Building Math Confidence

1. Building Math Confidence Ann-Marie Hunter

3. 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.

4. 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 learning environment that is meaningful to the learner, allowing him/her to explore topics with confidence, supports the creation of a positive learning environment. You can use Math teaching to reach this goal!

5. Words of Wisdom “I had a great feeling of relief when I began to understand that a youngster needs more than just subject matter.  Oh, I know mathematics well, and I teach it well.  I used to think that that was all I needed to do.  Now I teach children, not math.  I accept the fact that I can only succeed partially with some of them.  I have found further that my own personhood has educatable value.  When I don’t have to know all the answers I seem to have more answers than before, when I tried to be the expert.  The youngster who really made me understand this was Eddie.  I asked him one day why he thought he was doing so much better than last year.  He gave meaning to my whole new orientation. “It’s because I like myself now when I’m with you,” he said.”    ~ a quote from a teacher          

6. Workshop Outline • Brain research - how it can sharpen your teaching • 8 critical Topics and Strategies: • Problem solving Word Questions • Place value • Focus on the Facts • Mental Math & Estimating • Fractions & Decimals • Mastering the Basics – Power of Ten • Geometry & Measurement • Games and tricks • Additional strategies to enhance your Math instruction • Building your own math confidence

7. Use Brain Research to Sharpen Your Teaching • Semantic memory • People can say “The Earth is the third planet from the sun”, without having any specific experience in going to space to see that the Earth is in that position. • Episodic memory • A person may remember a recent trip to Paris, mentally reliving events that happened there, in the mind’s eye seeing again the places visited, sights seen, sounds heard, aromas smelled, and people met. • Procedural memory • Driving a standard vehicle or riding a bike is an example of use of procedural memory.

8. 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

9. 1) Problem Solving – Word Questions*Chooseactivities to 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. 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.

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

11. 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. And 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.

12. 2) Have students create word questions BEFORE they are asked to answer textbook questions. Give choices in their word question challenge Example: • Word Question Criteria: • Use decimal numbers or fractions in your question. • Use numbers that are either less than 20 or more than 50. • Ensure that there is more than one correct answer to your question.

13. 3) Guide your students with methods for solving word questions. (Find Word Question Strategies on the Wiki)Strategies to Find Solutions • Get Started - Record important details in an organized fashion • Use a Diagram to represent the parts of the question • Make the question Simpler using Easier Numbers • Get Unstuck – try a different approach

14. 4) Use the Place Mat Activity to celebrate and share students’ ideas. This is where the word question is written. Post finished Place Mats to celebrate diversity of solutions.

15. 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

16. Write numbers in words: • 67 893 542 Sixty-seven MILLION, eight hundred ninety-three THOUSAND, five hundred forty-two

17. 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 that “we have all those units to cover!”

18. The truth is that helping a child to learn and understand the basic facts is one of the best ways to build confidence! • 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.

19. 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.

20. 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 first columns) (adding on the twos) 32, 34, 36, 38, 40, 42

21. 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.

22. Talk about multiples as ‘groups of #’ – to encourage the visual 3 X 2 means 3 groups of 2:

23. Talk about multiplication and division together – Fact Families 4 X 7 = 28, so 7 X 4 = 28, 28/7 = 4, and 28/4 = 7

24. 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 other patterns on the sheet

25. Fantastic Factors sheet • Given the answer (24), the students are challenged to find all the ‘questions’ – the factor pairs • Students can first list all the numbers that divide evenly into the number - use divisibility rules • 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

26. 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

27. Arrow Graphs – * offer opportunity for students to think creatively * demonstrate student understanding 40 000 divided by 10 000 1 + 1 + 1 + 1 9.5 – 4.1 – 1.4 8 - 4 4 16/4 ½ + ½ + ½ + ½ + ½ + ½ + ½ + ½ 300 - 296 (2 X 7) – (5 + 5)

28. LEARNING FACTS – Such an Important Part of Math Instruction! • This aspect of your Math instruction cannot be overestimated! • You are doing your students such a tremendous service by focussing on learning facts in a meaningful way and ensuring that they have solid knowledge of the facts when they leave your classroom.

29. 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.

30. 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. Share how the students’ thinking will improve when they can ‘see’ the numbers in their heads.

31. Estimating answers to questions before calculations are done • Use Vertical Number Lines to aid in Visualizing closest ten, hundred, whole number (decimal vertical number line). • Check your handout! • Estimation allows students to be able to predict the approximate answer before using the calculator. • Canada’s recent phasing out of the use of pennies is a real life situation requiring rounding to the nearest 5.

32. Practise multiplying by powers of 10 • 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.

33. Motivate students with Mental Math Tricks 1) Multiplying any 2-digit number by 11:

34. 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 X (7 + 1) = 7 X 8 = 56, then place ‘25’ on the end: 5625. 75 X 75 = 5625

35. 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

36. 4) Multiplying from Left to Right: • 25 X 32 = (25 X 30) + (25 X 2) = • = (25 X 3 X 10) + 50 • = (75 X 10) + 50 • = 750 + 50 = 800 • Encourage students to share their own methods Let’s try this!

37. 5) Fractions & Decimals Demystified • Relate fractions to decimals from the very beginning, using language: 0.23 = 23 hundredths = 23/100 • Find examples of ‘parts of a whole’ everywhere – all through the year. • Label parts of fractions with words: #of girls = 15 #of students 27 • Use a Visual Tool for ordering Fractions 0 1/4 1/2 3/4 1 0.0 0.25 0.5 0.75 1.0 (Check your handout)

38. 5) Fractions & Decimals Demystified • The Family Math Fraction Kit is a wonderful game – I suggest that it be played with decimal names included. • Ratios and Percent will be an easy transition from this understanding. • Use Factoring skills to develop confidence with writing equivalent fractions and simplifying fractions. Let’s Try This! = 53 hundredths = 53 %

39. 6) Mastering the Basics • Benefits of using the Mastering the Basics program • Strategies for running the program successfully

40. 7) Geometry & Measurement • Use measurement often throughout year • Discuss polygons and their names • Build Geometric 3-D figures • Classify triangles and quadrilaterals • ‘Regular’ polygons - equal side lengths • Use terms: Perimeter, Area, and Volume and the related Measurement skills throughout the year

41. 7) Geometry & Measurement • Use specific definitions: • Perimeter: distance along the outline of a figure • Area: number of square units inside the outline of a figure • Volume: space inside a solid • Clarify units used for each of these measurements • Hands-on recording of length • Visual tool for Metric Conversion (Check handout). • Clarify the difference between prisms and pyramids (Check handout)

42. 8) Games and Tricks • You cannot overestimate the power of play! • Uses Episodic Memory • Journals enrich learning • Family Math Games are great! • Power of Ten games – super! Let’s try out a mental math game!

43. Additional Strategies & Ideas for building your own Math confidence • Please take a moment to read over the guidelines for Math teaching – highlight those that you think would be helpful for you to try out. • Let me know if you would appreciate clarification of any of the strategies listed. • Let’s talk about how you can improve your own Math confidence • Decide which of these ideas you think you can follow right now – make a plan to do that!

44. Power of Ten Website • Power of Ten program – confidence building resource • Devised by Trevor Calkins – Victoria BC educator • Videos very helpful for early career teachers • 20% discount when you email Trevor and mention Ann-Marie’s workshop

45. Please join PITA ~Provincial Intermediate Teachers Association • It’s only $15 to join PITA if you are a TTOC, student, or teacher without a position. Attending a PITA workshop automatically makes you a member! • pita.ca – lots of resources on the Wiki and information about upcoming events. • PITA Facebook page with links to cool stuff • newsletters with great teaching ideas 3 times a year • amazing PSA – with a focus on providing great PD

46. Start UP! Your Class Workshops • startupyourclass.ning.com – is the Start UP! website. Part of PITA! • focussed on early career teachers • contains links to resources • blogs and info about upcoming events • Late August workshops - practical Unit Strategies in all subject areas • opportunities to connect with presenters and discuss your trials with new materials

47. Thank you for being a teacher!