The 7 Best Math Conferences for Teachers

8 Comments

The 7 Best Math Conferences for Teachers

What are the Best Math Conferences for Teachers?

What are the best math conferences for teachers? (Image Source: Mashup Math MJ)

Every math teacher should attend a conference at least once every few years.

Why? Because the benefits of attending math conferences for teachers can significantly shape your evolution as an educator. Conferences are a great place to network with fellow educators, learn new things (most conferences give you the flexibility to pursue topics that you are most interested in), discover emerging trends in math education, collect some awesome goodies and gifts, and make new friends.

Beyond these benefits, attending a conference allows you to meet popular math education experts in person, engage in world-class professional development, acquire cutting edge knowledge and teaching ideas that you can bring back to your school, invest in your own personal development, and become inspired.

Attending a math conference for teachers really is the best way to expand your professional circle, interact with educators from around the world, and access your favorite speakers and brands.

So, the only thing left to ask yourself is, which of the following math conference for teachers will you attend?

Top 7 Math Conferences for Teachers

1.) National Council of Teachers of Mathematics (NCTM) Annual Meeting and Exposition

The NCTM annual meeting (held in a different U.S. city every spring) is the premier mathematics education conference. At this conference, you can network and swap ideas, engage with the latest trends and innovation in math education, and discover new teaching strategies that will boost your students’ performance for years to come. Learn More

 
 

2.) International Society for Technology in Education (ISTE) Annual Conference

The annual ISTE EdTech Conference (held in a different city in late spring each year) is the premier event for anyone interested in how to use technology to engage students and boost learning outcomes. The conference is a place where tested strategies joined with proven tech tools and resources are on display and teachers are empowered to use technology to transform both teaching and learning. ISTE is also a prime networking event as most major math education brands are in attendance and accessible. Learn More

 
 
 

The SXWS EDU Conference is held in Austin, Texas each year. (Photo by Ryan Duffy on Unsplash)

 

3.) South by Southwest (SXSW) Education Conference and Festival

Held in Austin, Texas each year, the annual SXSW EDU Conference includes a diverse mix of keynote speakers, education workshops, unique learning experiences and research-backed teaching strategies, discussions on educational policy, and films aimed at inspiring and empowering all members of the educational community. Learn More

 
 

4.) Long + Live + Math Institute by Carnegie Learning

The Long + Live + Math conference is sponsored by Carnegie Learning and is held in a different U.S. city each year. The annual conference brings together some of the most passionate and influential math educators and thought leaders. With a common goal of helping all of your students reach their highest math potential, this conference is focused on sharing effective and proven math teaching strategies and empowering math teachers to transform their role as educators and become better able to make a difference in the lives of their students. Learn more

 
 

“I always look forward to getting my Mashup Math newsletter email every week. I love the free activities!”

-Christina R., 5th Grade Math Teacher, Dallas, TX

Do YOU want free math resources, lesson activities, and puzzles and games for grades 1-8 in your inbox every week? Join our mailing list and start getting tons of free stuff (including a free PDF workbook)!

 
DzTjD3wWwAAFItR.jpg
 

5.) ASCD Annual Conference

The Association for Supervision and Curriculum Development (ASCD) Conference on Teaching Excellence is a master class for teachers in the most effective and highest trending strategies for effective assessment and instruction. Teachers from around the world attend this event each year to hear expert speakers from all backgrounds share their stories and insights in how to transform your role as an educator and how to best meet the needs of every student. Learn more

 
 
 

Which math conference will you attend this year? (Image Source: Mashup Math MJ)

 

6.) MAA Joint Math Meetings

The Mathematical Association of America (MAA) hosts the Joint Math Meetings in a different U.S. city every year. The conference is the largest mathematics meeting in the world and is geared towards mathematics enthusiasts and those interested in trends and advancements in the field of mathematics and the corresponding research, how to make math more accessible and enjoyable for people of all ages, and networking with the worldwide mathematics community. Learn more

 
 



7.) National Council of Supervisors in Mathematics (NCSM) Annual Conference

Each year, the NCSM hosts a short conference geared towards networking, learning how to create and/or support a successful math program in your school, and strategies for building interest and enthusiasm for learning math in your school. NCSM is a great place for aspiring to math specialists, administrators, and/or anyone interesting in taking on a leadership role in math education. Learn More

 
 

Keep Learning:

Featured
Log Rules Explained! (Free Chart)
Log Rules Explained! (Free Chart)
Idea: How to Engage Your Students at the Start of Any Lesson
Idea: How to Engage Your Students at the Start of Any Lesson
Celebrate Pi Day 2025 with These Fun Facts
Celebrate Pi Day 2025 with These Fun Facts
Free Printable Ruler with Fractions
Free Printable Ruler with Fractions
Graphing Inequalities on a Number Line Explained
Graphing Inequalities on a Number Line Explained
How to Convert Percent to Decimal in 2 Easy Steps
How to Convert Percent to Decimal in 2 Easy Steps
How to Convert Decimal to Percent in 2 Easy Steps
How to Convert Decimal to Percent in 2 Easy Steps

8 Comments

What is Point-Slope Form in Math?

Comment

What is Point-Slope Form in Math?

What is Point-Slope Form?

Arranging equations in a particular format gives us insight into specific features of an equation. The point-slope form is one such form used with linear equations and is useful when building an equation of a given straight line.

Let’s walk through what the point-slope form is, and learn its use cases with examples.

By the end of this lesson guide, you will be able to construct linear equations in the point-slope form and interpret features like slope, y-intercepts, and x-intercepts.

What are the different forms of linear equations?

A linear equation or an equation of a straight line can be represented in three main forms. These forms are namely:

  • Standard form

  • Slope-intercept form

  • Point-slope form

The major differences between these forms are the way that the properties of a linear equation are presented within the equation. The key properties that are involved in a straight line are the slope and its intercepts (y-intercept and/or x-intercept).

 The standard form, also known as the general form of linear equations, is Ax + By = C, where A, B, and C are constants. Using the standard form to represent a straight line makes it easier to obtain the y and x-intercepts using substitution.

The slope-intercept form is the most commonly used form and is of the form y = mx + b, where m and b are constants. The benefit of using the slope-intercept is that the slope and y-intercept of the straight line can be obtained directly by observing the equation, as m is the slope, and b is the y-intercept.

What is Point-Slope Form?

The point-slope form is another form in which a linear equation with two variables can be represented. As the name suggests, to construct an equation in the point-slope form we require a point on the straight line and its slope.

Definition: The point-slope form of a line is expressed using the slope of the line and point that the line passes through.

Formula: y-y1 = m(x - x1) where m equals the slope of the line and x1 and y1 equal the corresponding x- and y-coordinates of a given point the line passes through.

The general structure of an equation in the point-slope form is: y - y1 = m*(x - x1)

Here (x1,y1) is any arbitrary point on the straight line, and m is the slope/gradient of the straight line. Following is a table that shows a side-by-side comparison of the same straight line represented in the three forms mentioned above.

Again, notice each equation is a different way of expressing the same linear function, namely one with a slope of 2/3 and a y-intercept of 5.

One of the unique properties of the point-slope form compared to the other forms is the flexibility in its structure. This flexibility comes from the fact that you can use any point on a particular straight line to build the point-slope form equation.

In fact, below are some out of infinitely many other valid point-form equations of the straight line above.

  • y - 9 = ⅔*(x-6)

  • y - 3 = ⅔*(x+3)

  • y +1 = ⅔*(x+9)

 Next, let’s find out more about the fundamentals behind the point-slope form.

Fundamentals of the point-slope form

The main concept behind the point-slope form is the formula for determining the slope of a straight line. The formula that is used to calculate the slope of a straight line is :

m = (y2 - y1)/(x2 - x1)

Here, m is the slope of the straight line, while (x1,y1) and (x2, y2) are the coordinates of any two points on the given straight line.

Let’s apply the slope formula to find the slope of the line given in the graph below:

(y - y1)/ (x - x1) = m

Multiply both sides by x - x1, and we get

y - y1 = m * (x-x1), which is the general structure of the point-slope form.

As mentioned before, we can replace (x1,y1) with the coordinates of any point that lies on the given straight line. Note that if you select the y-intercept (b,0), then you will end up with the slope-intercept form of the equation.

y - b = m*(x-0)

y - b = mx

y = mx + b → the slope-intercept form

Therefore, the slope intercept can be considered a special case of the point-slope form.

Now with this fundamental understanding let’s see how we can construct the equation of a straight line in point-slope form using a variety of examples.

Point-Slope Form Examples

The information provided in a scenario can be different, but the goal is to determine the slope and the coordinates of a point that lies on a straight line.

Example #1 Finding the point-slope equation from slope and a point

Problem: Consider a straight line that has a slope of -7 and passes through the point (5, -3)

We can directly substitute the given data into the point-slope general equation below:

y-y1 = m*(x-x1)

Here m is the slope, hence it is -7 in this example. The point (5,3) is the arbitrary point (x1,y1). By substituting the terms we get:

y - - 3 = -7*(x - 5)

Hence,

y + 3 = -7*(x - 5) is the point-form equation of the straight line.

 

Example #2 Finding point-slope equation from two points

Problem: Consider a straight line on which the points (-2,1) and (1,10) lie. Determine the equation of the line in point-slope form.

 

First, we can use the slope formula to determine m (slope) of the line.

m = (y2- y1)/(x2-x1)

Substituting (-2,1) and (1,10) we get:

m = (10-1)/(1- - 2)

m = 9/3

m = 3

Now that we have determined the slope of the line to be 3, we can build the point-slope equation.

y-y1 = m*(x-x1)

We can pick any point on the line for (x1,y1). Here let’s use (-2,1).

y - 1 =3*(x- -2)

Hence,

y - 1 = 3*(x+2) is the point-form equation of the straight line.

 

Example #3 Determining features from the point-slope equation

Problem: Which of the following graphs represents the straight line of equation y - 4 = -2(x + 3)

 

The equation provided is in the point-slope form. By comparing y - 4 = -2(x+3) and y - y1 = m*(x-x1), we can work out that:

m = -2, and (x1,y1) is (4,-3)

So we must look for a graph that has a slope of -2 and passes through (4,-3). Since only black, red, and blue lines clearly pass through (4,-3), we can eliminate the rest.

 

Amongst the three, only the black has a negative slope. Hence the line that represents the point-slope equation of y - 4 = -2(x+3) is the black graph.

 

Looking for more point-slope form example problems?

Are you ready to extend your thinking and work through 5 more point-slope form practice problems with step-by-step explanations and answers included? Click the link below to access our free guide for students:

⇥ 5 Point-Slope Form Example Problems for Students

Conclusion: Point-Slope Form

Amongst the three main forms of representing linear equations, the point-slope form can be considered the most versatile. By identifying the slope and a single point that lies on a straight line you can determine the point-slope of an equation. The type of information you get about a straight line may change, hence you should utilize the necessary formulas and/or visual interpretations of graphs to extract what you need.

Keep Learning:

Comment

5 Point-Slope Form Examples with Simple Explanations

Comment

5 Point-Slope Form Examples with Simple Explanations

5 Point-Slope Form Examples for Students

When it comes to graphing lines on the coordinate plane, there are several different ways to express a linear equation and figure out how to determine a given line’s slope, y-intercept, points it passes through, and what its graph looks like. Being able to understand and solve problems involving linear equations in various forms, including point-slope form, is an immensely useful and important algebra skills that will help you to solve math problems involving linear equations.

The following lesson will take you step-by-step through solving 5 point-slope formula examples (sample problems) that we will solve and find the final correct answer together. By working through these 5 examples, you will gain a much better understanding of point-slope formula, what it means, and how to use it to solve problems on future homework assignments, quizzes, tests, and exams.

But, before we start working on the point-slope form examples, we will quickly review some very important vocabulary terms and review some key information regarding lines, equations, slopes, and y-intercepts. It is helpful to review this information, even if you are already familiar with it, as you will be building upon it as this lesson progresses and having a strong foundation makes a world of difference.

What is Point-Slope Form?

In math, there are more than one way to express the equation of a line (also referred to as a linear equation).

Most algebra students first learn about slope-intercept form: y=mx+b, where m equals the slope of the line and b equals the y-intercept.

With slope-intercept form, as long as you know the slope and y-intercept of the line, you can determine its equation, graph the line on the coordinate plane, and figure out what points the line passes through.

What is point-slope form?

Definition: The point-slope form of a line is expressed using the slope of the line and point that the line passes through.

Formula: y-y1 = m(x - x1) where m equals the slope of the line and x1 and y1 equal the corresponding x- and y-coordinates of a given point the line passes through.

Unlike slope-intercept form, point-slope form does not require you to know the function’s y-intercept. Instead, you are only concerned with the slope and the coordinates of one point that the line passes through.

If you find this definition confusing, take a look at the graphic below that compares slope-intercept form and point-slope form and further analyze the key similarities and differences between the two forms.

In terms of similarities, both slope-intercept and point-slope form require you to know the slope of the line.

(Looking to learn how to find the slope of a line? click here to access our free guide )

However, the key difference is that slope-intercept form requires you to know the y-intercept of the graph, while point-slope form requires you only to know the coordinates of one point that the graph passes through (this point can be anywhere on the line).

Now that you are familiar with the point-slope form formula, you are almost ready to work through some point-slope form examples. But, before we explore point-slope form further, let’s take a quick look two simple situations involving graphing linear functions using given information.

▶ Situation A: Graph the Linear Function

Problem: Graph a line with a slope of 3 and a y-intercept at 6 and write its equation in y= form.
Notice that Situation A gives us enough information right from the start to write the equation in y=mx+b form since we already know the slope, m, and y-intercept b.

  • m=3 and b=6

 We can write the equation as follows:

  •  y=3x+6

 This line has a slope of 3 (or 3/1) and a y-intercept at positive 6. We can now graph this line as follows:

 

Situation B▶: Graph the Linear Function

 Problem: Graph a line with a slope of 3 that passes through the point (2,12) and write its equation in y= form

Notice that situation B does not give us enough information to write the equation of the line in y= form since we only know the slope and not the y-intercept.

 This is where point-slope form comes into play!

In cases like this, m represents the slope, which is 3 and x1 and y1 are the corresponding x- and y-coordinates of whatever given point the line passes through.

Since we already know that the line passes through the point (2,12), we know that x1=2 and y1=12 

We can substitute these values into the point slope formula as follows

 

 After substituting m=3, x1=2, and y1=12, you end up with the following equation in point-slope form:

  • y-12 = 3(x-2) 

If we want to graph the line on the coordinate plane, it may be easier to rearrange this formula into y=mx+b form as follows:

 

To convert from point-slope form to slope-intercept form:

  • y-12=3(x-2) ➞ y-12=3x-6 ➞ y=3x+6

Now that we have converted the equation into y=mx+b form, we can go ahead and graph this line since we know that the slope is 3 and the y-intercept is positive 6.

 

Notice that the line does pass through the point (2,12).

What else do you notice about this graph? It turns out that situation A and situation B both represent the same linear equation, just in different forms.

  • Situation A: slope-intercept form

  • Situation B: point-slope form

If you are comfortable with solving problems involving equations in y=mx+b form (slope-intercept form), then you can surely be successful at solving problems involving point-slope form (y-y1=m(x-x1).

To take this next step, practice is key! So, now let’s look at 5 examples of solving algebra problems involving point-slope form to give you some more experience.

Point-Slope Form Example #1

Problem: Determine the point-slope form of a line that has a slope of 1/2 and passes through the point (8,2).

To determine the equation of this line in point-slope form, you have to know the following pieces of information:

  • the slope of the line, m

  • the coordinates of a point that the line passes through, (x1, y1)

In this first example, both of these pieces of information are given to you, so you are ready to write the equation of the line in point-slope form by substituting m=1/2, x1=8, and y1=2 as follows:

 

Answer: The equation of the line in point-slope form is: y-2=1/2x(x-8)

Point-Slope Form Example #2

Problem: Determine the point-slope form of a line that has a slope of 3/4 and passes through the point (4,-6).

Again, to determine the equation of this line in point-slope form, you have to know the following pieces of information:

  • the slope of the line, m

  • the coordinates of a point that the line passes through, (x1, y1)

Just like example #1, both of these pieces of information are given to you, so you are ready to write the equation of the line in point-slope form by substituting m=3/4, x1=4, and y1=-6 as follows:

 

In this example, the value of y1 is a negative number (-6). When you substitute this value into the point-slope formula, on the left-side of the equation, you end up with: y - - 6

You can simplify this double-negative by rewriting it as a positive: y- -6 ➞ y + 6

Answer: The equation of the line in point-slope form is: y+6=3/4x(x-4)

Point-Slope Form Example #3

Problem: Determine the point-slope form of a line that passes through the points (1,10) and (3,16)

Just like the previous two examples, to determine the equation of this line in point-slope form, you have to know the following pieces of information:

  • the slope of the line, m

  • the coordinates of a point that the line passes through, (x1, y1)

Unlike the first two examples, in this case you are not given all of the required information upfront. While you know that coordinates of a point that the line passes through (you actually know two of them), you do not know the slope of the line.

Luckily, you can use the slope formula to find the slope of a line that passes through two given points.

 

The slope formula is equal to change in y over change in x.

To correctly use the slope formula, you have to correctly label and identify the (x1, y1) and (x2, y2) values so you can substitute them into the formula. The first point that you use will have the 1’s and the second point that you identify will have the 2’s.

  • (1) First Point: (x1,y1) ➞ (1,10) where x1=1 and y1=10

  • (2) Second Point: (x2,y2)➞ (3,16) where x2=3 and y2=16

You are now ready to calculate the slope as follows:

 

By substituting the values of (x1,y1) and (x2,y2) into the slope formula, you end up with :

  • m = (16-10)/(3-1) = 6/2 = 3

After simplifying 6/2 to 3, you can conclude that the slope of the line, m, equals 3

Now that you know the slope of the line and the coordinates of a point that the line passes through, you can write the equation of the line in point-slope form. Note that you can choose either given point that the line passes through (1,10) or (3,16). Below, we will use the first given point (1,10):

 

Answer: The equation of the line in point-slope form is: y-10=3(x-1)

Point-Slope Form Example #4

Problem: Determine the point-slope form of a line that passes through the points (-5,15) and (-10,18)

Again, in order to determine the equation of this line in point-slope form, you have to know the following pieces of information:

  • the slope of the line, m

  • the coordinates of a point that the line passes through, (x1, y1)

Just like in example #3, you are not given all of the required information upfront. While you know that coordinates of a point that the line passes through, you do not know the slope of the line.

Following the same process as example #3, you can use the slope formula to determine the value of m as follows:

 

By substituting the values of (x1,y1) and (x2,y2) into the slope formula, you end up with :

  • m = (18-15)/(-10- -5)

Notice that the double negative in the denominator can be rewritten as: (-10- -5) ➞ (-10 + 5)

  • m = (18-15)/(-10 + 5) = 3/-5

You can express these results as -3/5, so you can conclude that the slope of the line, m, equals -3/5

Now that you know the slope of the line and the coordinates of a point that the line passes through, you can write the equation of the line in point-slope form. Just like the last example, you can choose either given point that the line passes through (-5,15) or (-10,18). Below, we will use the first given point (-5,15):

 

Answer: The equation of the line in point-slope form is: y-15=-3/5(x+1)

Point-Slope Form Example #5

Problem: Graph the line with the following point-slope form equation: y-4=2(x+6)

In this final example, you will have to graph a line and all that you are given is a linear equation in point-slope form.

All that you need to graph a line is the slope of the line and a point that the passes through—which is exactly what you can find when you look at the equation in point slope form.

Remember that point slope form is as follows: y-y1 = m(x = x1) where m equals the slope of the line and (x1,y1) are the corresponding x- and y-coordinates of the point the line passes through.

So, in this example, we can see that the slope of the line m=2 (or 2/1)

Furthermore, we can see that the y1=4, but what about x1?

Since we see that ‘+’ sign on the right-side of the equation (x+6), we know that a double-negative must have occurred, so the x1 value is equal to -6 (not positive 6).

Now we have all of the information that we need:

  • Slope: m=4

  • Point: (x1,y1) = (-6,4)

All that we have to do now is graph the line. Start by plotting the (x1,y1) point, which is (-6,4) in this example as follows:

 

Next, use the slope m=2/1 to “build” more points by using the rise over run method (rise two units, and run two units to the right) as follows:

 

Finally, draw the line that intersects the points that you plotted to complete your graph:

Answer:

 

Keep Learning:

Comment

Calculating Percent Decrease in 3 Easy Steps

1 Comment

Calculating Percent Decrease in 3 Easy Steps

Calculating Percent Decrease in 3 Easy Steps

Being able to calculate percent decrease is an extremely useful and important numerical skill that can has implications far beyond the math classroom. An ability to calculate, understand, and analyze percents will not only help to excel on quizzes, tests, and examples, but in real world situations as well. While students often believe that calculating percent decrease to be challenging task, the process to getting correct answers is actually very easy and straightforward.

(Looking for a Percent Decrease Calculator to make a super-fast calculation: Click here to access our free Percent Decrease Calculator)

The following free Calculating Percent Decrease step-by-step lesson guide will walk you through calculating percent decrease using an easy and simple three-step method. By learning to follow these three steps, you will be able to quickly and accurately solve problems in math involving percent decrease.

Before we start learning about calculating percent decrease and the three-step method, lets perform a fast review of a few important math vocabulary terms and concepts related to this topic.

Looking to learn how to calculate percent increase or percent change? Use the links below to download our free step-by-step guides:

Percent Definition

In mathematics, the term percent refers to parts per one hundred and the mathematical symbol for percent is %.

For example, the value 40% is defined as 40 per 100. If you observe the below diagram, you will see that the blue shaded region makes up 40% of the entire grid.

We can also say that percent represents a ratio of a value out of one hundred.

Another example would be 20% meaning 20 out of every 100. Looking at percent as a ratio, when can say that if 20% of 300 students have an exam on Monday, then 60 total students have an exam on Monday (20 out of every hundred means three 20’s out of 300 total students).

Percent Decrease Definition

The next question we have to ask is what is the meaning of percent decrease?

In mathematics, the percent decrease between two values is the difference between the final number and the initial number (which we will refer to as the starting number in this guide). Percent decrease is always expressed as a percentage of the starting number.

Note that percent decrease is a value that will be expressed as a percentage and will include the % symbol.

For example, if you had $80 dollars in savings at the start of the month and $60 in savings by the end of the month and you needed to calculate the percent decrease, the final number would be 60 and the starting number would be 80.

 

Being able to correctly identify the starting number and the final number is extremely important when it comes to correctly solving percent decrease problems.

Calculating Percent Decrease

Now it’s time for you to learn how to calculate percent decrease using our simple three-step method.

Let’s revisit the previous scenario involving money in your savings account decreasing between the start of the month and the end of the month:

Calculating Percent Decrease Example #1

For the first example, let’s find the percent decrease for the following scenario:

If a total amount in your savings account of $80 at the start of the month had decreased down to $60 by the end of the month, what is the percent decrease?

Here is how you can apply our three-step method:

 

Step 1: Find the difference of the values by subtracting the final value from the starting value.

In this example, the difference of starting value and the final value can be calculated as follows:

80 – 60 = 20

In this case, the difference of the two values would be 20. Note that, when calculating percent decrease, you will always be subtracting the smaller value from the larger value.

Step 2: Divide the difference by the starting number.

The next step is to take the difference (20 in this example) and divide it by the starting number (80 in this example) as follows:

20/80 = 0.25

Always express your answer as a decimal (this is crucial for performing your final calculation in Step 3).

Step 3: Multiply by 100

The third and final step is to multiply the decimal result from Step 2 by 100 and then express that result as a percent using the % symbol.

0.25 x 100 = 25

Final Answer: 25% Decrease

You’re done! By using the three-step method, you can conclude that there was a 25% decrease in how much money you had in savings from the start of the month to the end of the month.

Need more help? No worries. Let’s move onto another example where we will calculate percent decrease using the same three-step method.

Looking for a free Percent Decrease Calculator?

If you need a faster way to calculate the percent decrease between two numbers, check out our free Percent Decrease Calculator tool, which lets you input the starting and final values to get an instant answer!

▶ Click here to access our free Percent Decrease Calculator for students

Calculating Percent Increase Example #2

Last week, Zoe sold a total of 51 chocolate cupcakes at her bakery. This week, she sold a total of 34 chocolate cupcakes at her bakery. What was the percent decrease in the total amount of chocolate cupcakes sold between last week and this week?

To solve this problem, note that the starting value is 51 and the final value is 34.

 

Step 1: Find the difference of the values by subtracting the final value from the starting value.

In this example, the final value minus the starting value can be calculated as follows:

51– 34 = 17

Step 2: Divide the difference by the starting number.

For step two, take the difference (17 in this example) and divide it by the starting number (51 in this example) as follows:

17/51 = 0.3333333…

Notice that the result is a repeating/non-terminating decimal. You can round this result to the nearest hundredths decimal place to make things easier. In this case, you can round the result to 0.33

Step 3: Multiply by 100

The last step is to multiply the decimal result from step two by one hundred and express the final result as a percent. So…

0.33 x 100 = 33

 Final Answer: 33% Decrease

We’re all finished! We have concluded that there was a 33% decrease in the total amount of chocolate cupcakes sold at Zoe’s Bakery between last week and this week.

 

After this first example, you should be feeling more confident about your ability to correctly calculate percent decrease e using the three-step method. Let’s gain some more experience by looking at another example.

Calculating Percent Decrease Example #3

Last school year, 414 students attended the Delta High School Winter Ball This year, only 112 students attended the Delta High School Winter Ball. What was the percent decrease in students who attended the Winter Ball between last year and this year?

 Just like the last two examples, you can solve this problem by following the three-step process:

Step 1: Find the difference of the values by subtracting the starting value from the final value.

 In this example, the starting value minus the final value can be calculated as follows:

414– 112 = 302

Step 2: Divide the difference by the starting number.

Let’s continue with step two as follows:

Find the difference (190 in this example) and divide it by the starting number (414 in this example) as follows:

302/414 = 0.7294685…

Just like in example 2, you can round the result to the nearest hundredths decimal place to make things easier. In this case, you can round the result to 0.73

Step 3: Multiply by 100

The last step is to multiply the decimal result from step two by 100 and express the final result as a percent. So…

0.73  x 100 = 73

Final Answer: 73% Decrease

 

At this point, you should feel much better about your ability to calculate percent decrease and solve any math problems involving percent decrease our three-step method. But, if you feel like you need more practice, it is highly recommended that you work through examples one through again on your—be sure to do the problems by hand and take notes as you go along!

Conclusion: Calculating Percent Decrease

You can calculate percent decrease given any two values by using the following 3-step method:

Step 1: Find the difference of the values by subtracting the final value from the starting value.

Step 2: Divide the difference by the starting number. Express result as a decimal.

Step 3: Step 3: Multiply by 100. Express result as a %.

What about Calculating Percent Increase and Percent Change?

Learn how to calculate a percent increase or a percent change between two numbers using our free step-by-step guides. Click the links below to get started.

Don’t forget about our Free Percent Decrease Calculator

Click here to get started using our free Percent Decrease Calculator

Keep Learning:

1 Comment

Are You Using This Genius Strategy for Math Writing?

2 Comments

Are You Using This Genius Strategy for Math Writing?

Image Source: Mashup Math MJ

Writing about math helps kids to organize their thinking, use key vocabulary, and communicate mathematically—which leads to deep and meaningful understanding.

Over the past few years, math teachers are incorporating more writing activities into their lesson plans—a trend that is being driven by the use of highly engaging think-notice-wonder writing prompts that spark deep mathematical discussion and are highly effective as warm-up or cool-down activities. 

This strategy has recently been endorsed by the National Council of Teachers of Mathematics:

By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems.

How does it work?

Math teachers often struggle to find topics for their kids to write about. Sometimes the best way to encourage creativity and exploration is simply posting an image and asking students to describe what they think, notice, and wonder about what they are seeing.

The best way to use think-notice-wonder activities is to choose an image every day and project it as large as you can at the front of your classroom.

Then, have students write 3 sentences about the image starting with:

      •     I think…

      •     I notice…

      •     I wonder…

✔  You may want to have students share their entries in a daily math journal. This practice will get them used to writing about mathematics regularly.

✔  Try not to give too many prompts. You’ll be surprised by how creative and detailed student responses will become over time!

✔  Try to choose images that work with the day’s topic/theme

What would think-notice-wonder look like in YOUR classroom?

 

Image: Mashup Math MJ

 

Imagine an unusual day where your kids enter class expecting a normal warm-up practice problem but are caught by surprise.

They see the above image of a drone delivering a package displayed on the board along with a writing prompt that calls for them to complete the statements I think..., I notice..., and I wonder...

What kind of creative thoughts and ideas would they have?

How much weight can the drone carry? How many packages can it hold at once?

How would thinking about this image activate their prior knowledge and spark their curiosity?

What are the dimensions of the largest and smallest box it can hold? Does it have to be square?

What kind of anticipation would it build for an upcoming lesson or activity?

Does the drone use GPS coordinates to get from point to point?

Why Think-Notice-Wonder?

Engaging in think-notice-wonder writing activities at the start of a math class is a great way to ignite student thinking, spark creativity, and build anticipation.

Even if students are not directly engaged in mathematical problem-solving, their curiosity and interest will carry on throughout the day’s lesson.

Be mindful that your kids will need some time to get used to these kinds of activities, but after a week or so, you’ll be pleasantly surprised by the spike in engagement, boost in student enthusiasm and high quality of responses!

Are you ready to try it with your kids?

Here are a few more sample graphics for you to try in your classroom:

Want more? Download 101 Daily Think-Notice-Wonder Writing Prompts for Engaging Your Kids

You can now share 101 Daily Think-Notice-Wonder Writing Prompts with your kids with our PDF workbook!

Do you have experience using think-notice-wonder activities with your math students? Share your thoughts and suggestions in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

2 Comments