• Students will learn to work as part of a group
• Teachers will get to know Mathematical background of students.

Maths attitude questionnaire

"The answer is 10”

• Student voice is an integral part of the new year 9 course. The words offered to describe Maths can collected as a "word cloud", which (hopefully) can be contrasted with a similar cloud at the end of the year. The final question (using sigma notation) is there to measure student willingness to attempt to engage with Mathematics - I don't expect that any student will get it correct!
• The rationale behind "the answer is 10" is explained in the document. It is the first of several lessons aiming to build "a learning community."

1-2
Outcome:

• Students will learn to work as part of a group

• Students will understand the BEDMAS convention for order of operations.

Starter:
Number talk: 5 x 18
Number talk: 5 x 31

Main lesson:
BEDMAS

Four Fours Problem

10Ticks Level 5 Pack 5 page 7.

Bedmas Treasure Hunt. Instructions.

This document describes the use of number talks. The teacher writes the sum (5 x 18) on the board, and accepts and discusses answers. The class contribute by putting up thumbs, which is visible to the teacher but not to the rest of the class (and is therefore less intimidating than raising hands). It is crucial that the teacher accepts mistakes for discussion. This clip shows teacher Cathy Humphreys conducting a number talk. Here are some of Jo Boaler's students explaining their approaches to 5 x 18

Laminated aids for teachers using Number Talks.

The Four Fours problem lends itself to paired work, the 10Ticks worksheet is individual work, and the Treasure Hunt can be run either in a team of two or individually.

The "Learn Alberta" BEDMAS manipulative is useful for students who find this hard; it requires students to click on the operations in order, but performs the calculation for them.

3 -4
Outcome:

• Students will learn to work as part of a group

• Students will understand the BEDMAS convention for order of operations.

Starter:
Number talk: 4 x 23
Number talk: 5 x 21

Main Lesson:
The Laws of Arithmetic

The Laws of Arithmetic covers distributive, associative and commutative properties, as well as order of operation. The lesson structure is described in the document, and the philosophy etc of the lessons is described in this brief teacher guide.

Use only the section headed Suggested Lesson Outline. The key instruction is that "for each area card there are at least two expresions cards."

1-3
Outcome:

• .Students will have at least one strategy for multiplying 2-digit numbers
• Students will understand the need for resilience in approaching problems.

Main Lesson:
The lesson notes for this sequence of lesson is contained in this document.

The skills used in multiplying whole numbers develop some of the algebraic skills needed later. Students may already have a range of methods (especially those who have had a solid grounding in the Numeracy Project), however it still appears that many resort to the “standard” algorithm, even when they do not understand it or even perform it correctly. This is a chance for students to explore multiplication in a problem-solving context.

Teachers should emphasise the need to approximate an answer, and should also introduce a range of algorithms/methods.

This clip is Jo Boaler talking about the strength of using a range of methods, and using “Number Sense”:

One way to introduce new ideas to students is through a number talk.

This is Cathy Humphreys using a number talk to dissect a multiplication problem:

Since this section of work comes after the unit “Laws of Arithmetic”, then teachers can use the ideas contained there to draw pictures for, say, 18 x 5 and 23 x 25. These pictures anticipate the use of the “grid method” for expanding brackets.

Whichever method is used, students should be taught the importance of estimating an answer FIRST.

http://nrich.maths.org/5612 shows a range of multiplication methods.

1-3

Outcome:

• Students will solve a complex problem.
  
• Students will estimate solution to multiplication problems.
• Students will multiply up to 2 digit-by-2 digit numbers
• Students will be introduced to spreadsheet use.

What to do...
Sports Hall
Answers

Decimals Pre-test

This is a somewhat complex "wordy" problem, of a type which most students find quite daunting. It practices multiplying skills, but the most imporatnt part of the lesson is the discussion about "what to do when stuck" , which introduces the major theme for the year. Teachers can create the poster with the class (eg by brainstorming) or discuss and add to it.

The poster should be referred to constantly over the course of the year.

Spreadsheet use can be used as an extension or demonstrated by the teacher.

Sometime during this sequence of lessons, students should complete the Decimals Pre-test, which needs to be marked to form the groups for the next unit. The decimals section is based on reasearch done at the University of Melbourne into The Incidence of Misconcptions in Decimal Notation.

Marking the test requires a Colour Key and Interpretation Sheet.

Student groups should be categorised, and the students put into groups of 3/4 with DIFFERING misconceptions (either LL, SL, TE or AE).

4

Outcome:

• Students will solve a complex problem.

Another chance to get stuck!

Students should be grouped into 3s, and can discuss the intial problem as a tink-pair-share

1-2

Outcome:

• Students will begin to understand place value in decimal numbers.

Marking Homework

Brad's HW

Caitlin's HW

Courtney's HW

Maria's HW

Ricardo's HW

Group the class by misconception (see above). Allow each group 5 minutes to discuss and then mark each of the homeworks, and then discuss as a class.

Outcome:

• Students will understand place value in decimal numbers.
• Students will understand why addition and subtraction algorithms work with decimal numbers.

Decimals Poster.

Extension: Decimals Extension Booklet.

10Ticks L4P4 p.29-33

Decimals grids (A4)

cm squares (A3)

Use decimals grid (projected) to discuss the values of a decimal number. (unit square, tenths, hundredths etc).

The 10Ticks worksheet checks understanding of ordering decimal numbers.

This is one of the few instances where a "differentiated task" is available. The extension booklet investigates indices and standard form. It is intended as self study for "task experts". Some of these students may opt to do some of the posters in any case (especially those with +/- arithmetic).

Summation: Teachers should show how the visual methods for adding/subtracting negative numbers link with the standard algorithms (also emphasise estimating).

Outcome:

• Students will estimate answers to multiplications involving decimal numbers
• Students will muliply decimal numbers with 1 dp.

Make a poster to show that:

2 x 1.3= 2.6

1.5 x 2.3 = ?

0.7 x 0.3 = ?

0.4 x 0.6 = ?

Decimal multiplication worksheet

The lesson structure is given at this site. (although I don't teach the 'standard' algorithm for multiplication. The lesson works equally well with the 'grid' method). Unfortunately, we do not have (yet) any decimal blocks, so students will have to make the shapes using decimal grids.

All students can complete this lesson, though some may choose to start at 1.5 x 2.3, and advance to using the 'grid' method for 2 dps (eg 1.25 x 0.85.

6

Outcome:

• Students will be able to round numbers to a given number of decimal places.

7

Outcome:

• Students will solve a complex problem

Getting Stuck.

An opportunity to use the skills learned to solve a problem. Most students should not use a calculator.

1-2

Outcome:

• Students will be able to calculate a fraction of an amount.

Fractions

Fraction message

Box trails

Challenge: Lions and Tigers

Fraction of an amount.

The basic method is to find a unit fraction (eg one quarter) and multiply. Showing a picture of this may help.

All students should complete the fractions sheet. Most students should complete Fraction message, and then create their own puzzle. Some students may opt to do the challenge problem (to which there exists an interesting variety of approachs). The answer is 1/2.

3-4

Outcome:

• Students will be able to use equivalence to order fractions.
• Students will be able to cancel a fraction down to it's simplest terms.

Buzzing around the bakery

Smile Booklet L5NO page 11-12

Ten Ticks L 5 P2 p9-11

Farey Sequences

Peaches

Fraction equivalence and ordering fractions

Start with the Buzzing Around the Bakery worksheet. Pair students on a confidence line. Complete the worksheet as a pair. If you can do it, try to convince your partner that your answers are correct. Can you draw pictures?

All students should complete the equivalent fractions sort, but then some may opt to do the extension activities Peaches and Farey Sequences, instead of Fraction Walls. There probably needs to be a further extension activity added here.

5-7

Outcome:

• All students will be able to add, subtract, multiply and divide fractions with a calculator.
• Most students will be able to add, subtract, multiply and divide fractions without a calculator.

Ten Ticks Level 5 Pack 2 p.13

adding fractions

subtracting fractions

adding and subtracting fractions

adding mixed fractions

subtracting mixed fractions

fraction stencil

using the stencil

Fraction arithmetic

The adding and subtracting worksheets here need replacing with something much more conceptual. No student should complete all of these worksheets.

The fractions stencil can be used to reinforce fractional equivalence but was designed to teach the concepts of fraction muliplication. The note 'use of stencil' are lesson notes rather than a worksheet, and need extending to investigate division.

All students should know how to use the fraction functions on their calculator.

1

Outcome:

• Students will be able to calculate common percentages mentally.

100% of 500 is 500

What else does this tell us? 
(eg 10% of 500 is 50, 200% of 500 is 1000, 50% of 500 is 250 etc). Brainstorm.

This will be the basis for number talks over the next few lesson.

100% of 70 is 70.... etc

2-4

Outcome:

• Students will be able to convert freely between fractions, decimals and percentages

1. Text book: Alpha p113 Ex. 8.2

2. Text book: Alpha Ex7.21 p109 and 7.22 Ex 1.10

Extension worksheet: Recurring decimals

At this stage, students should be able to convert f/d/p (using the cycle shown).

They can make the cut out reviser. The cards to make them with are jumbled.

10Ticks Level 5 Pack 2 p33 onwards has a series of puzzles/games, including dominoes. Also 10Ticks Level 4 Pack 5, pages 5-6 have simple dominoes.

Summative worksheet: F D P

1. Percentages and fractions are the same. A percentage is a fraction with denominator 100.

2. Fractions can be converted to decimals by a division.

3. So to change a percentage to a decimal, divide by 100 (which implies to change a decimal to a percentage, multiply by 100.

5-6

LO: Students will calculate a percentage of an amount.

Percentages Puzzle from SMILE L6NO Note: unfortunately there is a mistake on this worksheet. the '65' tile should be '60'.

Alpha Ex. 8.5 p116-117

Ten Ticks L6 P3 page 4. Worded problems.

What is 1% of 500? So what is 10% of 500? (encourage multiple ways of working this out). What is 30% of 500? etc.

This leads to an algorithm: /100 then multiply. Demonstrate equivalnce to change to decimal and multiply (which is more efficient on a calculator).

7

LO: Students can calculate one amount as a percentage of another.

Alpha Ex8.6 p118

8

LO: Studets solve a complex problem

9

LO: Revision