Mathematics

November Update

I have been so impressed by the Sulwe mathematicians, who have transferred their knowledge of solving equations to solving systems of equations using graphing, elimination, and substitution. Today, they tried their first system of 3 equations, and it was mighty challenging! They should be proud of their incredibly hard work. Have a wonderful holiday, Sulwe mathematicians!

---

October Update

In Sulwe Mathematics, we have been looking at patterns and discussing their growth patterns. Students can craft tables, graphs, and equations and draw connections between them. The Sulwe students are experts at linear equations! 

We also began writing our own one-variable inequality stories, challenging the class to write inequality statements, solve them, and graph them on a number line. Soon, we will be doing two-variable inequalities!

---

September Update

In Sulwe Mathematics, we have been building a strong foundation of Pre-Algebra by exploring expressions and multi-step equations. Students now have several methods for solving equations, such as hands-on origami, undoing the order of operations, and using a foldable, all of which can be found in their notebooks. 

We are also investigating the essence of algebra -- that it is visual, logical, and creative. We will have a quiz next week all about expressions, equations, and linear relationships. After mid-term break, we will dive into inequalities. Below is a description of the unit we are working on:

In this unit, students revisit strategies for solving one-variable equations and inequalities and extend their knowledge to make sense of multi-variable equations and two-variable inequalities.

Section 1: One-Variable Equations (Lessons 1–5)

Students revisit strategies for solving one-variable equations, including making balanced moves and using inverse operations.

Lesson 1: Students revisit a model for solving equations from Math 6–8: balanced hangers.

Lesson 2: Students use inverse operations and balanced moves to solve equations.

Lesson 3: Students focus on each step of solving an equation. They determine and explain whether or not two equations are equivalent, meaning that they have the same solution.

Lesson 4: Students practice solving one-variable equations.

Lesson 5: Students practice solving equations in context and interpreting their solutions, including equations with no solution or infinite solutions. This lesson also highlights the effect of dividing by a variable when solving.

Section 2: Multi-Variable Equations (Lessons 6–9)

Students represent situations using two variable equations and rewrite those equations to highlight a variable of interest.

Lesson 6: Students are introduced to different forms of two-variable equations. They interpret the values in these equations and consider their solutions in the context of sitting and standing capacities in a subway.

Lesson 7: Students apply what they learned about solving equations with one variable to solve equations with variable coefficients.

Lesson 8: Students revisit the idea that graphs can be a useful way to represent relationships and connect graphs to the equations they represent.

Lesson 9: Students put together everything they have learned about representing situations with two variables, including solving equations for one of the variables.

Section 3: One-Variable and Two-Variable Inequalities (Lessons 10–16)

Lesson 10: Students explore connections between constraints and one-variable inequalities.

Lesson 11: Students use reasoning to determine the solutions to a one-variable inequality and graph those solutions on a number line.

Lesson 12: Students solve one-variable inequalities by solving its corresponding equation and testing values.

Lesson 13: Students make sense of two-variable inequalities, their solutions, and graphs.

Lesson 14: Students learn how to graph all the solutions to a two-variable inequality given the graph of its corresponding equation, including determining which region to shade and whether to include the boundary line in their graph.

Lesson 15: Students extend their understanding of how to determine and interpret the solutions to two-variable linear inequalities.

Lesson 16: Students use two-variable inequalities and their solutions along with real-world constraints to make sense of an issue in society: water as a limited resource.

Please be checking in with your learner to confirm that they have their two assignments (practice packet and Creative Communication) ready to turn in on Monday. Never hesitate to reach out to me about Mathematics!

Friday, 27 September

This month, we began our course with an introduction to geometry, covering topics such as:

• Points, lines, and planes

• Angles and triangles

• Polygons

• Circles

• Mathematical notation

Additionally, we launched our student-centric unit on shadows, where students are exploring and experimenting with the factors that affect shadows. They will engage in mathematical modeling, data collection, and data analysis while learning about various geometric concepts, including triangles and angles.

November Update

In Pre-Calculus, we concluded our unit on Limits by taking a unit assessment. Students are currently working on a creative assignment, which will be a gift to our beloved classmate, Andrew, as he continues his academic journey elsewhere. You will be truly missed, Andrew!

---

October Update

In Pre-Calculus, we have been exploring different types of discontinuities, which include holes, asymptotes, and jumps. The students seem to be really enjoying the content and can now write domains using interval notation. They are encouraged to not grow wearing in doing their homework, as building new skills requires practice. Keep up the good work, Enjubas!

---

September Update 

In Pre-Calculus, students have been passionately pursuing the definition of limits in graphs, expressions, and tables. They have mastered the unit circle and have a beginning understanding of trigonometric functions. Next week is our first quiz, assessing their understanding of lessons 1-9. 

Unit 1 - Limits and Continuity

        1.1 Can Change Occur at an Instant?

        1.2 Defining Limits and Using Limit Notation

        1.3 Estimating Limit Values from Graphs

        1.4 Estimating Limit Values from Tables

        1.5 Determining Limits Using Algebraic Properties

              (1.5 includes piecewise functions involving limits)

        1.6 Determining Limits Using Algebraic Manipulation

        1.7 Selecting Procedures for Determining Limits

              (1.7 includes rationalization, complex fractions, and absolute value)

        1.8 Determining Limits Using the Squeeze Theorem

        1.9 Connecting Multiple Representations of Limits

Mid-Unit Quiz - Unit 1

        1.10 Exploring Types of Discontinuities

        1.11 Defining Continuity at a Point

        1.12 Confirming Continuity Over an Interval

        1.13 Removing Discontinuities

        1.14 Infinite Limits and Vertical Asymptotes

        1.15 Limits at Infinity and Horizontal Asymptotes

        1.16 Intermediate Value Theorem (IVT)

Unit Test - Unit 1

Check in with your student to ensure they have their homework ready on Mondays. Encourage them to ask questions to gain a strong understanding of the concepts.

I'm so proud of these driven, curious, fun students!