Using Equations to Solve Problems

We looked at equations that can be used to solve real-life problems, such as the formula that allows us to convert temperatures from one scale to another (˚C to ˚F or vice versa). Knowing where to stick the numbers into the equation are key to solving the problems correctly.

Tonight's Homework: ACE 3 (23, 43 - 45)

Finding the Point of Intersection

As we continue our study of linear functions, we spent time today looking at situations where two lines intersect. One common example uses a company's costs vs. income data. Another example looked at speeds of different people walking and when they might be at the same spot. We looked at how using equations could give us the same result as a graph and a table, and might be a quicker way to solve the problem.

Tonight's Homework: Complete the first page of the ivory colored packet called "Does Order Matter?" Then do ACE 3 (25, 27, 38, and 42). For each of these problems, make a graph and a set of equations to help you answer the questions.

Using Algebraic Expressions to Solve Number Tricks

Using algebraic expressions to represent situations can be both educational and useful. Today we looked at another way to use them--for fun! We explored several magic number "tricks" and discovered how they work by using both pictures and symbols to represent the different steps of the "tricks". Students were first amazed, and then satisfied to understand the algebra behind the tricks.

Tonight's Homework: Complete the rest of the pink packet on number tricks. Do ACE 3 (24 and 26).

More on Solving Equations and Looking for Patterns

Today, we focussed on developing strategies for solving linear equations. Once again, order of operations played a big part in ensuring student success in the process. We also worked on recognizing subtle shifts in equations and how these shifts affect the solution to a given problem.

Tonight's Homework: ACE 3 (22, 32) and finish problem 3.4 on page 54 of your book.

Solving One and Two Step Equations

In order to solve equations efficiently, students reviewed the rules for using order of operations. Next, we solved a variety of equations involving either one or two steps to solve. Students realized that to solve equations, you really need to do the opposite of what is asked for in the original equation. Students were introduced to the formal check step today.

Tonight's Homework: ACE 3 (15-19)

Bags and Coins = Two Step Equations!

After going through a number of examples using pictures of bags and coins, students were urged to use expressions to represent the bags and coins. These algebraic expressions were then put into algebraic equations, and we used statements of equality to start solving for the unknown variable.

Tonight's Homework: ACE 3 (6 - 14, 38 - 41)

Looking at Equations

We began our study of solving equations today by looking at pictures and trying to figure out what might be placed in the bags to make each statement true. Then we used symbols to represent the pictures. These introductory steps should help students to transition from the concrete examples to the more abstract nature of algebraic expressions and equations.

Tonight's Homework: ACE 3 ( 2 - 5 )

Checking for Understanding on Rates of Change

During a shortened class period, students turned in homework and then took a quiz over using graphs, tables and equations to represent rates of change for particular situations. Most students had enough time to complete the quiz. Those who didn't finish should plan to come in on Tuesday during lunch or after school to finish.

Tonight's Homework: None. Enjoy the long weekend!

Seriously? The Page Was Ripped From the Teacher's Manual?

We spent the first half of the period reviewing how to use tables, graphs and equations to help with solving problems related to given situations. This review should help students prepare for Friday's quiz. We then looked at ways to solve problems where two different situations end up having one point that works for both of them. On a graph, this is the point where both lines intersect.

Tonight's Homework: Finish all parts of problem 3.1 from the Moving Straight Ahead book.

Odds and Ends

We spent the day completing a variety of tasks. Students started on the Tile problem. Some students made up work they were missing today in class.

Tonight's Homework: Complete the Tile Problem. Do all problems on pages 113 and 114 of the Home Book.

Clear Solo Cups?

Students were served lemonade today, but there was a catch . . . they had to measure the height of the liquid in their glasses as they took drinks, and record the information in a data table. This information will be transformed into a graph and an equation as a part of tonight's homework. Due to changes in my meeting schedule, I have moved the quiz over this material to Friday, January 18th.

Tonight's Homework: Finish the table, graph and equation for the lemonade drinking activity we did in class today. Also, do both problems on page 45 of the Moving Straight Ahead book. Finally, don't forget, there's a quiz over this material on Friday, so start preparing now.

Understanding the Parts of an Equation

An equation can help us understand where points will end up on a grid, and can help us interpret a line. We took some time to identify "up front costs" and the cost per unit, and where these show up in different types of equations. Students will take a quiz over this material on Wednesday.

Tonight's Homework: ACE 2 (15, 16, 29, 33, 34, 38)

Pulling Things Together

Today, we looked at how the equations, graphs and tables can help us triple check our work to ensure we have the right answer. We even did a little algebra to show that it, too, can lead us to the correct answer.

Tonight's Homework: ACE 2 ( 6 - 10 )

Comparing Costs Using Slope and the Y-Intercept

After discovering a page was ripped out of the teacher's manual yesterday, we eventually got back on track and talked about how our equations related to the graphs we could make of them. We identified that the y-intercept would be the value we add or subtract in the equation, and that the slope of the line would be the coefficient of the variable in the equation. We'll continue to explore this relationship in the coming days.

Tonight's Homework: Complete all parts of problem 2.3

Using Tables, Graphs and Equations

Today, a guest teacher taught the lesson, as I was at a district meeting. Students looked at tables, graphs and equations that describe a particular situation to help them answer questions related to the situation. Many of today's problems involved lines that intersected, and what that intersection meant in the context of the situation.

Tonight's Homework: Finish problem 2.2 if you did not do so in class today. Then do ACE 2 (1 - 5)

Happy New Year!!!

Welcome, 2013! Students had a chance to redo a portion of the field trip problem today in class. This allowed everyone to warm up their math brains, while improving their scores on that particular assignment. We revisited walking rates by looking at problem 2.1 and ensuring that everyone understood how using a graph, data table and equation would help to solve the problem.

Tonight's Homework: Get your grade slip signed and bring it back to school tomorrow. Do page 25, problem 2.1, parts A and B. If you didn't turn in the pink worksheet and/or the field trip problem today, be ready to do so tomorrow.