This lesson is about famous mathematician Karl Gauss, it combines to 2 parts: The mathematical problem as well as an inquiry part. The maths problem will enable students to investigate different ways to work out the sum of all numbers when added from 1 to 100. The second part requires students to investigate a bit about Karl Gauss’ life as well as his contributions to Maths.
Australian Curriculum Links:
- Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)
- Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)
1. Start off with a little story about Karl Gauss, (the story goes) “When a teacher asked him to add up the numbers between 1 and 100, (to keep him busy) Gauss quickly found a short cut for the answer in 3 minutes!”2. Give students the worksheet which will enable you to see their workings out at the end. Let students work independently. (I preferred to let the kids work on their own as it gave me an accurate indication of the strategies they ued to work out the sum.)
3. Roam around to students offering advice and questioning them on how they are solving the problem.
4. Half way through the lesson, offer students a chance to share the way they are working it out. Start off specifically asking a student who is adding the numbers like 1+2+3…. etc. “is there a more economical way?” Take more suggestions off students how they are working them out. **This part will also help the lower learners gain some useful strategies to use themselves.
5. Let students continue solving the problem. Once they reach the answer (5050), get students to complete the investigation side about Karl Gauss and his contribution to mathematics.
** This part I actually turnd into a mini project which students created an biography of Karl Gauss and they then presented their findings to the class in a small presentation, which cross into the English domain.
6. Once majority of people have found the answer, invite students to come up to the front and share their findings to the class. The goal is to show the students that their is more than one way to find the answer to a problem and that there is no right or wrong answer.
7. Personally, I showed the video link below, which shows how Karl Gauss calculated it so quickly. This ties it up nicely and the kids will probably enjoy the accent in the video!
8. “Ticket out the door”- I often use this, where students write down how they solved the problem on paper which gives you another idea of how they worked it out.
- Using the worksheets, you can see how the students arrived at the answer as well as the strategies they used.
- Anecdotal Notes- These can be taken whilst watching the students complete the task.
- “ticket out the door”- I often use this