Last night for homework, students were asked to find the 75th shape in a Geometric Pattern. I quickly circulate around the room and I use this time to look at student approaches. Some identify the base of the pattern and use division to find the nth shape. Others extend the pattern with drawing. This helps me recognize what prior knowledge students draw from when solving pattern problems.
I ask students to share their strategies, calling first on a student who drew each shape until she had 75 on her paper. Next, I asked a student who used counting, not drawing to explain her approach.
I praise both for being persistent and persevering through a tough problem. One phrase that I use regularly with the students is effective and efficient. I asked the students who used the approaches if their strategies were very efficient, they agreed that it took some time.
Next, I asked a few students to explain their strategy. One student found the base, then multiplied to see how close she could get to 75, she determined that she would be 3 away, then knew the 75th step would be the 3rd shape in the pattern.
A few more students built off of this, saying they used division. Then, I modeled their approach in a methodological way.
To extend this, I asked the students to find the 1203rd shape.
I bring recent learning to the front of the students minds by saying, "For the past few days, you've practiced solving expressions with more than one operation. You practiced looking for the strongest connections and solving those first".
I ask them to explain which part of an expression they would solve first (parenthesis), and why. Then next (multiply or divide) and finally (add and subtract).
The 4 operations are not the only way to connect numbers. Some of you have been asking me "what about exponents?" Today we will practice simplifying expressions that include exponents as well as the 4 operations.
Here is a clip to get you thinking about these more complex expressions: PEMDAS Don't Stress
Together we simplify two expressions on the board. Each expression has a variable and exponent. I included a variable because I wanted to help the students who had a misconception yesterday.
Usually, I have the students write the guided practice examples. For today, I select pre-made problems because I don't want the numbers to become negative yet. Since this is the students' first experience simplifying complex expressions, I want the focus to be on following the order of operations, connecting this to the prior "strength of connections" lesson and working on staying organized as they rewrite each expression. Controlling the examples at this time to avoid adding a new concept, negative numbers, is important.
For this problem, The variable was c = 2. 3c + 22
I modeled the problem using a think-aloud approach, replacing the c with a 2 and working with 32. Immediately, the students opened a discussion about this error.
After one problem together, I felt they were ready to give it a try on their own.
Today, students work with a partner from their "simple machines partner" list. This variation of clock buddies allows students to have predetermined partners, it ensures that everyone is included. Also, students are able to work better together when they have had some choice in the partnership. It is important for me that the students are working in an environment that they feel safe. At this grade level, safety refers to physical safety, but also academically. I want the students to take risks, communicate about their thinking, and collaborate as a learning partnership. Allowing some type of choice helps with this goal.
Students choose at 5 expressions from their textbook to simplify and/or solve. After completing an example, they are asked to check their work with the answer key provided on the window sill.
It is so important that the students check their work after simplifying each expression because it is more challenging to "unteach" an incorrect or bad habit. While students are working, I circulate and have mini conferences with the pairs of students. I focus on the revise step when I can. Therefore, I provide the students with an answer key (not a solution key) and ask them to:
• Ask for help if you're not sure where your mistake is.
Students who complete at least 5 correctly may choose to answer more for additional practice or try some problem solving questions from their book.
*See video resource for an example
(6c + c) / 22 - 1)
This ticket out poses challenges that lead to frustration for some of my students. I make more time during snack to go over it with them.