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Partitioning and Ordering

Lesson

Partitioning

When we partition numbers, we break them into parts. We can use a number expander to help us, just like this one that breaks 423 up into its parts. We can also use a place value table to do the same thing, the choice is yours.

Algorithms

This word might be new to you, so in the video you'll see how it means that we follow a set of steps. To start out, we'll use an example of getting dressed, then see how we can use an algorithm to sort some coins into order by value. 

Practice Questions

Have a go at expanding this number into its place value parts, using the algorithm, or steps.

Question 1

Write $327$327 in expanded form by following these steps:

  1. First write down the hundreds part.

  2. Next write down the tens part.

  3. Now write down the units (ones) part.

  4. Now write the number in expanded form by adding these three numbers together.

    $\editable{}+\editable{}+\editable{}$++

In the next question, you'll use an algorithm to sort coins, like we did in the video. But this time, they may be in a different order, so be sure to pay attention.

Question 2

We want to place these four coins in order by following the algorithm below:

  1. Find the coin with the lowest value.
  2. Place this coin in the first empty position.
  3. Repeat this process for the remaining coins.
  1. Following the algorithm, which coin should go in the first position?

    A

    B

    C

    D

    A

    B

    C

    D
  2. Which coin should go in the second position?

    A

    B

    C

    D

    A

    B

    C

    D
  3. Which of these options shows the four coins sorted according to the algorithm?

    A
    B
    C
    D
    A
    B
    C
    D

Finally, this algorithm has more steps, and as you work through them, you may find you don't need them all!

Question 3

We want to order these three digit numbers from smallest to largest by following the algorithm below:

$705,281,106$705,281,106

1. Order the numbers from the lowest to highest hundreds digit.
2. Is there more than one number with the same hundreds digit?
  • If no - STOP
  • If yes - Order them from the lowest to highest tens digit.
3. Is there more than one number with the same hundreds and tens digits?
  • If no - STOP
  • If yes - Order them from the lowest to highest units digit.
4. STOP
  1. List the hundreds digit of each number from smallest to largest:

    $\editable{},\editable{},\editable{}$,,

  2. Will the algorithm STOP at step 2?

    Yes

    A

    No

    B

    Yes

    A

    No

    B
  3. Using your answers above, put the numbers $705$705, $281$281 and $106$106 in order from smallest to largest.

    $\editable{},\editable{},\editable{}$,,

What is an algorithm?

An algorithm is a set of steps that tells us what we need to do, and when. It can be used in lots of ways, but we have seen how to use it to sort numbers into different orders. 

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