Display container of 10,000 items e.g. paper clips, stickers
work on a class collection of 10,000 items over the course of a year
Place Value Dice Game
Have groups of 3-4 students roll a number cube 5 times to make a 5 digit number.
One group member writes the number in word form
A second group member writes the number in expanded form.
A third group member identifies the value of each digit in the number.
A fourth group member orally recites the number.
Groups then check and discuss one another’s answers to decide whether or not all the information is correct.
Newspaper Challenge*
search through magazines and newspapers to find examples of numbers used in real life
challenge them to find a number for each place value through 10,000
create a class place value poster and display the numbers in order
*Adapted from MacMillian/McGraw Hill Mathematics-Grade 3 / II / III
Spiraling Activity
periodically write a number in standard form on the board
students should copy the number

Day 1-write the number in standard form
Day 2-copy the number from the board in standard form and convert to expanded notation
Day 3-copy the number from the board in standard form and convert to word form
Day 4-copy an expanded notation number from the board and convert it to standard form or written form
Day 5-name the digits in each place value.

M-GLAnCE – 3rdGrade – Session 1 – Number and Operations: Place Value – Participant Packet

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How Close to 0? Record Sheet

Player 1 Player 2

Round 1 / 100
─ ___ / 100
─ ___
Round 2 / ─ ___ / ─ ___
Round 3 / ─ ___ / ─ ___
Round 4 / ─ ___ / ─ ___
Round 5 / ─ ___ / ─ ___
Round 6 / ─ ___ / ─ ___
Round 7 / ─ ___ / ─ ___

M-GLAnCE – 3rdGrade – Session 1 – Number and Operations: Place Value – Participant Packet

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Grade 3: Understand and use number notation and place value

Vocabulary

- is the same as ‘less than’

=- is the same as ‘equal to’ or two names for the same number

- is the same as ‘greater than’

-ascending order-numbers are arranged from smallest to largest

-descending order-numbers are arranged from largest to smallest

-digit-any of the symbols used to write numbers (0,1,2,3…9)

-expanded form-a way of writing a number as the sum of the value of its digits (100+20+3)

-number line-a line on which real numbers are assigned to points

-numeral-a symbol that names a number (the symbol 5 names the number 5)

-place value-the value given to a digit by its place in a number (123 means 1 hundred, 2 tens, 3 ones)

-standard form-a way of writing a number that shows only its digits (123)

-word form-a way of writing a number using words (123=one hundred twenty-three)

3000409

3049

300049

PLACE VALUE STACKERS

Student Examples

Discussion Questions:

What do children need to understand about 0 (zero) in place value?
How did the digit 0 (zero) affect the number?
What misconceptions might students have about 0 (zero) when learning about place value?
What strategy can assist students with proper placement of digits in place value?

M-GLAnCE – 3rdGrade – Session 1 – Number and Operations: Place Value – Participant Packet

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0 / 0 / 0
0 / 0
0

PLACE VALUE STACKERS II (Cut on bold lines)

0 / 1 / 2 / 3 / 4 / 5
6 / 7 / 8 / 9
0 / 1 / 2 / 3 / 4 / 5
6 / 7 / 8 / 9

M-GLAnCE – 3rdGrade – Session 1 – Number and Operations: Place Value – Participant Packet

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Trip Tick

Name ______

Point / Pedometer Reading / Difference between Current and Previous Reading / Difference Expressed in Expanded Notation
Starting Point / 0000
Point A
Point B
Point C
Point D
Final pedometer reading

Adapted from Navigating through Problem Solving and Reasoning in Grade 3

M-GLAnCE – 3rdGrade – Session 1 – Number and Operations: Place Value – Participant Packet

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Pedometer Strips

Run strips onto 4 different colors of construction paper. Each student will need one strip of each color.

9 / 9 / 9 / 9 / 9 / 9 / 9 / 9
8 / 8 / 8 / 8 / 8 / 8 / 8 / 8
7 / 7 / 7 / 7 / 7 / 7 / 7 / 7
6 / 6 / 6 / 6 / 6 / 6 / 6 / 6
5 / 5 / 5 / 5 / 5 / 5 / 5 / 5
4 / 4 / 4 / 4 / 4 / 4 / 4 / 4
3 / 3 / 3 / 3 / 3 / 3 / 3 / 3
2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
1 / 1 / 1 / 1 / 1 / 1 / 1 / 1
0 / 0 / 0 / 0 / 0 / 0 / 0 / 0

Adapted from Navigating through Problem Solving and Reasoning in Grade 3

M-GLAnCE – 3rdGrade – Session 1 – Number and Operations: Place Value – Participant Packet

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