OLD DOGS, NEW MATH ARIZONA’S COLLEGE AND Kyrene S chool Di strict CAREER READINESS M arch 2 6, 2 0 15 STANDARDS (AZCCRS) Alison Gaedke Math Coach *Lagos *Mariposa http: p://w /www.kyrene ne.org/Page/333 3365
MAIN TOPICS 1) What are these new strategies and why are we teaching them? 2) What can I do at home to support my child in math?
WHY DO WE DO IT “DIFFERENTLY” NOW? EXHIBIT A Find the sum. 298 + 26
WHY DO WE DO IT “DIFFERENTLY” NOW? EXHIBIT B
THE TRANSITION Move from just learning a single technique (HOW) to understanding the math behind it (WHY). given directions vs given map
ALGORITHM VS. STRATEGIES Standard Algorithm - a step-by-step procedure Carrying the 1 in addition – not taught until 4 th Grade (4.NBT.B.4) Borrowing in subtraction – not taught until 4 th Grade (4.NBT.B.4) Carrying in multiplication – 5 th Grade (5.NBT.B.5) Long division – 6 th Grade (6.NS.B.2) Strategies – build to an understanding of the operations used in solving problems - FLUENCY
FLUENCY
ADDITION STRATEGIES Direct Modeling – model the action or structure of problem, also described as ‘ Counting All ’ Most basic level (preK and Kinder)
ADDITION STRATEGIES Counting On – able to start at first number/largest number and count up from there It is okay for a child to use fingers to count at this stage.
ADDITION STRATEGIES Incremental Adding (using decomposition & friendly numbers)
ADDITION STRATEGIES Decomposing using an Open Number Line – break apart one number into smaller, friendlier numbers ( whatever makes sense for the child! )
ADDITION STRATEGIES Adding by Place Value – break apart (decompose) numbers into tens, ones, etc. and add like place values
ADDITION STRATEGIES Compensation – making the problem simpler by adjusting to a friendly number
Begin with using objects, pictures to represent both numbers Direct Model ADDITION SUMMARY Move into using fingers to keep track of counting Counting On Use simpler facts to solve problem Add by Place Value, Decomposing, Incremental Adding, Compensation Most efficient strategy to use depends on both the child and the problem.
SUBTRACTION STRATEGIES Direct Modeling – represent action or structure of problem
SUBTRACTION STRATEGIES Counting Down – start at larger number and count back, may use fingers or tallies to keep track of counting
SUBTRACTION STRATEGIES Incremental Subtracting (uses decomposing & friendly numbers) 82 82 – 49 49 82 – 10 = 72 72 – 10 = 62 62 – 10 = 52 52 – 10 = 42 42 - 9 = ___ 42 – 10 = 32 so it is 1 more, 33 33
SUBTRACTION STRATEGIES Counting Up - using addition to find the distance/difference between the two numbers
SUBTRACTION STRATEGIES Counting Up (using larger numbers)
SUBTRACTION STRATEGIES Counting Back Using an Open Number Line and Decomposition
SUBTRACTION STRATEGIES Subtracting by Place Value
SUBTRACTION STRATEGIES Compensation – using friendlier numbers and adjusting answer
Begin with using objects, pictures to represent both numbers Direct Model SUBTRACTION SUMMARY Move into using fingers to keep track of counting Counting Down, Counting Up Use simpler facts to solve problem Incremental Subtracting, By Place Value, Compensation
MULTIPLICATION STRATEGIES Direct Modeling – draw picture of problem, read ‘x’ sign as “groups of” 3 x 4 (3 groups of 4) Add up all dots to find answer.
MULTIPLICATION STRATEGIES Repeated Addition – skip counting, with or without number line
MULTIPLICATION STRATEGIES By Place Value – decompose number based on place value to use simpler facts to build to answer 13 x 4 (10 x 4) + (3 x 4) 10 x 4 = 40 3 x 4 = 12 Add products up… 40 + 12 = 56 56
MULTIPLICATION STRATEGIES Area Model – decompose larger numbers into smaller, friendlier numbers based on place value
MULTIPLICATION STRATEGIES Related Facts: using facts students already know to solve problems; other patterns that students discover such as Double & Half DOUBLE & HALF 5 x 6 is the same as 10 x 3 14 x 4 = 7 x 8
DIVISION STRATEGIES Direct Model – use pictures/objects to model the total being divided into groups (“dealing out”)
DIVISION STRATEGIES Repeated Subtraction – subtract divisor repeatedly to find how many times it can be subtracted At-home practice: Skip-count forwards AND backwards
DIVISION STRATEGIES Area Model – connect division as multiplication problem
DIVISION STRATEGIES Big 7 – help understand long division process by using smaller known facts to reach the solution The number of steps taken to solve the problem will vary based on students estimation skills and number sense.
DIVISION STRATEGIES Decomposing – breaking apart the larger number into smaller, friendlier numbers, basis of distributive property place value simpler facts (24 ÷ 4=6)
DIVISION STRATEGIES Related Facts – using facts students already know to solve problems
Begin with pictures, objects to represent problem. MULTIPLICATION Direct Model, Repeated Addition/Subtraction AND DIVISION SUMMARY Use simpler problems to build up to given problem Decomposing, Area Model, Related Facts
PARENT RESOURCES http://www.kyrene.org/Page/2770
HOW CAN I SUPPORT MY CHILD IN MATH? Attitude Help your child develop a “growth attitude” about math. Feedback – resist the temptation to give them the right answer. Instead ask them to talk through how they worked it out and lead them to the spot of the error. Ask questions when they get the answer right, too! Patience – learning doesn’t happen in an instant. Make math a natural part of life instead of just a subject in school. #1 rule - NEVER describe yourself as hopeless in math!!
HOW CAN I SUPPORT MY CHILD IN MATH? Dreambox - can be accessed at home
HOW CAN I SUPPORT MY CHILD IN MATH? Dreambox – PARENT ACCOUNT Review your child’s academic progress with a DreamBox Parent Account. Please follow these steps to create your free Parent Account: 1. Go to http://www.kyrene.org/Page/32735 and click on Dreambox. 2. Select your child’s school and have your child log in to their profile just as he/she would at school. 3. Click Setup Parent Access at the bottom of the page. 4. Follow instructions to create a new login and password. 5. Read Terms of Use and Privacy Policy . 6. Click "Submit". Log into your home account after set up: 1. Go to http://play.dreambox.com 2. Enter your email address and password. 3. To see student progress, click the "Parent Dashboard" button.
HOW CAN I SUPPORT MY CHILD IN MATH? Math Props – “talk math” and incorporate math into everyday life Digital and Analog clock – skip- counting by 5’s Traditional Wall Calendar – skip- counting by 7’s, patterns Measuring Cups/Tapes – customary and metric Dried beans, macaroni, M&M’s – counting, direct modeling Coin jars – dump out & count Indoor/Outdoor Thermometer – compare temperatures Money – cash back, estimating total, estimating tax
HOW CAN I SUPPORT MY CHILD IN MATH? Play Games! ! Dart board (Velcro darts) – addition, doubling, tripling Outdoor Games – Bean Bag Toss, Ladder Golf Board games with dice and/or spinners Regular deck of cards – endless games to play! **Have them keep score!
CARD GAMES!
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