Manitoba Math Consultants Consortium

December 18th, 2008

Marian Small Presentation 9:30-12:15

MMCC Meeting 12:45

Hosted by Interlake and LSSD

LordSelkirkSchool Division Board Office

205 Mercy Street, SelkirkMB

Attending: Karen Burgoine, Meagan Mutchmor, Dianne Soltess, Heather Knight, Sherry Perih, Carole Bilyk, Sandra Ferguson, Greg Sawatzky, Karen Mason, Sara MacPherson, Gail Peterkin, Trish Goosen, Heidi Holst, Linda Girling, Kim Koop, Karen David (p.m.)

Regrets: Brenda Evans, Harvey Peltz, Olga McIvor, Holly Forsyth, Christine Ottawa, Julie Cordova, Nicole Alain Fox, Todd Monster, Andrea Labelle, Carol Matsumoto, David Milley, Wendy Weight,

9:30 Marian Small Book Study – Notes attached

12:15Lunch – Thank you Sandra Lamont, Nelson Canada

12:45MMCC Meeting

  1. Breakthrough Mathematics – Heather

Ron Wescott –K-12 Session for problem solving – Heather will let us know

How to sustain professional learning and encourage reflection – Meagan

  1. Grades 3,4,7,8 implementation workshops – Heather

Winnipeg – April 30th, May 15th, May 23rd

Brandon – May 8thDauphin – May 11th

Cranberry-Portage - May 13thWinkler - May 19thThompson – May 21st

Register on-line

  1. Year-end assessments: What are divisions doing? – Greg

Louis Riel (Linda) – middle years - trying to get away from exams; some cumulative

Senior years still 30% final

RETSD – Karen 9 middle years – move away from final exam – moving away from percentages for next year middle years – year end projects

Interlake (Gail) – traditional exams 7-12 – cumulative; some mid-year, some June

LSSD – High School – end of semester exams; middle years changing – talking about different ways

Winnipeg(Meagan) – Two division wide mandated exams grade 8; New divisional assessment policy; beginning conversation about no percentages

St. James (Dianne) – Grade 6 & 7 – some school exams; divisional – grade 8 but not this year; in process of changing report card – will have word descriptors and percentages; superintendent will present position paper to board; discussions around what end of year assessment should look like; new report card next year 2010; high school – exams

Hanover (Greg) – looking at performance assessments; end of year project – interview; end of June – year end assessment activities - some people want tests

Sandra (Pembina Trails) – looking at middle years report card; next fall grades 5 & 6 no mark; transition piece – descriptive feedback and anecdotal comments; Grade 7 & 8 – what? No grades or friendly numbers? Parents want accountability…doing portfolios

Sunrise (Karen) – mix – some schools have end of year exams; some discord over that; depends on teachers; some using performance tasks – challenge with not knowing the math – appropriate descriptive feedback; need MECY money dedicated toward middle years mathematics

Discussion:

What about provincial assessments? Supposed to be formative, but some teachers are giving tests…eg. Grade 7 test in February (Meagan)

From theory to practice….how to get it into the classroom? (Meagan)

How is mark being determined? Just using mean of assignments? Using triangulation – valid and reliable ‘grade’. (Meagan)

Using summative assessment to inform teaching… (Meagan)

How to keep kids engaged and attending in June – project (Dianne)

Move away from end of year – learning every day - repeated ‘chances’ (Sandra)

What might a year-end assessment look like? (Greg)

Think about ‘big ideas’ (eg from Marian) – Do teachers know what needs to be learned from an activity? Discuss purpose of activity…What do I want kids to show me they know, and how? Eg, concept map on rational number beginning and end of year (pre/post) and compare (Meagan)

PD time for middle years – no subs

Sandra – after school sessions – pay for dinner – full

  1. Implementation of Senior Years Courses – Divisional Plans –Harvey

Following MECY – Louis Riel, Interlake

Not sure – RETSD, Winnipeg, St. James

Probably no early implementation

  1. Math Performance Festival – Carol M. –
  1. What are good Middle Years Resources? – Dianne & Heidi

How to find resources that are not workbooks/run off

Dianne:

Math Games series – graphic novels – characters presenting math concepts through stories

“Ignite Student Intellect and Imagination in Mathematics” – based on Bloom’s taxonomy (from Middle Years Association

ISBN 1-56090-198-5)

“Hands-on Standards” (different grade levels) – How to use manipulative materials to teach various concepts(

“Mathematical Literacy – helping Students Make Meaning in the Middle Grades” ISBN 12:978-0-325-01123-3

Open Ended Maths Investigations Blake Education ISBN 1-921143-55-X (Australia)

Origo – Fundamentals - Order from Kerry Kuran (order form)

Mathworks…Using Math to be….eg. a Zoo Vet, Survive in the Wild, on a Space Mission, Design a Roller Coaster, etc. etc. (math facts, data, challenge) GarethStevens ISBN 0-8368-6041-1 (Scholar’s Choice)

Greg – NCTM Illuminations site; AIMs books (Spectrum)

Meagan – Harcourt – Open-ended performance tasks grade levels

Sandra – Smartboards – How to develop lessons engaging students

Karen – People delivering Smartboard PD may not know the math

Meagan – New Zealand Math site has PD training modules for early numeracy (incl. videos)

Dianne – Alberta Education – lesson ideas

  1. Using Math Manipulatives in the Middle Years – Dianne & Heidi

Meagan – Rational workshop - rich task problems (difficult at adult level) using cuisenaire rods, buttons, tangrams – teachers struggled to show thinking using tools - then had them use tools such as pattern blocks to design richer question for students

Eg. Exam question – given yellow stick note – told it represented 2/3 and asked to determine 1 ½ - teacher misconceptions

Meet early at next meeting to continue? Check with Andrea

  1. Resource sharing (see above)
  1. Next Meeting: RETSD February 23rd, 2009 (Andrea, Harvey, Karen)

The Educational Resource Centre (ERC), BernieWolfeSchool – 2nd Floor - 95 Bournais Dr.

10. Next meeting April – Sandra Pembina Trails

Happy New Year! Gail and Heidi

Marian Small – Book: Big Ideas from Dr. Small Grades 4-8

  1. Warm Up

 Using fingers to multiply by 9

“Tricky” to way to multiply two numbers between 5 and 10?

 using fingers – anchoring to 5 (reason: explore multiplying by binomials)

 Eg. 7 x 8 - Hold up both hands; one hand – how much more is 7 than 5? Two – hold up two fingers; Other hand- how much more is 8 than 5? Three – hold up three fingers; Look at fingers up – five so product starts with fifty; Look at fingers folded down – two and three – Multiply – Six  So answer is fifty six….

  1. Book

Explains underlying math content

Big picture pedagogical approaches through big ideas

Teaching activities to bring out big ideas

Is not a full teaching resource with lesson plans, activities etc.

How is content addressed?

Eg. Perimeter – Two formulas that are equal  2l + 2w or 2(l+w)

How is pedagogy addressed?

Eg. Measurement

Definition/comparison stage  non-standard units stage  standard units stage

(eg. wedges for angles)

Area

using square and non-square units

measure same area/different units

measure different areas/same unit

measure using transparent grid

Formulas – ‘do something easy to get something hard’.

  1. The Main Event – Content meets pedagogy where Big Ideas are introduced

Ideas that underpin problems, concepts, ideas we want students to learn

Big idea is NOT a topic like fractions, but might be an idea such as ‘a fraction makes sense only if you know the whole’.

Simplifies teacher’s job of prioritizing and organizing – time and attention to outcome

Critical look at resources – look for big ideas

Helps teachers create appropriate assessments (assess big ideas)

Helps students build essential connections

Eg. Big Ideas for Measurement

Same object may be measured in different ways

Any measurement may be determined in more than one way

Estimation

Benchmark measurements

Unit affects numerical value

Smaller units or subdivisions allow more precision

Standard measurements simplifies communication

Formulas allow us to use accessible measurements to make less accessible measurements

(Eg. radius/circumerference)

  1. Teaching ideas in margins
  1. Facilitator’s Guide (Ten2 hour sessions for 4-8) incl. DVD with video clips

Goals of course

Overview of session, materials, preparation

Suggestions for modifying re time limit and/or grades

  1. Activity: How Did it Change?

Some operations were performed on the number 4 and it turned into a 10. What could have happened?

Eg. Double and add 2, add 6, multiply by 5 and divide by 2 etc.

How are these expressions of change?

Describe visually….Eg, use dots

How could we use variables? Eg. 2k + 2 – describe using words?

How is using variables ‘handy’? – Takes less work…(ink, space)

Big ideas for algebra:

Explains mathematical relationships and to describe and analyze change

Using variables is a way to efficiently and generally describe relationships that may be described using words

  1. ‘One million’ placement (used words rather than numerals to elicit responses other than just numerical)

Which of the things you wrote show that you understand the place value system?

Which of them show that you have compared one million to other benchmarks?

Which did both?

How is this useful as an assessment for learning tool?

Follow-up ideas: (benchmarks/place value)

Ask students to think about

How many loonies make $1 000 000? How many $100 bills?

How long would line of 1 000 000 pennies be? How many would you measure? Why wouldn’t you measure 7?

How long would it take to roll 1 million pennies?

What place value ideas did you use to help you answer…?

  1. In Between – Rebecca said that to get a fraction between two other ones, just add the numerators and add the denominators, and form a fraction.

Eg. Between 4/10 and 8/15 is 12/25

Between 3/8 and 5/6 is 8/14

Comparison strategies: - Multiple models

Common numerator

Common denominator

Benchmarks

Coordinate geometry

  1. Represent 4/10 in different ways
  1. Activity 4 Fraction and Decimal Tasks (BLM 3)

 Look at tasks – What questions would you ask to draw out big idea?

  1. Geometry – Imagine….A 3D object has 18 edges. What could it look like?

Eg. Hexagonal prism; nonagonal pyramid

What other numbers could describe these shapes?

Are there ways to describe shapes without using numbers?

12. Big Ideas for Shapes and Their Properties:

Some attributes quantitative; others qualitative

Many 2D properties also apply to 3D

Decomposition and recomposition of shape helps for understanding other shapes

Many geometric properties and attributes of shapes related to measurement

  1. Activity: Fit It In - How many ways can you fir this shape into its outline (eg. 4)

Create a different shape that will fit into its outline in more than two ways.

Eg. Equilateral triangle, Red Cross symbol, circle, nuclear power symbol

All have…rotational symmetry

Describe your thinking. What makes these shapes special?

  1. Activity: (Similarity) Which is the miniature version? – Looking at proportionality

With rectangles, superimpose and look at diagonal

  1. Transformations video clip

Used 3 different transformations while eliciting responses from students. Teacher used a square on grid paper to help students visualize & communicate what they were doing.

Allow students to use informal language and gradually work towards formal language.

What Big Idea do you think it was about? (multiple ways of seeing transformations)

Using regular shapes is more ambiguous as to what it going on as opposed to irregular shapes

  1. How Many Measurements?

I need to calculate the perimeter of a shape, but I only needed to take two measurements. What could my shape be? (isosceles triangle, rectangle, “step” shape)

The formula for a perimeter lets us know how many variables to measure.

  1. Choose one activity

How can we make a specific idea clearer to students by looking at what BIM it is and the page numbers associated with it. What tasks can we create to help?

  1. Activity: Human circle graph (use yarn etc.) – How are circle graphs useful? What do they show?

18. Big Ideas for Data Display….see book

  1. Summary:

Big ideas – Connections

K-3 also available