Developing Number Sense in Young Learners preK-2nd grade CARS+ Conference February, 2011
What Are We Going To Teach? CA Preschool Learning Foundations: At around 60 months of age
• 1.1 Recitenumbers in order to 20 • 1.3 Identify, without counting, thenumber of objects in a collection of up to 4 objects • 1.4 Count up to 10 objects, using 1:1 correspondence
Preschool Learning Foundations (con’t) • Understand when counting, that thenumber nameof thelast object counted represents the total number of objects in thegroup • Compare, by counting or matching, two groups of up to 5 objects & communicate, “more,” “sameas,” or “fewer” (or “less”)
Preschool Learning Foundations (con’t) Understand that: • Adding 1 or taking away 1 changes thenumber in a small group of objects by exactly 1 • Putting 2 groups of objects together will makea bigger group & that taking objects away will makea smaller group
Preschool Learning Foundations (con’t) • Solvesimpleaddition & subtraction problems with a small number of objects (sums up to 10), usually by counting
CA Common Core Mathematics Standards Kindergarten: • • • •
Know number names & count sequence Count to tell thenumber of objects Comparenumbers Understand addition as adding to and subtraction as taking apart & taking from • Work with numbers 11-19 to gain foundations for placevalue
CA Common Core Mathematics Standards First Grade: • Extend thecounting sequence • Represent & solveaddition & subtraction problems • Understand therelationship between addition & subtraction • Add & subtract within 20 • Work with addition & subtraction equations
CA Common Core Mathematics Standards Second Grade: • Represent & solveproblems involving addition & subtraction • Add & subtract within 20
Our Focus • • • • • •
Counting 1:1 Correspondence Conservation of Number Beginning Addition & Subtraction Mathematical Language Math Reasoning
How Are We Going To Teach Number Sense? Young Learners learn best with: • Hands-on experiences with real objects • Repeated experiences with real objects in many contexts (up to 100 student responses/30 minutes)
• In an environment that is interesting, stimulating, & fun
Three Ideas to Understand Before We Begin • Inclusion • 1:1 Correspondence • Conservation of Number
Counting • Memorization skill: Don’t assumestudent understands quantity,morethan, less than, etc • Can betaught with enough repetition • Goal: To beableto count forward and backward starting and stopping at various points
Rote Counting Activities • Counting with Physical Movement – Count & Turn – Stand & Sit – Ankles to Head – Clap & Slap – TakeOver – Grandpa Wolf
Rote Counting Activities • PendulumCounting (to vary rate) • CircleGame
Counting & 1:1 Correspondence • • • •
Slide& Check with Xylophone Count & Dump Find a Match (Concentration) Cubes on Fingers
Independent Counting Activities • • • • • • •
Paper Clips on a Card Flowers in a Vase Clothespins on a Hangar Piggy Banks Buttons in Egg Cartons Cans with TongueDepressors Build a Tower (next slide)
Build A Tower
Review Tell your neighbor two ideas you will useon Monday
Why is the concept of more & less important?
Concept of More & Less Theseactivities arenot meant to bedoneas a “unit” beforeaddition & subtraction, but rather integrated into thestudents’ day and math instruction throughout theyear
More & Less Activities • • • • •
More& Less Roll I t (next slide) Grab Bag Stacks Stack, Tell, Spin, & Win (MTW) Conversations/Observations All Day Long— TableGame
less
more
Review Discuss with your partner why it is important to teach theconcepts of moreand less.
Addition & Subtraction Important Teacher Strategies: • Movefrom concept
representational
symbolic
• Useaddition & subtraction simultaneously • Useaccurate& varied math vocabulary
Addition & Subtraction Activities • Number Stories – Everyday, all day – First, real people, real events – Second, objects represent real people& events – Finally, symbols represent events
Who’s At the Table? Math Game 1. Sit around a table(in this example, thereare5 people) 2. Each person takes a turn telling a number story about themembers Examples: • •
“2 peoplehavegreen eyes & 3 peopledon’t, 2+3=5” “3 ears haveearrings and 7 don’t, 3+7=10”
Addition & Subtraction Activities • Snap It (or “DivideIt” if not using cubes) – All “read” together – This is not a test
• The3 Math Their Way Games: – Tub Game – Peek Over theWall – CaveGame
• Finger Cubes
Addition & Subtraction Activities • Number Trains (3/4” squares) • Grab Bag Subtraction • Equation DiceToss (MTW) (next slide)
Equation Dice Toss
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Review Sharewith your neighbor 3 addition/subtraction ideas you can useon Monday
“The most powerful tasks have value in being repeated over and over again. Each time children do a task they will be working at a different level as they develop understanding and increase competence.� ~ Kathy Richardson