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### Strategies for Building Math Confidence

Ann-Marie Hunter

Reasons for Building Math Confidence

- Math can be a huge source of anxiety;
- often students are made to feel that they are destined to fail.
- Your efforts to reduce Math anxiety can alter students’ attitudes towards their own abilities and create success.

Many parents and educators act as though only some people can do Math.

- Communicating to your students that you believe everyone can do Math, motivates them to do their best.
- Work on creating a hands on, meaningful learning environment to engage students.

Workshop Outline

- Mastering the Basics – Power of Ten
- Brain research - how it can sharpen your teaching
- Place value
- Focus on the Facts
- Mental Math

Mastering the Basics Program

REINFORCES BASIC SKILLS

- student choice of topic - opportunities to rewrite
- students develop ownership of their own progress.
- results are private – no whole class sharing
- each student works on areas ofhis/her own need.
- parents like the goals - they can easily help their children.

Record sheet used for each student:

- record scores from Basic Facts Tests as # of errors.
- each test day, record topic & form
- after marking, record % score
- after 80% mastery has been reached, check off Topic Mastered column
- Average all passing scores for Term Average
- Copy this form and include the copy with each child’s report card

2) Use Brain Research to Sharpen Your Teaching

- Semantic memory
- Knowing what a bike is and being able to describe it is using Semantic memory.
- Episodic memory
- Having experienced riding a bike and remembering the multitude of times you enjoyed biking is using Episodic memory.
- Procedural memory
- Being able to get on a bike and ride it without thinking is using Procedural memory.

Using Brain Research ~Adjust your teaching in these ways:

*FABULOUS FOUR*

- Personalize instruction to promote retention
- Use visual, hands-on tools for learning
- Verbally reinforce learning as much as possible
- Incorporate movement within each lesson

3) Place Value – Reading numbers

____ “hundred” ____ “tee” ____ then say the final digit.

Example: 572 reads as:5 hundred, 7 tee, two.

Read any number:

__ __ __ MILLION __ __ __THOUSAND __ __ __ . __

and tenths

__ __ __ MILLION __ __ __THOUSAND __ __ __ . __ __ and hundredths

Activity #1

1 - Convert numbers to words, capitalizing the ‘SPACE NAMES’:

67 893 542

sixty-seven MILLION,

eight hundred ninety-three THOUSAND,

five hundred forty-two

2 – Convert words to numbers, ordering the periods (groups of 3) of digits

- Focus on the 3-digit numbers between the space names.
- Place those series of numbers in order.

five hundred six MILLION,

506

two hundred seventy-eight THOUSAND,

278

ninety- seven

097506 278 097

Using ‘reading numbers’ to develop student confidence and understanding of place value

- Which digit is in the ten thousands place?
- Example: 258 673 910
- Students think: 258M673Th910
- Identify the THOUSANDS period

(the period in front of the THOUSANDS space name)

- Look at 673 andfind the tens place.
- In this example, it’s 7

Use Models for Decimals

- Convert Base Ten Blocks to demonstrate the relationship between units, tenths, hundredths, and thousandths

Large Cube: ones (units)

Flats : tenths

Rods: hundredths Small cubes: thousandths

4) Focus on the Facts

- “After learning to read, learning the multiplication facts is probably one of the most important things we learn in elementary school.” - Trevor Calkins
- We sometimes think we can’t give students time to build timestables knowledge because … “ I have all those units to cover! ”

The truth is – you can’t ignore students’ need to understand and know Basic Facts. Knowing basic facts BUILDS CONFIDENCE

and CREATES SUCCESS!

After a child knows the facts, everything seems easier – and IS easier!

Mental Math confidence begins to grow.

Knowing Math facts allows students to confidently engage in learning new concepts.

Power of Ten Cards

Power of

Ten Card

for 8

Power of

Ten Card

for 7 Check out the

Power of Ten cards

at your table

VISUALIZING NUMBERS BUILDS NUMBER SENSE

- Use Power of Ten cards to give visual aid
- Practise subitizing to 10

1 + 9 = 10 2 + 8 = 10 3 + 7 = 10 …

- Talk about mentally combining numbers, encouraging students to visualize them.

7 + 7 = (7 + 3) + 4 = 10 + 4 = 14

Discuss the thinking involved Activity #2

Use Visual Tools to reinforce the meaning of multiplication and division:

- Power of Ten multiples sheet – visually shows groups of numbers

6 groups of 7 Activity #3

6 X 7 = 5, 10, 15, 20, 25, 30 (skip counting full columns)

then - (adding on the twos) 32, 34, 36, 38, 40, = 42

Other ways to represent multiplication facts

Cross lines:Arrays:

Count the intersections. Shade a section of graph paper.

3 X 9 = 27 3 X 7 = 21

Record the total for Record the total for

each line each row

Use tiles to make rectangles that represent multiplication/division

- For example, 24 divided by 6
- Use 24 tiles
- Evenly placed into a rectangle with 6 rows (or columns).
- Identify how many columns (or rows) are created, thus giving 4!
- Link these discoveries with Fact Families practise.
- Continually allowing students to discover Math facts with concrete objects gives them a visual tool to link to understandings, becoming confident.

Activity #4

Talk about multiplication and division together – Fact Families

4 X 7 = 28,

so 7 X 4 = 28,

28/7 = 4,

and 28/4 = 7

Use Triangular Flash Cards!

Memorization Advice

Memorization is about speed, efficiency, and freeing up brain space for other Math thinking ~ Greg Tang

It has been repeatedly shown that knowing sums to 10 and knowing the timestables, contributes significantly to Math success. The increase in speed, efficiency and free brain space, converts to less frustration and greater confidence. ~ Ann-Marie Hunter

Triangular Flash Cards

- MEMORIZATION of timestables should NOT HAPPEN until AFTER having lots of time with concrete examples.
- TRIANGULAR FLASH CARDS:
- Each cardis a triangle with two factors and the product written in corners
- Students cover one corner - try to identify the covered number using the other two numbers

Reduced Times Tables sheet

- Visually looks like half as many to learn
- Helps students to practise what they know in an organized manner
- Use the blank sheet on one side, with answers on the other, to encourage pairs of students to study together
- Stress importance ofPerfect Squares: 2 X 2, 3 X 3, 4 X 4 …
- Students build their recall of other facts based on what

they already know

- Power of Ten ‘All the Facts’ sheets can be used as a regular check on timestables progress
- Students make triangular flash cards for ones they don’t know

Practise multiplying by powers of 10 - powerful skill for estimating/mental math

- 3 X 10 = 30
- 7 X 100 = 700
- 2 X 1000 = 2 000
- 40 X 300, (4 X 3) = 12
- place the #of zeros (3) behind the 12 12 000
- 200 X 500, (2 X 5) = 10
- place the 4 zeros behind the 10 100000
- Partners challenge each other and check answers on calculators. Activity #6

Double Digit Multiplication

45 Use Multiplying by Powers of Ten skills to X 37 (30 + 7)help with the multiplication

315 (7 X 45) algorithm

+ 1350 (30 X 45)

(because we’re multiplying by 30, we place a zero at the end of the second line and then pretend we’re multiplying by 3)1665

Additional Resources to make learning timestables fun:

a) Timestables the Fun Way! - Judy Rodriguez –

Contextual representation of the multiplication facts.

Example #1: Sean - kite flyer from top of hill

Happy to turn 16 and gets his driver’s license

Can drive his 4 X 4 instead of walking!

Remember: You need to be 16 to drive a 4 X 4,

so … 4 X 4 = 16!

Example #2: 6 X 6 – Oasis in a desert(thirsty sixes)

Additional Resources to make learning timestables fun:

b) TIMEZ ATTACK – online video game format - teaches and reviews timestables

- Free and Paid version

www.bigbrainz.com

c) MATHLETICS–online individualized Math explorations.

Mathletics Live students compete with kids all over the world on Basic Facts. They love it!

www.mathletics.ca

Arrow Graphs * opportunity for students to think creatively * demonstrate student understanding * easy to incorporate into your planning

40 000 divided by 10 000

1 + 1 + 1 + 1

9.5 – 4.1 – 1.4

8 - 4

4

16/4

300 - 296

½ + ½ + ½ + ½ + ½ + ½ + ½ + ½

(2 X 7) – (5 + 5)

Optional Activity

4) Mental Math skills

- Model Mental Math: Describe how you do Math in your head – no writing
- Encourage visual toolsto support Mental Math.
- Eventually, students will be able to ‘see’ the numbers in their heads!
- Discuss how always using a calculator limits thinking! – disables the learner!
- Practising Mental Math builds confidence with numbers!
- Talk about how to do Mental Math

Power of Ten cards build Mental Math skills

EXAMPLE: What is 8 + 7?

(How much do I need to add to 8 to get 10? Answer, 2)

So … I’ll use 2 of the 7 to make a 10

and then there’ll be 5 left over from the 7.

I can add that to the 10 to get 15!

So… 8 + 7 = 15

These skills then can be adapted to

Finding 28 + 37, adding the tens first!

Optional Activity

Encourage Mental Multiplication

Example #1:

5 X 26 = (5 X 20) + (5 X 6)

= 100 + 30

= 130

Example #2:

3 X 19 = (3 X 10) + (3 X 9)

= 30 + 27

= (30 + 20) + 7

= 50 + 7 = 57

Activity #7

Motivate students with Mental Math Tricks

1) Multiplying any 2-digit number by 11:

Motivate students with Mental Math Tricks2) Squaring any 2-digit number that ends in a 5:

- Multiply the first digit times one higher
- finish the number with ‘25’

Example: To square 75 (finding 75 X 75)

- Use ‘7’, and multiply 7 by (7 + 1) = 7 X 8 = 56,
- then place ‘25’ on the end: 5625.
- So … 75 X 75 = 5625

Other Materials in your package

- Fantastic Factors sheet & Factor Frenzy game
- Geometry hands-on activity
- Find the Digits worksheet
- Measurement Conversion chart & game
- I Have … Who Has? - blank sheet
- Vertical Number Line – for number sense, estimating

Power of Ten Website

- Power of Ten program –

confidence building resource

- Devised by Trevor Calkins – Victoria BC educator
- Videos are very helpful

10% discount when you email Trevor

and mention ‘Ann-Marie’s workshop’

Please check out PITA ~Provincial Intermediate Teachers Association

- Attending a START UP! or PITA workshop automatically makes you a member! So…
- WELCOME TO THE CLUB!
- www.pita.ca – lots of resources and information about upcoming events.
- You receive newsletters throughout the year!

Upcoming PITA Conferences

- Whistler Conference – May 9th, 2014 all day workshops.
- PITA Fall Conference

– Oct. 24/25, 2014

Langley

Check them out at: www. pita.ca

Start UP! Your Class Website

- startupyourclass.ca– is the Start UP! website. Sponsored by PITA
- helpful for early career teachers; also great for experienced teachers
- Start UP! program of workshops on practical subject area units and strategies - August
- contains links to many resources
- blogs and info about upcoming events
- opportunities to connect to other

teachers – & compare experiences

Divisibility Rules – to find factors

A number is evenly divisible by:

- 2, if the number ends in a 0, 2, 4, 6, or 8

(the number is an even number)

- 3, if the digital sum is a 3, 6 or 9

(add all the digits of the number to get the digital sum)

e.g. 351 is divisible by 3 because 3 + 5 + 1 = 9

Divisibility Rules – to find factors

A number is evenly divisible by:

- 5, if the last digit of the number is a 5 or a 0
- 4, if dividing the number by 2 gives an even #
- 10, if the number ends in a zero

Fantastic Factors sheet

Students check numbers from 1 to 24,

FACTORS = #s that divide evenly into 24: (1 and 24 are obvious!)

- 1, 2, 3, 4, 6, 8, 12, 24Use‘RAINBOWS’ to link up the pairs:

1, 2, 3, 4, 6, 8, 12, 24

- List of Factor Pairs:
- 1 X 24

2 X 12

3 X 8

4 X 6

Activity #8

FACTOR FRENZY GAME– gives students practise at building their knowledge of number factors

- See handout for game rules and sheet – copies can be found in the Start UP! website, Math resources.
- Either use blank ‘Fantastic Factors’ sheets – students fill in
- Or hand out the completed ‘Fantastic Factors’ sheets
- After some practice, students should be able to play the game without referring to the factor sheets.

Prime Factorization

120

12 X 10

2 X 6 2 X 5

2 X 3 Circle the primes!

So 120 = 2 X 2 X 2 X 3 X 5 or 23 X 3 X 5

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