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### Building Math Confidence

Ann-Marie Hunter

Reasons for Building Math Confidence

- Math skills are often seen as a source of anxiety; students are sometimes made to feel that they are destined to fail.
- Your efforts to reduce Math anxiety can alter their attitudes towards their own abilities and create success for students.

Connecting to the learners in your classroom is one of the most important aspects of teaching

- It conveys to the learners that they can trust you and that you believe they can succeed.
- Focussing on creating a hands on, meaningful learning environment supports the creation of a positive learning environment.
- You can use Math teaching to reach this goal!

Workshop Outline

- Brain research - how it can sharpen your teaching*
- 8 critical Topics and Strategies. We will discuss these ones today:
- Problem solving Word Questions *
- Place value *
- Focus on the Facts and Power of Ten Cards *
- Mental Math & Estimating *
- Fractions & Decimals
- Mastering the Basics * – Power of Ten
- Geometry & Measurement
- Games and tricks

Please refer to your handout for ideas about the topics we will not be discussing today and feel free to contact me with any questions/clarification on those topics.

Use Brain Research to Sharpen Your Teaching

- Semantic memory
- Knowing that a hammer is used for nailing even when you’ve never used one is Semantic memory.
- Episodic memory
- Remembering a time when you nailed your thumb while using a hammer, recalling the pain of the injury, where you were when it happened, how you cried out and who you were with is Episodic memory
- Procedural memory
- Being able to use a hammer to put up drywall without having to think about how to ensure that you don’t nail your thumb, is Procedural memory.

Using Brain Research ~Adjust your teaching in these ways:

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

1) Problem Solving – Word Questions*Help students feel empowered to think aloud and share ideas with others in solving word questions. *Use word questions that have more than one answer.*Use and encourage student writing of word questions that apply to their individual areas of interest.

If Joe and his brother were playing basketball outside and Joe took three times as many shots as his brother, how many shots could Joe have taken if they took no more than 40 shots in total.

1) Teach Word Question Vocabulary. (In your handout)

- 2) Have students create word questions BEFORE they are asked to answer textbook questions.
- 3) Guide your students with strategies for solving word questions. (Find Word Question Strategies on the Wiki)
- 4) Use the Place Mat Activity to celebrate and share students’ ideas.

Word Question Vocabulary

- sum - the answer when you add numbers.
- difference - the answer when you subtract numbers.
- product- the answer when you multiply numbers.
- quotient - the answer when you divide numbers.
- total - the amount that is gained by the addition of smaller amounts.

Word Question Vocabulary

- factor – an integer you can multiply times a number to get

another number

Example: 3 is a factor of 6 because 3 X 2 = 6.

2 is another factor of 6!

- multiple- the result of multiplying a number by an integer

Example: You can identify a multiple of 4 by multiplying 4 by 2.

4 X 2 = 8 makes 8 a multiple of 4.

Another multiple of 4 is 12, since 4 X 3 = 12.

This is where the word question is written.

Post finished Place Mats to celebrate diversity of solutions.

2) 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 __ __ __ . __ tenths

and

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

and

Write numbers in words, capitalizing the ‘SPACE NAMES’:

- 67 893 542

Sixty-seven MILLION,

eight hundred ninety-three THOUSAND,

five hundred forty-two

- Then have them practise converting words to digits.

Applyingreading numbers to understanding place value

Which digit is in the ten thousands place?

Students look for the THOUSANDS period and then locate the tens place.

Example: 258 673 910

Students think: 258 M 673 Th 910

So finding the THOUSANDS period (the set of three digits in front of the word THOUSAND): 673, they then use h,t,o, to look for the digit in the tens place. In this example, it is the digit 7 that is in the ten thousands place.

Ensure that students can add and subtract numbers using a visual tool – Power of Ten cards are so valuable in developing these vital skills.

- Ex: 7 + 8 = (5 + 2) + (5 + 3),

= (5 + 5) + (2 + 3),

= 10 + 5,

= 15 Let’s Try This!

Eventually, they will ‘see’ these relationships in their heads without using the cards.

3) 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 do not give the needed attention to this part of Math instruction, thinking, “But I have all those units to cover!”

The truth is - helping a child to learn and understand the basic facts is one of the best ways to build confidence and bring about success in learning Mathematics!

- After he/she knows the facts, everything seems easier – and IS easier! His/her Mental Math skills begin to develop.
- Knowing Math facts allows students to confidently engage in learning new concepts.

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

- Power of Ten multiples sheet – visually shows groups of numbers Look in your handout for this page!

6 X 7 = 5, 10, 15, 20, 25, 30(skip counting the 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 each line. Record the total for each row.

Talk about multiples as ‘groups of #’ – to encourage the visual

3 X 2 means 3 groups of 2:

Talk about multiplication and division together – Fact Families

4 X 7 = 28,

so 7 X 4 = 28,

28/7 = 4,

and 28/4 = 7

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
- Teach Perfect Squares: 2 X 2, 3 X 3, 4 X 4 … and encourage students to look for other patterns on the sheet.

Practise multiplying by powers of 10 (mental math application)

- 3 X 10 = 30
- 7 X 100 = 700
- 2 X 1000 = 2 000
- 40 X 300 = (4 X 3) = 12 then place the number of zeros in the question (3 zeros) behind the 12 to get 12 000.
- 200 X 500 = (2 X 5) = 10, then place the 4 zeros behind the 10. Answer: 100 000
- Partners challenge each other and check answers on calculators.

Use place value to show the real meaning of Double Digit Multiplication

- Example: 24 X 32

32 (30 + 2) No Carrying!

X 24 (20 + 4)

8 (4 X 2)

120 (4 X 30)

40 (20 X 2)

600 (20 X 30)

768

Fantastic Factors sheet

- Given the answer (24, for example), find all the ‘questions’ – the factor pairs
- First, list all the numbers that divide evenly into the number - use divisibility rules

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)
- 5, if the last digit of the number is a 5 or a 0
- (Other rules for divisibility for 4 and 10)

Fantastic Factors sheet

Students find these numbers that divide evenly into 24:

- 1, 2, 3, 4, 6, 8, 12, 24
- 1, 2, 3, 4, 6, 8, 12, 24
- Then use ‘RAINBOWS’ to link

1 X 24 up the pairs:

2 X 12

3 X 8 Let’s practise this!

4 X 6

Arrow Graphs – * offer opportunities for students to think creatively * demonstrate student understanding * are 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)

4) Mental Math/estimating skills

- Model Mental Math: Talk about how you do calculations in your head, without writing anything on paper
- ask students to share their methods of doing the same.
- Encourage the use of visual tools to support Mental Math.
- Students’ thinking will improve when they can ‘see’ the numbers in their heads.

Motivate students with Mental Math Tricks

1) Multiplying any 2-digit number by 11:

2) Squaring any 2-digit numbers that end in a 5:

Multiply the first digit times one higher and 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. 75 X 75 = 5625

3) Adding and Subtracting from Left to Right

- 46 + 36 = (40 + 30 = 70), (6 + 6 = 12), so the answer is 70 + 12, which is (70 + 10) + 2, or = 80 + 2 = 82
- 95 – 33 = (90 – 30) + (5 – 3)

= 60 + 2 = 62 Let’s Try This

- Encourage students to share their own methods for using Mental Math

Estimating answers to questions before calculations are done

- Use Vertical Number Lines
- aid in Visualizing closest ten, hundred, whole number (decimal vertical number line).
- Check your handout!
- Estimation skills build ability to predict the approximate answer before using calculator.
- Canada’s recent phasing out of pennies:
- - real-life situation requiring rounding to the nearest 5.

Additional Resources to make learning fun:

Timestables the Fun Way! - Judy Rodriguez

- Contextual representation of

the multiplication facts.

Example 1:

- Sean climbs to the top of the hill to fly his kite.
- He’s so happy when he turns 16 and gets his driver’s license,
- because then he can drive his 4 X 4 to the top of the hill.
- 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.

6) Mastering the Basics

- Benefits of using the Mastering the Basics program
- Strategies for running the program successfully

Mastering the Basics Program

- Reasons for using the Program and Guidelines (in handout).
- Main benefits:

1. students have the choice of topic

2. given multiple opportunities to rewrite; scores are not averaged into their Math mark until they are passing grades.

3. develop ownership of their own progress.

4. results are private – no whole class sharing

5. each student works on areas of their own need.

6. 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

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

- A ‘Winter Olympics project’ will be posted on the website free in December. You can get a sense of it by looking at the current ‘Summer Olympics project’ under free downloads.

Please check out PITA ~Provincial Intermediate Teachers Association

- Attending a PITA workshop automatically makes you a member! So… WELCOME TO THE CLUB!
- www.pita.ca – lots of resources on the Wiki and information about upcoming events.

CHECK OUT PITA

- PITA Facebook page with links to cool stuff
- Newsletters with great teaching ideas 3 times a year
- Get paid when your ‘teaching ideas’ write-ups are used in the newsletter!
- amazing PSA – with a focus on providing great PD

Start UP! Your Class Website

- startupyourclass.ca– is the Start UP! website. Part of PITA!
- focussed on early career teachers
- contains links to resources
- blogs and info about upcoming

events

- opportunities to connect with

presenters and discuss your trials

with new materials

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