**Starters of the Week for IB students**

I have designed a number of IB Maths starters – these are intended to enrich and (hopefully!) stimulate. Some are aimed at strong HL students and could be developed to interesting coursework tasks, and others are more general access for all classes.

If you are a teacher and find these useful, then please also visit my new site: intermathematics.com for over 3000+ pages of content for teaching IB mathematics including worksheets, mock exams, investigations, enrichment tasks, technology guides, exploration support and investigations.

**1. Square Dance**

For the unit square shown above with vertices at (0,0), (1,0), (0,1) and (1,1), how many different types of functions can you find that go through at least 2 points? You can download a pdf solution here.

**2. Message in the logs**

A nice activity for Christmas time – can students find the hidden message? You can download a pdf solution here.

**3. Make 2023**

Using the numbers in order, the standard arithmetic operations and brackets, can you make the number 2023?

You can download a pdf solution here.

**4. Decidedly average**

In the grids, each blank square should be filled with the mean of the two numbers in adjacent squares.

You can download the solution pdf here.

**5. Circular logic**

Find the area of the shaded shape when the radius, *r*, of the original circle is 1. You can download a pdf of the solution here.

**6. The sum of 3 cubes**

How many of the numbers from 1-20 can you form as the integer sum of 3 cubes? You can download a pdf of the solution here.

**7. A reciprocal sum**

This is a good introduction to more formal mathematical techniques for finding upper/lower bounds for functions – and also in working with generalized functions. The pdf solution can be downloaded here.

**8. Hunting integers**

How many values of n give an integer answer? You can download the pdf answer here.

**9. Disappearing fractions**

What is the value of the above product? You can download the pdf solution here.

**10. As smart as Pythagoras**

Can you use the diagram above, with squares ABCD and EFHG to discover Pythagoras’ Theorem? You can download the pdf solution here.

**11. The million dollar maths problem**

“Every even integer greater than 2 can be written as the sum of 2 prime numbers.” How many solutions can you find? Prove it and enter the mathematical history books! You can download a pdf of the solution here.

**12. Time dilation**

Students calculate the effects of time dilation in one of the most amazing mathematical discoveries of all time. You can download a pdf of this solution here.

**13. A Penny for thoughts**

What is the value of R/r for the model of the Penny Farthing? You can download a pdf of the solution here.

**14. On reflection**

Can students reflect the graph of y = x^2 around a straight line? You can download a pdf of the solution here.