2. Ryan Goodwin

3. Essential Questions For All Grade Spans 1. What patterns or relationships do we see in each type of mathematics? 2. How do we use math in real life situations?

4. What patterns or relationships do we see in each type of mathematics? K-3: Counting and grouping numbers is important. Ex: (I,2,3,4,5,6…) 4-7: Patterns get more complicated. Ex: (4,5,7,10,14,19,25) Algebra: Being able to use and extends patterns is critical to problem solving and algebraic reasoning Ex: find the sum of first natural number using a pattern.

5. How is math used in real life situations? K-3: 2 nd grade students learn to count coins and bills. Students learn what the value of money is and how to use it. 4 th -7 th : 6 th graders learn math concepts involving ratio and proportional relationships. For instance, a recipe that has a ratio of 3 cups of flour to 4 cups of sugar, which means ¾ cup of flour for every cup of sugar. Algebra: Analyzing anything uses Algebra. Whether you’re analyzing the cost of two products, or determining the profit of a business, Algebra is related.

6. Essential Questions for “Let’s Count to 10”Kindergarten Lesson What are numbers used for? Student Responses: a student extended his index finger and another student said “we count with them”. On a Step to 10 chart, how did you show the number 3 on the chart? I chose this question because demonstrating and explaining how to derive a 3 on a chart was an example of higher level thinking. What does the zero mean? This question encompasses all three grade spans.

7. 5 th Grade Place Value Lesson Observation Students were learning place value through the billions. The lesson had a lack of discourse and was un-stimulating for the students.

8. Changing 5 th Grade Place Value Lesson Add a big idea question for this chapter “How does place value help you in solving other mathematical problems? This question would get the students thinking cognitively and would create more mathematical discourse. I would facilitate a discussion by having students think-pair-share the question, then probe them to come up with some cognitively stimulating answers, which should motivate them to learn place value.

9. Outcome of Big Idea Question

10. Making Place Value Questions Essential Mrs. Iles 5 th Grade Teacher Mr. Goodwin, SDC Teacher Define periods in math What is the place value of the 5 in 1,456,000,166? Use expanded form to write 2,154,354,240. What are periods in math and give an example? Try to explain what the period means? How did you find the place value of 5 in 1,456,000,166? What different ways can we read and write 2,154,354,240?

11. Algebra 1- Audio Lesson Constant Dimensions

12. Big Idea Question: How do we use measurement in the real world? It created mathematical discourse Sparked student interest Foster students to think critically

13. Problem of the day: Using standard and alternate forms of measurement what remains constant when the units of measurement change? This question I considered to be a high–level demand question in the category of doing math tasks question. I felt this question didn’t have a predictable pathway and students were going to have to use a considerable amount of cognitive effort to solve it.

14. Essential Questions for Constant Dimension Lesson What patterns did you see with the data given? I found this question to be a procedures with connections tasks because the answers could be solved with a graph, and there were suggestive pathways to follow. By looking at your data can you see any type of ratio or algebraic expression you could make out of it? This was a procedure with connections task because the problem required cognitive effort and the ability to identify the right algebraic equation to use. What do we know if all of our ratios are about the same? This question was a procedures with connection task because a students need to know that the slope ratio never changed and remained constant due to the ratios being similar.

15. Reflection of Lesson Positive Negative Students started thinking critically. Used Think-Pair-Share and other response strategies to engage learners. Asked a variety of cognitive demanding questions. I asked too many questions at one time, which made the lesson confusing. Didn’t give students time to process questions. Failed to give students time to answer the problem of the day. Gave students questions that led to the answer.