Understand numbers and relationships of numbers

Sample Power of 10 Connections to Number Worlds D

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	-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)	D:Unit 1:1 Constructing Whole Numbers Lessons 1 Concentration
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	D:Unit 1:1 Constructing Whole Numbers Lessons 2-3 Start With Five Fill the Ten Frame How Many? Ten Frame Quick Facts
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)	D:Unit 1:2 Numbers on a Line Lessons 1 – 5 Steve’s New Bike One Hundred Houses Number Line Race to 100 Plus-Minus Race to 100 D:Unit 1:3 Whole Number Relationships Lesson 2-4 Feed the Animals Party Hungry Alligators D:Unit 4:1 Subtracting Quantities Lesson 1 Mystery Number
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	D:Unit 1:4 Tens and Ones Lessons 1 – 5 Rosemary in the City Hotel Room Service Double-digit Number Composition Building and Trading Numbers
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
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	D:Unit 3:2 Writing Addition Equations Lesson 4 Acting Out D:Unit 4:1 Subtracting Quantities Lesson 3 Shopping Trip
Compute fluently and make reasonable estimates 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 1^st 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.	D:Unit 1:1 Constructing Whole Numbers Lesson 4 - 5 Concentration to 20 D:Unit 3:1 Adding Quantities Lessons 1-5 Count and Compare Dragon Quest Making and Writing Eq’s Drop and Add D:Unit 3:2 Writing Addition Equations Lessons 1-3 Secret Number Game Grab and Add Three-Area Counter Drop D:Unit 3:3 Adding Successive Quantities Lesson 1 – 5 The Fiercest Dragon Let’s Add Some More Triple Spin Thumbs Right, Thumbs Left D:Unit 4:1 Subtracting Quantities Lesson 2 They’re Gone D:Unit 4::2 Writing Subtraction Equations Lessons 1 – 5 Going Fishing Subtracting to Zero Counting Back How Many Are Left? D:Unit 4::3 Subtraction Tools and Strategies Lessons 1 – 5 Take It Back Take It Way Back Missing Number Missing Middles D:Unit 4:4 Mastering the Basic Facts Lesson 1 – 5 How Many More? Break It and Connect It Halves and Near Halves Differences Around the Room
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,	D:Unit 3:4 Mastering the Basic Facts Lessons 1 – 5 Using the Addition Table Even or Odd One More, One Less Make It Easier
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,	D:Unit 1:3 Whole Number Relationships Lesson 1 Estimation
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,
Compute fluently and make reasonable estimates
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