Try to figure out what these mean Bigger and Better Ex: Top secret Too funny for words Half hearted Once in a blue moon Jack in the box H2O Robin Hood Scrambled eggs
How do I think mathematically?!? AHH! Don’t worry, you’ll get there…
Puzzling and Persevering • Math is just a collection of rules to know and follow… right? • WRONG! Real problems (in school and in the real world) are not that simple. • You might not always know where to start or what to do next. There’s no “rule” or “formula” for some problems. • Working with puzzles helps to develop skills in figuring out where you can start, and where you can go next. • You must stick with them…. PERSEVERE! • This will help you to become thoughtful, creative and an “out of the box” thinker.
Puzzles to Try: • Four piano students—Ashley, Brandon, Cassie, and Damian—will give a recital. • Cassie insists on playing immediately after Brandon. • Ashley might be late, so she can’t go first. • Damian and Ashley are playing the same piece, so at least one other player must come between them. • Help their teacher figure out in what order to have them perform.
Seeking and using structure • 3x + 5 = 26 • Usually this would require a particular set of steps in a particular order to solve. • The steps do help! And helps you to understand the process… • BUT you also must see the structure of the problem. What it all means rather than just going through the motions. • It will help you to make sense of WHY you are going through the motions.
How and WHY?? • 3x + 5 = 26 Initial Problem- Solve for X • What do we know about the “=“ sign? • -5 = -5 +5 -5 = 0 • Why on the other side too? 26 – 5 = • 3x + 0 = 21 What can we do with the 0? Why? • 3x = 21 • ÷3 = ÷3 3 ÷3 = Why on the other side too? 21 ÷3 = • 1x = 7 What can we do with the 1? Why? • x = 7 • Does it fit??
Describe Reasoning • Explain how YOU arrive at an answer. Not everyone does it the same. • Let’s try it. • A football team lost 5 yards and then gained 9. What is the team's progress? • Sara is twice as old as her brother John who is 8. How old will Sara be when John is 20? • Be Clear on how you are explaining- Make sure everyone can understand the steps that you went through (whether on paper or in your mind).