This week's homework is a maths problem-solving task. 
Details can be found in homework books and also here:
 

Maths Homework - The Number Boxes Challenge

In maths this term, we will be focusing on our critical thinking, reasoning and problem-solving skills. 

Choose 6 digits between 0 - 9. You may only use these six digits. Write them at the top of your page. 

You have four boxes. You could draw them into your book to help you. You must put one of your six digits into each box. Digits may not be repeated.

Your task:

1. Make two 2-digit numbers from your six digits.

2. Add the two numbers together.

3. Your total must be as close to 100 as possible.
    

What to do:

• Try different combinations of digits.

• Record:

  • the digits you chose

  • the two numbers you made

  • Your workings and calculations

  • the total

• Decide:

  • Can you get exactly 100?

  • If not, what is the closest possible total?
     

Need another step for challenge? (optional)

• Which digits are most powerful when placed in the tens column?

• Does swapping digits between tens and ones always change the total by the same amount?

• Are some digits never useful for getting close to 100?

• How many different totals can be made from the same six digits?

Need one last push to make this even trickier? (optional)

• Prove or disprove:
  “If the four chosen digits add up to 18, it is always possible to make exactly 100.”

• Find:

• The minimum and maximum total possible from one set of six digits.

• The range of totals and explain why no others are possible.

• What happens if the target is 200?

• What if the numbers must be multiples of 5?

• What changes if you make three 2-digit numbers instead of two?

Strategy Challenge:

• Devise a systematic method that guarantees the closest total without trial and error.

Justify why your method always works.

Spelling words can be found on Google Classroom and edshed as well as below: