Math Weekly (23/10 - 29/10)

Math Weekly (23/10 - 29/10)

1. Point

2. Reference

1. Point

1. 2^10 ~ thousand (1 kb) / 2^20 ~ million (1 mb) / 2^30 ~ billion (1 gb)

2. Gauss' Trick

   • Technique 1: Pair Numbers

   • Technique 2: Use Two Rows

   • Technique 3: Make a Rectangle

   • Technique 4: Average it out

3. Variations

   • Instead of 1 to n, how about 5 to n?

   • How about even numbers, like 2 + 4 + 6 + 8 + … + n?

   • How about odd numbers, like 1 + 3 + 5 + 7 + … + n?

4. Arithmetic gives us tools to smoosh, slide and stretch numbers.

5. Seeing arithmetic as a type of transformation prepares you to make sense of seemingly-weird concepts, like the square root of -1, and visualize problems in a new way.

6. Developing a sense of scale helps us better understand the world and better convey that understanding.

7. remember there are two ways to measure something:

   • Are we measuring a difference (distance, time)? Then do regular subtraction to get a span.

   • Are we counting items? Then subtract and add 1 (b - a + 1) - we want the number of items the span touches.

2. Reference

1. Mental Math Shortcuts

2. Techniques for Adding the Numbers 1 to 100

3. Rethinking Arithmetic: A Visual Guide

4. How to Develop a Sense of Scale

5. Learning How to Count (Avoiding The Fencepost Problem)