Thursday, September 21, 2023

# How To Teach Elementary Algebra

## True Or False Working With Inequalities

How to Teach Algebra Concepts in Elementary School : Elementary School Math

Another similar concept is true or false equations with expressions on both sides. The key here is to try and move beyond rote computation. Can students make connections between the numbers to help them answer? Can they use their number sense to identify if something is an equality? For example:

101 + 22 = 100 + 23

We want students to be able to immediately identify that the equation above is true without having to complete the computation, just like with the previous examples above. But, by giving two expressions that need to be computed, we help students see that the equal sign doesnt mean to compute, but shows the relationship between both expressions. There isnt a missing number box, or a variable for an unknown. Instead, theyre applying their learning by answering a true/false question.

Be sure to give students examples with inequalities as well! A great next step is identifying what would be needed to make the equation true. I have seen kindergarten students engage in this discussion! Students likely have different responses to that question since there usually several different possibilities of changes. But thats some of the power of working with inequalities- the discussion thats drawn out from the responses.

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## How To Teach Elementary Math As Effectively As Possible

A good educator makes a difference in how students learn and how they feel about their learning.

When you teach elementary math, you have a tremendous opportunity to not only teach your students foundational concepts theyll use throughout their schooling, but to instill a love of math from a young age.

Keep reading for the best ways to create effective and engaging math lessons in your elementary classroom!

## Unknowns In Any Position

One of the easiest ways we can incorporate intentional algebra practice with young students is to include unknowns in any location in an equation and moving the location of the equal sign. By working with various formats of equations, students build an understanding of what each of the numbers represents and the purpose of the equal sign. For example:

_ + 2 = 5

5 = _ + 2

Both equations show an unknown addend. Many students will solve the second equation differently than the first. With a poor understanding of the purpose of the equal sign, students struggle with solving the second example. Even students much older than 1st grade! With continued exposure and dialogue with the various formats of equations and the meaning of the operations, students develop proficiency with both the operations and equality.

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## How Do I Teach Algebra

I find that soon I’ll be working with high school students that are struggling with math. In particular, we’ll be talking a lot about algebra and some basic trigonometry. The latter I have experience with , but I have legitimately no idea how one would teach algebra. If I see \$3x+5=14\$, it’s obvious to me what to do, and unlike, say, calculus, I can’t really even see how someone would get confused on that

This is a bit broad, but how do you teach introductory algebra? Do you have any references for new teachers?

As a personal tutor, Ive been teaching algebra to kids from ages 8 to 16 for many years. Mostly I find myself in the position of picking up the pieces when the kids are failing and fearing more failure.

The root of the problem, in my experience, is the way algebra is taught as something alien, and in particular, different from arithmetic, which it really isnt .

So first off, constant emphasis on the fact that \$x\$ is just a number you dont know yet. So it behaves like a number, and you can do all the stuff to it, that you can do to numbers.

Next, the nature of equality \$2 + 3 = 4 + 1\$.

And from there, the fact that when you do the same thing to both sides, you still end up with two things that are equal.

Always do the same thing to both sides , never move this from one side to the other and change the sign .

The manipulation of each line is easy, once youve got them to decide what theyre going to do at each stage.

## Vancouver Police Gave Toy Guns To Elementary Students Teacher Says

An anecdote about police giving toy guns to students at a Vancouver elementary school was shared during a recent school board meeting.

Luey McQuaid told trustees she was working at the Alderwood Family Development Centre, which provides treatment services and schooling for children with complex needs, when the Vancouver Police Department provided the gifts during the 2019 holiday season.

Police had asked Alderwood about delivering the gifts in person, but McQuaid replied that they could only accept if officers did so in plainclothes, without identifying themselves as law enforcement.

She said there were concerns the experience might otherwise be upsetting for some of the vulnerable young students whose families had negative interactions with law enforcement, including a child in foster care.

“He was only 10 years old at the time, Indigenous, and was taken away from his mother,” McQuaid said during the board’s Nov. 21 meeting.

“He had already experienced trauma from police, and that included being handcuffed and also included being harmed by police.”

The department declined the school’s conditions, according to the teacher, and ultimately provided gifts that staff did not feel were appropriate.

“They were all toy guns,” McQuaid said, adding that the presents were not passed along to students. “We don’t support guns in the Alderwood program.”

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## What Types Of Jobs Use Algebra

Algebra is a skill that is applicable in many types of fields and professions in todayâs economy when you solve equations. You may be surprised by the number of jobs and occupations that require a working knowledge of algebra to complete day to day requirements. Below are a few examples of professions that require algebra skills and what could be common tasks.

Business professionals who use algebra on a daily basis would be accountants. As an accountant, you need to be able to balance spreadsheets, forecast costs, and create spending reports for your company and team. Another example of business professionals who need a working knowledge of algebra includes bankers. Bankers need to be able to calculate interest rates, taxes, and more for their customers on a frequent basis. Business owners also use algebra to calculate run rates, revenue, the margin of profitability, and so much more for their shareholders to showcase growth potential and secure financing and investment.

Medical professionals need to know and understand algebra to administer drugs, detect pattern irregularities, fill prescriptions and more for their patients. Converting different drug doses is relatively common in the medical field, so having algebra solving problem skills will regularly come in handy. Especially when the time is at a crunch and equipment is space, you will need to know how to prescribe different medicine by factoring in weight, age, dosage, and more for your patients.

## Building An Understanding Of Equality And Equations

Understanding equality is a pivotal part of algebra, but truly all of our mathematics instruction. It is important that students see that the equal sign represents a relationship that the sides have the same value. Often, students see the equal sign as an indication of something to compute or solve. There are several ways we can present our computational problems that help students build an understanding of equalities.

Have you ever presented your students a seemingly simple equation thinking theyd easily solve it correctly, but they dont? It can be eye-opening.

9 + 6 = ___ + 5

If you gave your students this problem, how many of them would answer 15 instead of 10? My experience says, a large number especially if there hasnt been an investment in building algebraic thinking, or specific work with the equal sign. Every single one of my 3rd graders in one class said 15!

This type of representation can be used with any grade level of students. Very small numbers within 5 can be used with kindergarteners. Equations such as this one can start with first graders. Using manipulatives and models will help students understand how these equations work. And it can be applied with larger numbers, and other operations as well.

259 + 63 = 260 + ____

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## How To Learn Algebra

Learning algebra can seem intimidating, but once you get the hang of it, its not that hard! You just have to follow the order for completing parts of the equation and keep your work organized to avoid mistakes!

## Sound Mathematics Is Pleased To Offer Training Materials Suggesting How To Teach Elementary Algebra To College Students

How to Teach Elementary Math Without a Textbook

We offer an article and a power point presentation with suggestions on how to teach elementary algebra to college students. These training materials discuss difficulties experienced by STEM students when studying algebra as well as common mistakes and offer explanations of difficult points, which students find helpful. Of course, students succeed best if the newly acquired concepts are constantly reinforced throughout their STEM course. The materials have been prepared by Larissa Fradkin who has had a lot of experience teaching college algebra in under three weeks.

The materials cover ways to discuss:

• Negative numbers

## Solving Systems Of Algebraic Equations

An extension of the study of single equations involves multiple equations that are solved simultaneouslyso-called systems of equations. For example, the intersection of two straight lines, ax + by = c and Ax + By = C, can be found algebraically by discovering the values of x and y that simultaneously solve each equation. The earliest systematic development of methods for solving systems of equations occurred in ancient China. An adaptation of a problem from the 1st-century-ad Chinese classic Nine Chapters on the Mathematical Procedures illustrates how such systems arise. Imagine there are two kinds of wheat and that you have four sheaves of the first type and five sheaves of the second type. Although neither of these is enough to produce a bushel of wheat, you can produce a bushel by adding three sheaves of the first type to five of the second type, or you can produce a bushel by adding four sheaves of the first type to two of the second type. What fraction of a bushel of wheat does a sheaf of each type of wheat contain?

Using modern notation, suppose we have two types of wheat, respectively, and x and y represent the number of bushels obtained per sheaf of the first and second types, respectively. Then the problem leads to the system of equations:3x + 5y = 1 4x + 2y = 1

Rather than individually solving each possible system of two equations in two unknowns, the general system can be solved. To return to the general equations given above:ax + by = cAx + By = C

• 1Use pictures to make problems clearer. If you’re having a hard time visualizing an algebra problem, try using diagrams or pictures to illustrate your equation. You can even try using a group of physical objects instead if you have some handy.XResearch source
• For example, let’s solve the equation x + 2 = 3 by using boxes
x +2 = 3
+ =
At this point, we’ll subtract 2 from both sides by simply removing 2 boxes from both sides:
+- =-
• As another example, let’s try 2x = 4
=
At this point, we’ll divide both sides by two by separate the boxes on each side into two groups:
| =|
= , or x = 2
• 2Use “common sense checks” . When converting a word problem into algebra, try to check your formula by plugging in simple values for your variable. Does your equation make sense when x=0? When x=1? When x = -1? It’s easy to make simple mistakes by writing down p=6d when you mean p=d/6, but these are easily caught if you do a quick sanity check on your work before going further.
• For example, let’s say we’re told that a football field is 30 yards longer than it is wide. We use the equation l = w + 30 to represent this. We can test whether this equation makes sense by plugging in simple values for w. For instance, if the field is w = 10 yards wide, it will be 10 + 30 = 40 yards long. If it’s 30 yards wide, it will be 30 + 30 = 60 yards long, and so on. This makes sense we’d expect the field to get longer as it gets wider, so this equation is reasonable.
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## Give Frequent Feedback And Direction

Student learning is a journey, and youre the guide.

As students learn and grow, feedback on what theyre doing right and where they can improve is critical for helping them develop a growth mindset.

Aside from traditional parent-teacher conferences, classroom direction and feedback can come through:

• Well-crafted rubrics that clearly define the goals and expectations of a project
• Student-led conferences, where students give input on their work and discuss goals with parents and teachers
• Personalized learning strategies to help students address their own learning needs before they become larger issues

## Responses To How To Teach Elementary Algebra To College Students In 3 Weeks

• Larissa FradkinSeptember 27, 2012 at 11:03 pm#

Hi Galxy

Nice to know that you liked it! Maybe you have some specific questions?

I find that most algebra books are dreadfully confusing. If students have little time it is particularly important to simplify the subject to the bone and reveal as many connections as possible.

Factoring is the first stumbling block. Instead of making students study many different examples what works is giving them a simple general rule that would allow them to factorise any expression. I discuss it in my Lecture 2.

Larissa

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## Online Algebra Courses And Programs

EdX offers both introductory and advanced algebra courses. Get started solving equations and learning algebraic expression basics with the free online course from SchoolYourself. The self-paced algebra course will teach you how to work with integers, decimals fractions, and exponents, how to evaluate powers and roots and how to solve single and multi-variable equations and inequalities with online quizzes and algebra worksheets. Algebra is essential for both high school and college math curriculums and this will serve as a pre-algebra course. Working through these algebra problems will get you well-prepared for further math study.

For a more advanced algebra program, consider the College Algebra and Problem Solving course from ASU. This self-paced course uses the ALEKS learning system which helps to tailor the learning experience to the students personalized needs and pace. Learn how to apply algebra to a wide range of real-world problems and study critical algebraic concepts like functions, domains and ranges. This course can help you prepare for calculus and other math courses.

Explore additional online math courses and tutorials that cover Boolean algebra, algebraic geometry, abstract algebra and other advanced topics. Many courses are self-paced so you can enroll and learn on your own schedule.

## Allow Lessons To Build On One Another

In math class, concepts dont exist independently of each other they tend to stack up. Mastery learning can help each student to build on previous knowledge and set them up for long-term success.

Did you know that the average student in a mastery learning classroom achieves the same level as the top 15% of students in a classroom not using mastery learning? 90% of mastery learning studies have seen positive results, showing that students can achieve more when they learn at their own pace.

Use pre-teaching for maximum impact and effectiveness, or cover relevant background knowledge as it comes up. When students are equipped with everything they need to know, theyre more likely to have a positive attitude towards math!

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## How To Integrate Algebra With Elementary Students: Equality Equations And Discourse

How do you teach algebra in elementary school? Why would you? If you think of algebra as the class you took in high school and not a critical, intertwined component of mathematics, you might wonder why Im talking about introducing algebra with elementary students. As with all things, the work we do in the elementary years lays the foundation for students algebra work later. Key components of our elementary math instruction build algebraic thinking in students. And we can build students critical thinking and problem solving skills through incorporating algebra concepts in the elementary grades. Often, algebra identifies strong issues in a students mathematical understanding, which filter down to our instruction throughout their academic career. Students lacking number sense, struggling to understand the concept of the equal sign, and those that apply algorithms with little understanding struggle with algebra when they get to it. By introducing algebra concepts early, and focusing on understanding rather than memorization, we can build students number sense and math understanding thats critical for their future academic years and beyond. Algebraic concepts are now embedded within most states math standards.