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Congruence- Is the same size and shape
Similarity- Same shape different sizes. They are proportional

Pythagorean Theorem- is used to find missing sides of a right triangle. The one thing students stuggle with is understanding that A, B and C are real numbers and that you must find the square root.

Prime factorization which is a grade 6 skill comes into play with square roots.

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Quadratic Functions are non-lienaer and take the form F(x)=X^2. when graphing the shape is parabola. When x^2 is negative the parabola opens up downwards.

Properties of Exponents follow rules. These rules need to be applied in order to simplify and generate equivalent expressions. When teaching these properties it is usually best to expand the expression to show how the rule is derived.

When teaching Exponential relations I love explaining to my students the growth of money in the bank. Exponential growth is growth that happens quickly. We all want our money to grow fast not slow.

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I was aware of the differences and similarities of expressions and equations. However, I was not aware of their relationship to phrases and sentences. I think for the new school year I will meet with the ELA departments and see how math and ela can work together to help make these cross subject similarities a unit in the school curriculum.

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Comment from week 1: I never thought of how to relate expressions and equations to a phrase and sentence. This is definitely something I will add in my discussions for next year's course. This is something students can relate to on all levels.

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1. What do you know, and what should you know, about Segment 1's mathematics topics?

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1. What do you know, and what should you know, about Segment 1's mathematics topics?

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How is the curriculum structured across the grades to build deeper understanding of Segment 1 topics and to prepare for the study of Algebra I?

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How is the curriculum structured across the grades to build deeper understanding of Segment 1 topics and to prepare for the study of Algebra I?

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3. What instructional strategies, pedagogical approaches, and resources offer appropriate support for both teaching and students’ understanding of the mathematics of Segment 1 topics?

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3. What instructional strategies, pedagogical approaches, and resources offer appropriate support for both teaching and students’ understanding of the mathematics of Segment 1 topics?

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Similarly to those who already posted, I was aware of the similarities and differences between equations and expressions. I have often noticed that this is a difficult topic for students, so it was nice to see alternate explanations to possibly aid in better student comprehension. Also, being able to note trends is helpful because it allows educators, and students to be mindful to prevent mistakes and misunderstandings.

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I agree with what many of my classmates have written that equations and expressions can greatly trip up students on all levels, particularly those who struggle with math as a whole. One of the areas I know can be confusing with expressions and equations is that fact that while both possess variables and numbers, they won't simultaneously reach at a standard answer. To me, this is where students can get thrown off. Overall, it might aid students to explain that EQUATIONS help you arrive at a solution/answer, while EXPRESSIONS help you break a particular problem down.

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Question 1 response: I know the difference between an expression and an equation. Through working with students in algebra 1 for 5 years I have learned what students know about the topic. As a mathematician I view expressions and equations in a different way than many of my students do. There are conventions associated with them that need to be said for example there can not be two operations next to each other and the need to close a parenthesis. Students need words along with the symbols to have a deeper understanding. Many times students confuse expressions and equations and what the prompt is. The slides that were provided by Prof. Gibbons clearly indicate that expressions have no equals sign so you must evaluate or simplify by doing all the operations and equations are used to solve something or find equality on both sides. Reaching back to prior discussions in the A4A course equations even need to be revised by teachers. Equations are often seen as do an operation and here is the answer, it needs to be clearly stated that equations are when two expressions are the same value or equal. One big takeaway from the slides that I will use next year with my students is how an expression is like a phrase and an equation is like a sentence. That an expression is part of an equation but not the other way around. Providing students with an analogy such as this can bring perspective to a struggling student. Math does rely on English language skills of students in order to interpret what they see before them. Next year I will focus more on students understand the structure of an expression and equation by using the words more to match it with the symbols. This will then help students understand linear trends in data and interpreting word problems into algebra. Many students do not see how algebra can easily help them figure out many day to day situations they face like phone bills and paychecks. I always tell my students about how I used to work on commission selling shoes and that I used a linear equation to determine if the pretax value on my paycheck was accurate.

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I know the difference between an expression and equation. Having taught upper elementary grades for the past few years, the students often get confused between the two. I often help my students to make the connection between "Equation" and "Equal" to help them remember that equation has an equal sign and expressions don't. I enjoyed the translating words into equations and I love how it showed the translations of words into equation with different operations as well. Also, the exercise section and answers were useful.

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From my experience teaching 1st grade I have noticed how our new curriculum Envision really tries to expose students to those tough concepts starting in 1st. When I looked through the last few topics I noticed how fractions was introduced to 1st graders in the geometry topic. They also, have started regrouping in 1st grade and it helps students be able to enter the lessons in later grades with some iudea of what is happening.

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1. What do you know, and what should you know, about Segment 3's mathematics topics?

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1. What do you know, and what should you know, about Segment 3's mathematics topics?

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How is the curriculum structured across the grades to build deeper understanding of Segment 3 topics and to prepare for the study of Algebra I?

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How is the curriculum structured across the grades to build deeper understanding of Segment 3 topics and to prepare for the study of Algebra I?

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1. What do you know, and what should you know, about Segment 2's mathematics topics?

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1. What do you know, and what should you know, about Segment 2's mathematics topics?

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How is the curriculum structured across the grades to build deeper understanding of Segment 2 topics and to prepare for the study of Algebra I?

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How is the curriculum structured across the grades to build deeper understanding of Segment 2 topics and to prepare for the study of Algebra I?

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3. What instructional strategies, pedagogical approaches, and resources offer appropriate support for both teaching and students’ understanding of the mathematics of Segment 2 topics?

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3. What instructional strategies, pedagogical approaches, and resources offer appropriate support for both teaching and students’ understanding of the mathematics of Segment 2 topics?

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Similarly to many that have posted already, I felt comfortable with powers. I often tend to pause, freeze/double/triple check my work when it has negatives in it. I feel like a student as soon as negatives pop up. I know that they are difficult for students and I want to make sure that I find the easiest way to present it to them, so I often overthink it. Knowing that I overthink it, makes me break everything down and rebuild, which, I hope helps students understand the concept.

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3. What instructional strategies, pedagogical approaches, and resources offer appropriate support for both teaching and students’ understanding of the mathematics of Segment 3 topics?

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3. What instructional strategies, pedagogical approaches, and resources offer appropriate support for both teaching and students’ understanding of the mathematics of Segment 3 topics?

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I think that as new curriculums come out there is a lot of effort to introduce and kind of spiral back to review. However, I noticed in the Envision the topics tend to be very short and I believe it does not give enough time for students to master the concept. I think that overall we need to evaluate the the important skills students need and focus on mastery. In first grade tgey try to teach students so many different topics and it can become overwhelming to even the teachers

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When learning exponents I believe students need a strong foundation in multiplication and counting. I believe that if students know how to add a number over and over such as 3 +3+3. If a student can easily identify a doubles fact and then add the same number again. Math is about identifying patterns and using those patterns to solve higher and more complex problems. I thin kas a student having a strong foundation in this will make you better capable of solving these problems topics.

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I think that as a teacher it is very important to understand these concepts of surface area vs area and volume. Sometimes it can be used interchangeable or in the wrong context. Also, showing students in when can we use these in the real world will help them understand the true difference between the concepts. For example demonstrating the volume of a shape.