T4 Patterns & Algebra

MA2 - 8NA Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

Lesson One

Watch this video clip and then in 60 seconds write down what you notice and what it makes you wonder about.

Then take another 60 seconds to discuss what you noticed and wondered with a neighbour.

The grey squirrel is a scatter hoarder - it hides its nuts in lots of different places.

Now estimate how many acorn nuts it would have by day 10. Remember, an estimate is not a guess - your aim is to get as close to the correct number as possible. To help you make a good estimate, think about what number would be "too high" and what number would be "too low" before you make your estimate.

Copy of Acorn Hoarding [Day 1] - How Many Acorns - 06 - ESTIMATION PROMPT PARTIAL REVEAL VIDEO.m4v

Watch this video clip and then update your estimate.

What strategies did you use to adjust your estimate?

Now have a look at this calculation.

Now watch this video clip about a red squirrel.

Copy of Acorn Hoarding [Day 1] - How Many Acorns - 09 - PRODUCTIVE STRUGGLE VIDEO.mov

What different strategies could you use to work this out?

Your teacher will discuss this with you.

Have a quick look at the images below and see if you could produce something like this to show your working out for this problem.

Below are images which could be used for extension.

Lesson - Investigation

Activity

Learning content: compare and describe the difference between models of even numbers and models of odd numbers

In this activity you are going to do your own investigation, and you need to make a "presentation" to explain your reasoning.

Those of you who can be completing challenge tasks should complete two investigations: one from A - D, and one from E - G.

You can present your investigation on paper and take a picture of it to upload to Seesaw, or you can present your investigation on a Keynote slide and upload to Seesaw. Your investigation needs examples and an explanation.

Instructions

1. Choose a statement to investigate.

2. Copy out your statement on your poster/slide.

3. Try some examples until you have decided whether the statement is true or false.

4. Write a sentence or two explaining how you know.

A. “If you add two even numbers together, the answer will be even.”

B. “If you add two odd numbers together, the answer will be odd.”

C. “If you multiply two even numbers together, the answer will be even.”

D. “If you subtract an odd number from another odd number, the answer will be odd.”

E. “If you add three odd numbers together, the answer will be odd.”

F. “All multiples of two are even.”

G. “All multiples of three are odd.”

Lesson - Counting Patterns

Activity

Learning content: generates number patterns

As a warm-up, try and work out the answers to the questions below.

Activity

2, 4, 6, 8, 10, 12 ......

Work to make some number patterns of your own. Share them with another person and see if they can add the next 2 numbers.

Complete the sheets below to revise counting patterns.

3_9_1_w2.pdf

3_9_2_w2.pdf

Activity

Learning content: understands and generates number patterns

Part One - Work out what the missing domino is in each row.

Part Two

Here is a picture of a complete set of dominoes.

Your task is to design and draw out your own pattern, leaving one or two dominoes blank and see if a friend can figure out what is missing!

Activity

Watch the video clip below.

Now follow the same pattern and create your own addition pyramid.

Choose a 4 row, 5 row or 6 row pyramid - challenge yourself if you can. (Just remember, the more rows you have, the bigger the additions become).

Use one of the pyramids supplied by your teacher.

Find these pyramid patterns in Seesaw.

Lesson - Tables

Activity

We can use patterns to work out information in tables.

Now work through the questions below.

Activity

Complete two or three of these pages to practise using patterns with charts and tables. Always look to work out what the rule is first, by checking two or three of the examples (don't just rely on checking one example, because it doesn't always work!)

3_9_4_w2.pdf

Grid patterns.pdf

3_9_6_w2.pdf

3_9_7_w2.pdf

Lesson - Inverse Operations

Activity

Learning content: completes simple number sentences by calculating missing values

One pattern to remember when you add or multiply numbers is that it does not matter what order you add or multiply the numbers in, you will always get the same answer.

Work through the worksheets below - complete the questions by working across the page.

Inverse operations.pdf

Commutative property.pdf

We sometimes call this type of number work fact families. When you understand the Inverse strategy, it means you can check your addition and subtraction answers and always be sure that you have the right answer!

Activity

Learning content: completes simple number sentences by calculating missing values

Have a look at this video to remind yourself how you can use the patterns between addition and subtraction to help work out number sentences. This pattern is call the inverse strategy. Then complete the questions that follow the video.

Relating addition and subtraction (video) | Khan Academy

Activity

This strategy can also be used for multiplication and division. Fact families or inverse strategies also work with multiplication and division. Watch the video below to see how the same pattern is used for both addition and subtraction, and multiplication and division.

Then try to write some multiplication and division number sentences that are the inverse of each other.

Commutative property 2.pdf

Roll a dice twice, then use the two numbers to complete this sheet using inverse multiplication and division number sentences.

Dice multiplication & division.pdf

Lesson - 2 part patterns

Activity

Learning content: generates number patterns, and completes simple number sentences by calculating missing values

Have a go at the challenge below. Look and think carefully so you don't get tricked!!

Activity

What do you notice? What do you wonder?

What would Figure 4 look like - draw and explain.

Could you explain it using a number sentence? Explain.

Take a picture of your work and upload to Seesaw.

Activity

Work your way through the questions below.

This is a thinking challenge for you. Try making a chart or table which has all the days on it across the top, and the pythons down the side. Below is an example to give you an idea.

Activity

Follow each of these patterns and work out the answer to each of the three challenges in order.

Lesson - Algebra

Activity

In each of the questions below you need to try to work out what number each of the shapes represents. They are different for each of the questions. Double check your ideas in each of the number sentences in the section.

Write your answers: 1. Triangle =

Circle =

Square =

Activity

Find a way of solving this problem. Look really carefully at the pile of oranges and see what you can work out.

Show your working out by using drawings, numbers and words.

Upload to Seesaw.

Activity

See how many of these challenges you can complete in 20 minutes. To help you work them out, you can use objects, paper, draw pictures, etc. Make sure that you show how you work them out and explain how you arrived at your answer and show the mathematical way of working (maybe using charts or tables).

Patterns and Algebra word problems.pdf

Lesson Nine

Your teacher will give you an assessment task.

Lesson Ten

You will complete some Number Sense activities.

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