1. Sierra November 21, 2016 Amy Ordonez Math Coach *Estrella *Sierra
PARENT MATH NIGHT Arizona’s college and CAREER READINESS STANDARDS (AZCCRS)
Sierra
November 21, 2016
Amy Ordonez
Math Coach
*Estrella
*Sierra

2. 1) What are these new strategies and why are we teaching them?
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?
How many of you enjoyed math as a student? How many of you still enjoy it as an adult?

3. WHY DO WE DO IT “DIFFERENTLY” NOW?
EXHIBIT A
Find the sum.
Thumb up when you have an answer.
How did you solve it?
As adults, it may seem like just common sense, but this is the math strategy of COMPENSATION. Don’t stress about the new names for the strategies.

4. When kids use “old math”
It’s not just Abbott and Costello who make mistakes with our traditional methods
With the latest brain research we know so much more about how our brains develop and learn.
“Insanity – doing the same thing over and over again and expecting different results.” –Albert Einstein

5. The transition
Move from just learning a single technique (HOW) to understanding the math behind it (WHY).
given directions vs given map
How many ways did we learn to add? ONE – line the numbers up, add vertically and carry
How many ways did we learn to subtract? ONE – line the numbers up and if you can’t subtract, you have to borrow from the neighbor
Learning one strategy worked for some of us, but it didn’t work for everyone. Now students have multiple strategies in their toolbelt and can choose which strategy is best for various problems.
ANALOGY: I want everyone to drive from here to my house. (give sample directions)
With a list of directions, making a mistake can send you down the wrong path. Or a problem is slightly different and your steps don’t perfectly work. (Accident on the 101 and the on-ramp is closed.)
With a map, you can plot your own most sensible route to get from start to finish. (Understand there are multiple routes from school to my house and you identify which path is most efficient and best for you.)
Math instruction now tries to help children develop mathematical maps they can use and apply in life, rather than having to remember a list of directions.

6. Algorithm vs. strategies
Standard Algorithm - a step-by-step procedure
Carrying the 1 in addition – not taught until 4th Grade (4.NBT.B.4)
Borrowing in subtraction – not taught until 4th Grade (4.NBT.B.4)
Carrying in multiplication – 5th Grade (5.NBT.B.5)
Long division – 6th Grade (6.NS.B.2)
Strategies – build to an understanding of the operations used in solving problems - FLUENCY
The techniques we learned in school are referred to as the “standard algorithm”. These algorithms are still being taught, but not as the first and only technique. PLEASE be patient with your child’s learning and don’t rush the standard algorithm. Time to build understanding and relationships between numbers.
Let’s take a closer look at the strategies your children are learning.

7. fluency Fluency standards – handout What is fluency?
Ex: Being fluent in another language (I can read, write, speak, have a conversation).

8. Addition Strategies
Direct Modeling – model the action or structure of problem, also described as ‘Counting All’
Most basic level (preK and Kinder)

9. It is okay for a child to use fingers to count at this stage.
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.
Fingers may still be used, but more efficient than Direct Model.
Some teachers have kids clap at starting number and then count up.

10. Addition strategies
Incremental Adding (using decomposition & friendly numbers)
This child knows that 36 can be decomposed into 3 tens and 6 ones.
Adding by tens is friendly and easily done using mental math (skip-counting).
Once child was out of tens, child chose to decompose 6 ones further to reach a friendly number of 110. Then added remaining ones.

11. Addition strategies
Decomposing using an Open Number Line – break apart one number into smaller, friendlier numbers (whatever makes sense for the child!)
Efficient use of number line

12. Addition strategies
Adding by Place Value – break apart (decompose) numbers into tens, ones, etc. and add like place values
Strategy may look like an unnecessary amount of steps, but it leads to strong mental math skills at an early age.

13. Addition strategies
Compensation – making the problem simpler by adjusting to a friendly number
Goal is to make 1 of the numbers into a friendly number that we can easily add mentally. Other number adjusts to compensate for change.

14. Begin with using objects, pictures to represent both numbers
Direct Model
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
ADDITION SUMMARY
Most efficient strategy to use depends on both the child and the problem.

15. Subtraction strategies
Direct Modeling – represent action or structure of problem
Again, this is most basic level of subtraction (preK and K).

16. SUBTRACTION STRATEGIES
Counting Down – start at larger number and count back, may use fingers or tallies to keep track of counting

17. Subtraction strategies
Incremental Subtracting (uses decomposing & friendly numbers)
82 – 49
82 – 10 = 72
72 – 10 = 62
62 – 10 = 52
52 – 10 = 42
= ___
42 – 10 = 32 so it is 1 more, 33
At-home practice:
Skip-count forwards AND backwards by 10’s and 5’s
49 is decomposed into 4 tens and 9 ones.
Subtracting by 10 is friendly and easily done using mental math.
AT HOME PRACTICE: skip-counting forwards and backwards
*Challenge – start at numbers like 12 (count by 10’s, 5’s)

18. SUBTRACTION STRATEGIES
Counting Up - using addition to find the distance/difference between the two numbers
Begin at smaller number and count up to reach larger number; open number line is a great tool for this strategy

19. SUBTRACTION STRATEGIES
Counting Up (using larger numbers)
Subtraction is the difference between the two numbers OR the distance between the two numbers on a number line.
Start with the smaller number and add up until you reach the larger number.

20. Subtraction strategies
Counting Back Using an Open Number Line and Decomposition
Use an open number line and subtract friendly numbers using knowledge of decomposition of numbers

21. Subtraction strategies
Subtracting by Place Value

22. SUBTRACTION STRATEGIES
Compensation – using friendlier numbers and adjusting answer

23. Begin with using objects, pictures to represent both numbers
Direct Model
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
SUBTRACTION SUMMARY

24. 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.

25. Multiplication strategies
Repeated Addition – skip counting, with or without number line

26. Multiplication strategies
By Place Value (partial products) - 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…
= 52
This child decomposed 13 into 10 and 3 because multiplying by both 10 and 3 are friendly and easily done with mental math.

27. Multiplication strategies
Area Model – decompose larger numbers into smaller, friendlier numbers based on place value
Similar to last strategy, but helps break down larger numbers with a visual reference. Great lead into distributive property. This same strategy can be used when multiplying fractions and even in Algebra.

28. 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
This strategy develops as students discover patterns and relationship within numbers.

29. Division strategies
Direct Model – use pictures/objects to model the total being divided into groups (“dealing out”)
24 objects being put into 6 groups. How many in each group?

30. Skip-count forwards AND backwards
Division strategies
Repeated Subtraction – subtract divisor repeatedly to find how many times it can be subtracted
At-home practice:
Skip-count forwards AND backwards
Opposite of repeated addition for multiplication
AT HOME PRACTICE: skip-counting forwards and backwards
*Challenge – start at numbers like 12 (count by 10’s, 5’s)

31. Division strategies
Area Model – connect division as multiplication problem
Just like an area model can be used for multiplication, it can also be used for division.
Students use known facts to build up to solution.

32. 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.
Students use several steps to find the quotient by relying on known facts and multiples of 10. This strategy can be applied to more complex division problems.

33. Division strategies
Decomposing – breaking apart the larger number into smaller, friendlier numbers, basis of distributive property
place value simpler facts
(24÷4=6)
How to break up larger number depends on each student (efficiency is unique)

34. Division strategies
Related Facts – using facts students already know to solve problems

35. MULTIPLICATION AND DIVISION SUMMARY
Begin with pictures, objects to represent problem.
Direct Model, Repeated Addition/Subtraction
Use simpler problems to build up to given problem
Decomposing, Area Model, Related Facts
MULTIPLICATION AND DIVISION SUMMARY

36. Parent resources http://www.kyrene.org/Page/2770
If you want to increase your own knowledge base, take a look at the Roadmaps.

37. How can I support my child in math?
“Do’s”
#1 - Help your child develop a “growth attitude” about math.
Recognize there is more than one way of solving a problem.
Ask questions when they get the answer right, too! (handout)
Pretend you don’t know – have you child teach you.
Play games & puzzles (develop numeracy & logic skills)
SET, Mancala, Yahtzee, Mastermind, Blokus, Guess Who?, Dartboard
Brainteaser puzzles (problem-solving, critical thinking)
Lego blocks, K’nex (spatial reasoning)
Watch the NCTM video. Refer to questioning handout in their packet.
Getting it done fast doesn’t mean it’s done correctly. They may not be able to do something immediately, but that doesn’t mean they will never be able to do it. Struggle is a good thing. There is a difference between positive struggle and frustration. We shouldn’t let them get to the point of frustration, but we shouldn’t spoon feed them the answer either.
Sometimes people get the right answer for the wrong reasons. Plus, if you only ask for an explanation when they get the question wrong, they begin to associate being asked to explain with failure and will begin to clam up rather than learn from their mistakes.

38. How can I support my child in math?
“Don’ts”
Focus on speed (i.e. flash cards)
Just give them extra math work
Simply give the correct answer. Try to give feedback – ask your child to talk through how they worked it out and lead them to the spot of the error.
Expect them to “get it” after you’ve explained it once – Be patient!
#1 rule - NEVER describe yourself as hopeless in math!!
There is no such thing as the “math gene”!

39. How can I support my child in math?
Dreambox - can be accessed at home
Start with some online resources.
Dreambox is a website the students can do both a school and at home. It is adaptive – it differentiates content, pace, and sequence to match your child’s needs.

40. How can I support my child in math? Dreambox-parent account
Need to create parent account using child’s log-in info. Contact teacher if you do not know their log-in.

41. Helpful books