Posts Tagged “math investigations”

How Can We Achieve Our Potential As Mathematicians?

We are currently working on the last part of our Unit 5 math unit, Landmarks and Large Numbers. Over the last few weeks, we’ve been working hard on challenging ourselves as mathematicians and showing everything we know. We’ve used the five states of mind, craftsmanship, flexibility, interdependence, efficacy and consciousness, to push our thinking and help us grow as learners.

Here are some questions you can ask yourself to help you be more aware of how you’re doing as a learner (Consciousness):

*How can I use the ‘I can’ statements to improve my learning?

*How can I use assessments to build on my learning?

*Am I aware of what I need to learn?

*How can I make my strategies more efficient?

*What are my strengths and areas of need?

 

Remember, Good Mathematicians:

(Craftsmanship, Flexibility, Efficacy)

*Estimate before they solve a problem

*Use the problem solving process

*Use multiple strategies

*Use efficient strategies

*Use words, numbers and pictures to explain their thinking

*Check their solution is reasonable

Over the last few weeks, we’ve been working on adding to our addition and subtraction strategies. We’re developing our strategies so that we can use at least two efficient strategies for both addition and subtraction. The short algorithm can be used, but only as an additional strategy (after using two other strategies) or as a strategy for checking our work.

Here are some charts to help you review the big ideas of the unit, as well as strategies for addition and subtraction:


Created with Admarket’s flickrSLiDR.

Tomorrow we will send home the Unit 5 pre-assessment and ‘I can’ statements to help you review at home. We’ll be continuing to work on these problems and ideas at school, so please bring the papers back to school each day.

Leave a comment to show:

*How you used your assessments to build on your learning

*Your strengths and what you’re working on to challenge yourself and improve

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Addition and Subtraction Strategies

Our latest unit in Math is Landmarks and Large Numbers. The unit focuses on place value, addition and subtraction. Remember, in addition, you need to be able to break apart the addends by place, add on to a number, or add on in parts. You should be able to show your thinking in words, numbers and pictures, using number lines or other diagrams to show what addition really is. You must be able to show an understanding of place value as you add and subtract.

Remember to clearly explain your thinking when you solve any problem. Even when math homework may seem easy (like last night), the you should be flexible in your thinking and always try to use multiple strategies. You should also show your thinking in many different ways (numbers, words and pictures). Good mathematicians estimate (using rounding) and check their work (using another strategy or the inverse operation). To meet standards you will be expected to use two different strategies for addition and subtraction, therefore it’s important that you don’t simply rely on the traditional algorithm. If you do use an algorithm you must be able to carefully explain each step.

Please use the math page at the top of the class blog to find resources for this unit. You can also use the Math Investigations website (Pearson Success Net) to access the student handbook pages. The student handbook gives you a number of strategies which we’ll be using in class for addition and subtraction. Your user name and password for Pearson can be found at the front of your agenda.

For a little bit of fun, and to extend your mental math skills, try out this fun link to a mental math mission.

Your mission: Solve the problems to unlock the bio rods.

Click on the picture or the link below to get started.

Mission Mental Math

 

Ready for a challenge in math?

Check out Calculation Nation for something to extend and challenge your thinking!

Parents, you’ll need to help your child sign up to the site with a user name and password.

Have fun!

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Multiplication and Division Strategies

Are you wondering what strategies you could use in our new Multiplication and Division unit?

Remember to take a look at the Math Investigations Student Handbook on Pearson Success Net to support your learning at home.

You could also take a look at the vocabulary and big ideas on the Math page at the top of the class blog.

Unit 8 Multiplication & Estimation
Multiplication Problem Solving Strategies
Which strategies do you use to solve multiplication problems?
Is there a new strategy you could use to expand your toolbox of strategies?

What strategies do you use for solving division problems?

Breaking the dividend apart, or finding a multiplication equation that is close to the dividend, are great strategies to start with.

Other resources that can help you add to your math vocabulary and toolbox of strategies are:

* Multiplication & Division Strategies

*Division Strategies

What strategies are you going to add to your math toolbox?

Division Strategies

 

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Here’s an old system of multiplying invented 400 years ago in Scotland.

Try the lattice method:

Napier’s rods or the lattice method was invented by a Scot, John Napier,  about 400 years ago to help calculate multiplication and division. The strips were originally made from bone.

Watch the video from 1 min- 2.30 minutes for an explanation of the lattice method:

[youtube]https://www.youtube.com/watch?v=y29XL99qM6s[/youtube]

For a simple explanation try Cool Math.

Take a look at these two examples:

Example #1:

Multiply 42 and 35

Arrange 42 and 35 around a 2 × 2 grid as shown below:
Lattice-multiplication-grid-image
Draw the diagonals of the small squares as shown below:
Lattice-multiplication-grid-image

Multiply 3 by 4 to get 12 and put 12 in intersection of the first row and the first column as show below.

Notice that 3 is located in the first row and 4 in the first column. That is why the answer goes in the intersection.

In the same way, multiply 5 and 2 and put the answer in the intersection of second row and the second column

And so forth…

Lattice-multilication-grid-image

Then, going from right to left, add the numbers down the diagonals as indicated with the arrows.

The first diagonal has only 0. Bring zero down.

The second diagonal has 6, 1, 0. Add these numbers to get 7 and bring it down.

And so forth…

Lattice-multilication-grid-image

After the grid is completed, what you see in red is the answer that is 1470

Example #2:

Multiply 658 and 47

Arrange 657 and 47 around a 3 × 2 grid as shown below:
Lattice-multiplication-grid-image

Draw the diagonals of the small squares, find products, and put the answers in intersecting rows and columns as already demonstrated:

Lattice-multiplication-grid-image

Then, going from right to left, add the numbers down the diagonals as shown before.

The first diagonal has only 6. Bring 6 down.

The second diagonal has 2, 5, and 5. Add these numbers to get 12. Bring 2 down and carry the 1 over to the next diagonal.

The third diagonal has 3, 0, 3, and 2. Add these numbers to get 8 and add 1 (your carry) to 8 to get 9.

and so forth…

Lattice-multilication-grid-image

After the grid is completed, what you see in red is the answer to the multiplication that is 30926

From basic-mathematics.com

Want to try out some more problems? Try nrich.maths.org

See Ms. Terry for some Napier’s rods strips to try it out for yourself.

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Here’s a fun way to multiply used by Russian peasants a long, long time ago!

The Russian peasant multiplication, also called the Russian peasant algorithm, uses a halving and doubling method to multiply whole numbers.

[youtube]https://www.youtube.com/watch?v=L6wYOpjgDZw[/youtube]

Method

When halving numbers, ignore any remainder. Just put the quotient in the halving column.

When the number in the halving column is 1, cross out all rows that have an even number in the halving column.

The answer is found by adding the remaining numbers in the doubling column

Example # 1: 11 × 12

Halving                              Doubling

11                    ×                  12

5                      ×                  24

2                      ×                  48

1                      ×                  96

The sum is 12 + 24 + 96 = 132

Example # 2: 37 × 42

Halving                              Doubling

37                    ×                  42

18                    ×                  84

9                      ×                168

4                      ×                336

2                      ×                672

1                      ×              1344

The sum is 42 + 168 + 1344 = 1554

From basic-mathematics.com

Or try another Youtube video.

You can also find out more on Dr. Math or Cut-the-knot or even on Trottermath

Your turn! Now try a few multiplication using the Russian peasant multiplication.

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Here’s a chance to explore multiplication strategies from around the world for International Week.

Are you ready to try something new?

Watch this video to find out how the ancient Egyptians multiplied:

[youtube]https://www.youtube.com/watch?v=3mAOnDZdhAg&feature=relmfu[/youtube]

Now try it out for yourself!

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Here’s a chance to explore multiplication strategies from around the world for International Week.

Check out the creative way that the Japanese multiply:

[youtube]https://www.youtube.com/watch?v=InzuBvT33GY&feature=fvwrel[/youtube]

Now try it out for yourself!

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Are you ready for a new challenge in algebra?

Try out this balance activity.

You need to balance the equations so they are equal.

Here’s a tip for getting started:

Enter 4 onto the red pan. Then, enter 9 onto the blue pan. What happens? Why?

Reset the balance. Enter 12 onto the red pan. Then, enter a sum (two numbers added together) onto the right pan that is equal to 12.

What happens? Why?

Can you find another sum equal to 12? Can you find another expression using a different operation?

Can you add up three numbers that balance to 12? four numbers?

What is the greatest number of numbers that you can add to balance with 12?

You have now found several expressions that equal 12. Enter one of your expressions in the red pan and another in the blue pan (Don’t use 12). What happens? Why?

What did you think of the activity?

Was it a challenge or just right for you?

How is your understanding of algebraic equations improving?

Leave a comment to let us know how you are finding algebra.

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In math class, we’re learning how to find patterns and write rules in our algebra unit.

Try out some practice questions for finding rules at this website: Function Tables

Can you find the rule?

Can you write an algebraic equation?

Leave a comment to tell us how you’re finding the algebra unit.

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Try this cool new Algebra game called ‘Stop the Creature‘.

Practice finding the rule in the function machine.

What did you think of the game?

Was it easy to find the rule?

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