Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Number Sandwiches

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Adding Odd Numbers

Age 11 to 16
Challenge Level

Why do this problem?

This problem, along with the rest of the problems in the Proof for All (st)ages feature, provides an excellent context for observing, conjecturing and thinking about proof, and for appreciating the power of algebra.

Possible approach

These printable cards for sorting may be useful:
Adding Odd Numbers Proof Sort

Key question

Is there a way to represent the sum of odd numbers that will help to explain the patterns you noticed?

Possible support

Encourage students to work in pairs on the proof sorting exercise.

Before embarking on this problem, students could take a look at I Like to Prove It!, which contains a collection of more accessible problems that also challenge students to develop convincing arguments.

Possible extension

Students could be encouraged to work on the rest of the problems in the Proof for All (st)ages feature.

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