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:

  1. What do children need to understand about 0 (zero) in place value?
  2. How did the digit 0 (zero) affect the number?
  3. What misconceptions might students have about 0 (zero) when learning about place value?
  4. 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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