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

ES: Teamwork. Works well with others to complete tasks and meet goals.

Curious and enthusiastic

Ten Tiles

Largest Product

Question prompt: Snowman

Question prompt: Beef and Bean Burrito Receipe

A number problem to start the year with. Reintroduce the problem-solving approaches ('What to do when I'm stuck'). In this case, this might include:

• trial and error (to start)
• making cards ('tiles') to move around

Answers are here.

Largest product is similar, but is easier to extend.

Then proceed to 'snowman'. Explain that in Maths, we not only answer questions, we ask them too, and this will be a theme for the year - finding questions that we might ask, and extending questions that we have been asked. We are not going to answer these questions just yet, but we'll find out how to during the year. There are lesson notes here, and a quote from Stephen Wolfram supporting this approach.

Think/pair/share questions to this prompt.

Then the recipe prompt. Questions (hopefully) will include 'what ingredients do I need for my family of only 4' or 'what are the amounts in grams'. These can be answered AFTER the next unit of work.

1-2
Outcome:

• Students will begin to think about proportionality, and link proportions to units (eg Km/h, kg/$).

ES: Teamwork. Works well with others to complete tasks and meet goals.

Resilience. Handles challenges and setbacks and does not give up.

Positive attitude. Is positive and has a “can do” attitude.

Slow Car Race

Potatoes

Run Rate

Cup Cakes

These activities can be set up as a circus. One of the activities on each of 4 tables. The idea is that all of the students at each table are working on the same exercise (and can therefore support each other).

It really needs a 5th activity (to help reduce the group size).

Creating a new puzzle (the extension activity in some of these) fits with the theme 'Asking Questions'.

3-4

Outcome:

Students link proportion and formal ratio.

ES: Teamwork. Works well with others to complete tasks and meet goals.

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.

5

Outcome: students can split and amount in a given ratio

Beta p 56

6-7

Outcome: students understand formal ratio notation.

Ratio and proportion sort cards

Ratio puzzle

Question prompt: Kayaking to Iceland

Can be used as group or individual tasks.

Finish with a prompt which uses ratio ideas.

1-2

Outcome: Students investigate and extend a problem involving powers.

ES: Thinking skills. Recognises problems and uses initiative to find solutions.

A problem-based introduction to powers (of 2 initially). The routine here might be a useful framework to this sort of problem. A discussion of how the problem might be extended sits with the theme 'Asking Questions.'

A possible extension would be:
I have a number of different cubes, and I make towers of a certain height. If I can make:
• 1296 different towers, how many colours do I have, and how high were the towers? (Ans: 6 colours, 4 high)
• What about 65536? (Ans: 4 colours, 8 high or 2 colours 16)

3

Outcome: Students understand what a 'power' of a number means.

ES: Willingness to learn. Curious and Enthusiastic

Powers

This lesson should be completed without a calculator (by most students).

There are obvious links here with binary (and ternary) numbers, which you might choose to exploit with some students.

This clip has a good explanation of binary numbers, with Marcus du Sautoy and Terry Jones.

4-5

Outcome: Students understand what a 'power' of a number means, and can use a calculator to find them.

ES: Willingness to learn. Curious and Enthusiastic

Cubes

Problem: What is the last (ones) digit of 7¹⁹⁹?

See if students can work out the notation amongst themselves. Then allow calculator use.

Again, some sort of problem solving strategy would be useful: at the very least making a record of the cubes 1-13!

Extension Problem

Support Problem

This is an old (but fun) activity that I've once found in an xmas cracker:

Magic Number Cards explained here. Some students should look to see the link with the earlier part of the lesson (in fact, an interesting extension would be to write cards using base 3 rather than binary).

6

Outcome: Students understand what a 'root' of a number means, and can use a calculator to find them.

ES: Willingness to learn. Willing to learn new tasks, skills and information

Square Roots

Square and Cube Roots

7

Outcome: Students understand what 'powers' and 'roots' of a number mean, and can use a calculator to find them.

ES: Willingness to learn. Curious and Enthusiastic

Calculator Buttons

Powers and Roots

1-2

Outcome: Students revise calculating percentage of an amount.

Act 1: Question Prompt

Act 2: Presenting Scenarios with a cheap object and an expensive object.

Act 3: Students investigate their own scenarios. See lesson plan.

This is a Three-Act Task, used to introduce/revise percentages. A Three-Act Task is a whole group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

3-4

Outcome: Students revise the link between farctions, decimals and percentages.

Fractions, decimals and percents

Money and Percentage 1

Fractions, decimals and percents is a MAP lesson. Just use the Suggested Lesson Outline section.

The second sheet (Money and Percentage 1) is a straightforward revision sheet.

5-6

Outcome: Students learn to increase/decrease by a percentage using a multiplier.

ES: Teamwork. Works well with others to complete tasks and meet goals.

Increasing and Decreasing Quantities by a Percent is a MAP lesson. Just use the Suggested Lesson Outline section.

There are some word problems to support this topic in 10Ticks L6P3 p4 and p6 gives some extension work (undoing increase/decrease).

7-8

Outcome: Students understand compound increases, and can calculate them efficiently.

Money and Percentage 6.

Problem Activity: Fun Park with Teachers' Notes

Links increasing by a percentage with powers.

The problem activity makes the link with tables, equations and graphs explicit.

1

Outcome: Students revise how to round decimal numbers to dps., and learn how to round to sig figs.

Beta p60-62 Old (blue) vesrion.

10Ticks Level 6 Pack 3 p.19

dps and sig figs

2-3

Outcome: Students will be able to use Standard Form to express large and small numbers.

ES: Teamwork. Works well with others to complete tasks and meet goals.

Standard Form.

A MAP lesson. Just use the Suggested Lesson Outline section. Make the point that Scientific Form is the same as Standard Form.

4

Outcome: Students will be able to use Standard Form to express large and small numbers.

Beta p63-68 Old (blue) vesrion.

Top Trumps

Standard Form.

The Top Trumps cards are difficult to print well. I have an idea for a Top Trumps game using researched information for the planets, which I need to create.

5

Outcome: Students will be able to use Standard Form.

ES: Willingness to learn. Curious and Enthusiastic.

1-4

Outcome: Students revise the skills covered in this unit, and how to use them in context.

Needs some materials writing to practice the range of skills covered.

The sorts of issues which may come up in the Excellence question should be covered (eg the need to extend, generalize and criticize), but not the specific issues in this assessment (otherwise, they are no longer excellence, as the opportunity to show independent thought has been removed). In general SOLO (Ach=understanding, Mer=relational thinking, Ex=thinking) should be emphasised, and the need to engage with a task.