Understand Numbers and Relationships of Numbers

Sample Power of 10 Connections to Number Worlds C

Understand numbers and relationships of numbers
Key Skills and Concepts / Activities and Experiences / Materials / Connections to….
·  Counting
  one-to-one correspondence
  rote (memorized) counting
  rational counting
  keeping track
  cardinality
  conservation of number
o  / -Have students pass out materials (one per…)
-Counting forward/backward, skip counting, starting at numbers other than one
-Touching/Moving Objects
- Counting Orally and Silently
-Asking “How Many?”
-Songs, Rhymes, etc. / (Red/Black Counters, Tiles, Small Physical Objects) / C:1 Counting
Drop and Count
C:3 More Counting and
Comparing
Concentration (Dot match)
C:4 Matching Dot Sets to
Numerals
Concentration to 20
C:15 Graphing and Comparing
Numbers
Linking and Thinking
(repr #’s on bar graphs)
·  Subitizing / -Asking “What do you see?” and “How do you see it?”
-Have students replicate the dot flash card (‘may have to give the card to student and let him/her actually build on the card, then build beside the card, then build with no card at his/her desk).
-Repeat the Process with 5-Frame and 10-frame Flash Cards / Dot cards, red/black counters, PowerPoint dot arrangements, Dominoes, Small red/black flash cards (for partner work),
Five-frame Flash Cards, Ten-frame Flash Cards
·  Representing numbers / Symbol Recognition
- Play Games
-Sort cards / Game Boards (Numerical Symbols/Dot Rep’s), Dice,
Multiple Rep’s for Numbers Cards
·  Composing/Decomposing numbers / -Build 5 with five-frame mats
“How many do you see?”
“How did you see it?”
“How do you know you are
correct?”
-Build 10 using Ten Frame mats
-Build 5 and 10 with frames, but flip some of the disks (2 colors), and say/write the number sentence created
-Given 5 or 10 objects, put them into two different shape “pens” and say/write the number sentence created
-Play “Frogs in the Pond”
-Repeat with numbers other than 5 and 10 / Five-frame Flash cards/mats, Ten-frame Flash cards/mats
Counters, 2-color Disks, base-ten blocks, bean sticks, craft sticks, small ten-frames, base-ten cards, Part-part-whole Mats/cards, Cloth tents, Small bowls or Cups / Picture Land Activity Sheets 3-8 could be used with 2-color disks.
·  Relative position and relationships of numbers / - Play Race to 10
-Play Primary Catch Me if You Can
-Hundreds Chart Activities
(missing parts, or cut out
puzzle)
-Number line activities
-Before/After
-More/Less
-Ask about 1 more/less, 2 more/less / Race to 10 Game Board, Number lines, Catch Me if You Can Boards, Clotheslines, flip-ups, word strips, hundreds charts (complete, missing numbers, and highlighted clues) / C:1 Counting
Feed The Animals
C:2 Counting and Comparing
Count and Compare
C:3 More Counting and
Comparing
Party
C:4 Matching Dot Sets to
Numerals
Bravo!
C:5 Number Sequences and
Number Lines
Delivering Mail
Magnetic Number Line Game
C:6 More Number Sequences
and Number Lines
Delivering Mail
C:7 Number Neighborhoods
Numbering the Neighborhood
C:8 More Number
Neighborhoods
Meet Your Neighbors
Building a Neighborhood
C:9 Adding Numbers
Can You Guess My Number?
C:10 More Adding
Can You Guess My Number?
C:13 Counting and Adding
Steve’s New Bike
C:24 Numbers to 100
Elevator Game
C:24 Numbers to 100
Number Line to 100
C:25 More Numbers to 100
Writing Numbers to 100
C:30 Making a Map
Hallway Map
·  Place Value / -Ask students to physically build numbers using more than one model
-Ask students to go back-and-forth between multiple representation of numbers (base 10 blocks/cards, ten frames, words, symbols, etc.) / Spinners, ten frames and ten frame cards, base-ten block/cards, craft sticks, bean sticks, arrow cards / C:27 Tens and Ones
Rosemary’s Super Shoes
(symbolic)
·  Reinforce Building 5 and 10 / Play Games
-Make 5 Go Fish
-Make 10 Go Fish
-Rummy
-Snappo
- Clear the Deck
- No Mate
- Make Ten Pyramid Solitaire
- Sum of Ten
- Catch Me if You Can!
- Math Basketball
- Math Baseball/Softball / Number Cards (5 frame and 10 frame), Game Boards, Dice, Spinners / C:17 Solving Equations
Counter Dropping
(2 Addends = 5)
Three Area Counter Drop
(3 Addends = 10)
Understand operations and relationships of operations
·  Addition and Subtraction / Story Problems in context / Power Point and Task Cards with Story Problems, Part/part/whole mat, counters, cards / C:26 Addition Stories
How Many Balloons?
C:29 Addition and
Subtraction Stories
How Many Are Left?
C:30 Making a Map
Feed the Pets
·  Composing and Decomposing Numbers
  combinations for 5
  combinations for 10
  1 more/less
  2 more/less
  0 more/less
  add/subtract 10
  doubles and near doubles
  using 10 as a bridge / -Continue to reinforce building 5 and 10
-Transition from 1 more/1 less relative position to +1, -1. Repeat with 2. Play Math Basketball or Baseball with cards and spinner
-Look for patterns for +10, -10
-Play Leap Frog on Number Lines
-Use Part-Part-Whole Cards (students build cards with mats and find missing parts, students make up stories for cards, etc.)
-Play Race to 100
-Use Double Ten Frames to add sums 11-20 (Ten As A Bridge)
-Use Sum Above Ten Cards to match problem with first step.
-Play Math Race with Sum Above 10 cards
-Use Open Number lines (“move” to nice numbers, build tens, skip count, etc.)
-Use Ten as a Bridge cards to find missing addends/sums.
-Play Intermediate Catch Me if You Can to practice
-Assess with Tent Problems
-Make other decade numbers
  turn over 2 digit cards to make a number and describe the decades this numbers falls between
  turn over 2 digit cards to make a number, spin the decade spinner and decide what you have to + or – to get to that decade number
- Play Making 100
- Have students build add/subtr problems for 2-digit numbers using more than 1 model.
-Have students solve add/subtr problems for 2-digit numbers using paper/pencil and 2 different strategies
-Other Strategies for addition
  using manipulatives
  add tens, add ones, combine
  start with one number, add tens, add ones to make next decade, add rest
  etc
-Other Strategies for subtraction
  using manipulatives
  start with 1st number, subtract tens, subtract ones
  add up using nice numbers
  subtract tens, subtract ones (may be negative), combine
  etc
- If grade appropriate, move on to operations with integers and play Integer Spin / 5-frame cards, 10-frame cards, ten beads/strings, make 5 & 10 games, number lines, open number lines, clothesline, calculator, hundreds chart, sum of ten and above cards, using ten as a bridge cards, spinners, 5-frame, 10-frame, double ten frames, Race to 100 game board, plain digit cards, cloth napkins (tents), craft sticks, beans, etc. / C:1 Counting
Drop and Count (add 10)
C:2 Counting and Comparing
Food Fun
C:6 More Number Sequences
and Number Lines
Plus-Minus Game
C:7 Number Neighborhoods
The Biggest Neighborhood
C:9 Adding Numbers
Dragon Quest 1 (symbolic)
C:10 More Adding
Drop and Add (symbolic)
C:11 Sequencing Numbers
And One More Makes
More Food Fun
C:12 Writing Equations
They’re Gone (2 addends)
Add Them Up (3 addends)
C:13 Counting and Adding
Secret Number Game
C:14 Making Equations Making Equations for
Beginners
Making and Writing Equations
C:15 Graphing and Comparing
Numbers.
Making and Writing Equations
(no pictorial sum)
C:16 More Counting and
Adding
Secret Shopping Game
(number line > symbols)
Changing Addends
C:17 Solving Equations
Counter Dropping
(2 Addends)
Three Area Counter Drop
(3 Addends)
C:18 Adding and Subtracting
Dragon Quest 2
Shopping Trip
C:19 Subtracting
They’re Gone (Review)
Tear It Up and Throw It
Away
Subtracting Counters
C:20 Subtracting and
Prediciting
Going Fishing
Adding Concentration
C:21 Adding and Comparing
Flip, Add, Compare
Roll, Add, Compare
C:22 Subtracting to Zero
Subtracting to Zero
Which Way Should I Go?
C:23 More Adding and
Subtracting
Counting Back (symbolic)
Dragon Quest 2 (symbolic)
C:24 Numbers to 100
Elevator Game
C:26 Addition Stories
And The Answer Is…
C:27 Tens and Ones
Dragon Quest 3 (symbolic)
C:28 Adding and Subtracting
Length
·  Fact families / -Sort Part-Part-Whole cards by fact families
-Play partner games with Triangle cards, Turnover cards, Sum/Difference cards, etc. / Part-Part-Whole Cards, Triangle Cards, Turnover cards, Sum/Difference cards,
·  Estimation / Ongoing – Everyday
Are we in the ballpark? Daily Questions and Activities:
-“Do we think the answer would be less than 5? More than 10?”
-“Approximately where would this number be on the number line?”
-Partners compete to determine if sum of two numbers is <10, >10, or =10 (cards, dice, or spinners)
-Etc. / Number cards, Dice, spinners,
Understand Operations and Relationships of Operations (cont’d)
·  Multiplication and Division / Story Problems in Context / Power Point and Task Cards with Story Problems, Counters (Beans, Tiles, Disks, etc,) Condiment Cups
·  Models for Multiplication
  Equal Sets
  Repeated Addition
  Array Model
  Area Models / -Transition from Story Problems (multiple ways to build the problems).
- Use array templates; match array models to problems.
- Use area models to organize and develop visual understanding of multiplication
- Have students sort the Multiplication Representations Cards / Beans, Tiles, Disks, etc. Condiment Cups Multiplication Representation Cards, Array Templates/Cards, Area Model Cards,
Compute fluently and make reasonable estimates
·  Building “Facts” / -Multiply by 0 and 1 in context.
-Multiply by 2 (Use a math game and a card – student multiplies the card number by 2)
-Play Double or Nothing
-Play Multiplication Bingo (0,1,2)
-Divide by 0,1, 2
-Multiply//Divide by 10
-Play Target
-Multiply by 5
-Build other Mult Facts with grid paper models
-Look for patterns (9’s, etc.)
-Play Smallest Remainder
-Alternate Strategies for Mult.
  Partial Products
  Lattice Multiplication
  Russian/Pheasant
-Alternate Strategies for Div.
  Forgiveness Method
-Use area model cards as practice “flash cards”
-Use Multiplication Turnover Cards to practice fluency
-Play math games with multiplication/division problems
  Math Baseball/Basketball
  Product Capture
  The Product Game
  Mult. Three in a Row
  Five Alive
  Four in a Row
  Seven-Up
  Number Capture
  Multiple Capture
  Seven Down
  Sum and Product Cards / Multiplication Turnover Cards, Math Games, Area Model Cards, Grid Paper
Understanding Fractions and Operations with Fractions
·  Fraction Models
  Region/Area
  Linear/Measurement
  Set/Discrete / -Begin with 1-half
- Find 1-half with different area models and units (‘Half of what?”)
- Find 1-half with different linear models and units (‘Half of what?”), Paper folding
-Given unit, find 1-half. Then given 1-half, find the unit.
-Find 1-half with set models
-Given unit, find 1-half. Then given 1-half, find the unit. (Draw/Build the other half)
-Connect Percentages to Paper Folding. (1-half becomes 50%)
-Find 50% in the 3 different models.
-Connect Decimals to Paper Folding
-Multiple Representation of 1-half (Equivalent Expressions)
-Use Fraction/Dec/% Cards for 1-half practice
-Use Unit/Fraction Cards to practice going back-and-forth
-Repeat process with 1-fourth, etc.
-Brownie Fractions (Equivalent Fractions)
-Brownie Fractions (Adding Fractions with Unlike Denom’s) / Fraction Circles, 2-color Chips, Paper Strips, Geometric Shapes (cut out from colored paper), Fraction Cards (Mult. Rep’s), Unit/Fraction Cards, Fraction/Dec./% Cards, Fraction Brownie Templates,
·  Comparing and Estimating Fractions / -Use benchmarks to compare fractions on number line (“Where would 3-fourths be?”)
-Use physical models to compare fractions
-Use Fraction Cards to Sort
(< 1-half, > 1-half, etc .)
-Use Fraction Cards to Build One
Ongoing – Everyday
Are we in the ballpark?
Daily Questions and Activities:
-“Do we think the answer would be less than 1-half? More than 1?”
-“Approximately what would 1-third of this shape be?” / Clothesline, Number Lines, Open Number Lines, Geometric Shapes, Paper Strips
·  Finding Percentages / -Emphasize Tenths with Paper Strips and Connect to Ten Frames
-Ten Frame Percents with Powerpoint Problems
-Fr.Dec.% Turnover Cards when ready for fluency / Powerpoint, Ten frames, Beans (counters), Paper Strips, Yarn/String,
Fr.Dec.% Turnover Cards

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