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These are the standards selected by LOSFA for the Summer 2019 Gear Up Camp Focus.

Each column on this padlet represents a standard and lists resources below it.

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Solve routine first-degree equations

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Work with cubes and cube roots of numbers

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Determine the slope of a line from an equation

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Test Packet # 16, 18, 19, 22

Find the slope for each equation
y = 6x + 12
3x + 20 = -4y
4x + 5y = -10

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How To Find The Slope Of A Line: THE EASY WAY!!

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Go to http://www.apluslearn.org/#!online-tutoring/u3heo for LIVE online tutoring! Learn how to easily find the slope of a line with this very detailed and step by step video lesson! Many students struggle with slope and you don't have to be one of them. Have fun learning how to find the slope a line the easy way with Math Motor Youtube channel!

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Pre-Algebra giving you a hard time? Shmoop's free Basic Algebra Guide has all the explanations, examples, and exercises you've been craving.

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Test Packet # 12, 14, 20, 23

Cube root of 1000
2^3 =
Cube root of 1

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Introduction to Perfect Cubes (Students have prior understanding of perfect squares from class notes)

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Introduction to cube roots | Numbers and operations | 8th grade | Khan Academy

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Test Packet # 13, 15, 17, 21

Solve for x in each equation
2(6x) + 8(2x+6)=-21
3(4x-7)=27
5(-3x)+2(-2x-4)=68

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Algebra Basics: The Distributive Property - Math Antics

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This website provides an equation solver. Simply type the equation in and it solves it step by step.

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Examples: 1+2, 1/3+1/4, 2^3 * 2^2
(x+1)(x+2) (Simplify Example), 2x^2+2y @ x=5, y=3 (Evaluate Example)
y=x^2+1 (Graph Example), 4x+2=2(x+6) (Solve Example)

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Algebra Calculator shows you the step-by-step solutions! Solves algebra problems and walks you through them.

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In these lessons, we will learn how to

Solve multi-step equations with whole numbers

Solve multi-step equations with fractions

Solve multi-step equations with decimals

Related Topics: More Algebra Lessons
Solving multi-step equations with whole numbers

The following diagram shows how to solve multi-step equations. Scroll down the page for more examples and solutions.

To solve a multi-step equation, we would start by trying to simplify the equation by combining like terms and using the distributive property whenever possible.

Consider the equation 2( x + 1) - x = 5. First, we will use the distributive property to remove the parenthesis and then we can combine like terms and then isolate the variable.
Solution:
How to solve multi-step equations by combining like terms and using the distributive property?
Examples:
1. 4x + 2x - 3x = 27
2. 4a + 1 - a = 19
3. 4(y - 1) = 36
4. 16 = 2(x - 1) - x Use distributive property to simplify multi-step equations
Examples:
1. 7(w + 20) - w = 5
2. 9(x - 2) = 3x + 3
3. Lydia inherited a sum of money. She split it into five equal chunks. She invested three parts of the money in a high interest bank account which added 10% to the value. She placed the rest of her inheritance plus $500 in the stock market but lost 20% on that money. If the two accounts end up exactly the same amount of money in them, how much did she inherit?

Solving Multi-Step Equations With Fractions

To solve an equation with fractions, we first try to change it into an equation without fractions. Then, we can solve it using the methods we already know.

Consider the equation . To remove the fractions, we would need to multiply each term of the equation with the LCM of the denominator. In this case, we will multiply each term with 4. The 4 will cancel and we are left with equation 2 x - 12 = 3. To isolate the variable, we will add 12 to both sides and then divide by 2.
Example:
Solve
Solution:
How to solve multi-step equations with fractions?
Examples:
1. 1/4 x + 3 = 2
2. 1/2 (k - 8) = 6
3. 1/2 d + 2 = 3/4
4. -3/4 x + 1/4 = 1/2 How to solve Multi-Step Equations with Fractions & Decimals?
Examples:
1. 3/2 n - 6 = 22
2. 2/5 x + 2 = 3/4
3. 0.035m + 9.95 = 12.75

Solving Multi-Step Equations With Decimals

The steps involved in solving multi-step equations with decimals are the same as those in equations with whole numbers. The complication may lie more in the multiplication and division of decimals rather than the steps. Another method would be to multiply each term of the equation by ten (or hundred) to convert the decimals to whole numbers and then solve the equation.

How to solve multi-step equations with decimals?
Examples:
1. 0.4x + 9.2 = 10
2. 0.4(a + 2) = 2
3. 1.2c + 2.6c = 4.56 How to solve multiple step linear equations involving decimals?
1. Remove parentheses by using the distributive property. Then combine like terms on each side.
2. Add or subtract, as needed, to get all variable terms on one side and all constant terms on the other. Then combine like terms.
3. Multiply or divide to solve for the variable.
4. Check all possible solutions.

Examples:
Solve each equation.
1. 1.2x - 5.12 - 0.9x = 1.6
2. 5x - 0.2(x - 4.2) = 1.8

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Solving multi-step equations (solutions, examples, videos)

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In these lessons, we will learn how to Solve multi-step equations with whole numbers Solve multi-step equations with fractions Solve multi-step equations with decimals Related Topics: More Algebra Lessons The following diagram shows how to solve multi-step equations. Scroll down the page for more examples and solutions.

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Locate important details in somewhat challenging passages

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Ensure straightforward subject-verb agreement

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Interpret most words and phrases as they are used in somewhat challenging passages, including determining technical, cogitative, and figurative meanings

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The skill of determining importance in a nonfiction text is an area in which students of all ages often struggle. For emerging readers, it can require so much attention to merely get through reading a nonfiction text, that it's easy not to process what the text actually says, much less pull out the important details and overall meaning. And for older students, increasingly complex texts can be dense with information and difficult to digest. Here are four strategies for determining importance in nonfiction texts - and they're usable in any grade.

Determining importance

Determining importance is the process of determining what is important in a text and what is not. "We decide, from among everything on the page, what is most important to attend to and remember," according to The Reading Recovery Training Center at Clemson University. "As proficient readers, we engage in that process continually while reading. We filter information and organize our thinking around the big ideas. Determining importance allows us to move through a text coherently, developing a line of thinking that helps our reading make sense."

Tanny McGregor, author of Comprehension Connections: Bridges to Strategic Reading, once explained determining importance to a class by providing a memorable visual. The premise is that our brain can't possibly remember everything we read, nor should it. Our job is to keep the really important stuff we read in our mind and strain out the rest. She demonstrated this using a literal kitchen strainer full of water and spaghetti, pouring out the water to leave just the pasta. "Your brain is like the strainer and the words are like the noodles. The spaghetti water is not important, so you don't have to keep it. When you read something, it's like it's pouring in through your eyes and then it goes through your brain."

"In nonfiction, readers need to learn to determine importance by identifying a text's main idea(s). Once they do, they are better able to sort through the details to figure out which are important and which may be interesting, but less important," says Jennifer Serravallo, author of The Reading Strategies Book: Your Everything Guide to Developing Skilled Readers. "As texts become more dense and filled with information, sorting through facts and information that are important to the central idea(s), versus those that are just interesting, becomes more challenging. Sometimes students have a hard time determining importance because they believe everything is important-the author put it all in there, after all!"

Nonfiction strategy: five-sentence summaries

When reading a whole text, it's easy for students to lose focus and get lost in what they're reading. Creating five-sentence summaries can help students stay active while reading, as well as pull out and sum up the most critical information.

How to do it: Students should use a pen to number sections of the text as they read them. Summaries are written in order. They can chunk the text and pull out the important points from the beginning, a little way in, the middle, almost the end, and the end of the text. Then, they can sum up each section in one sentence, finishing with a five-sentence summary!

For young readers: For learners who aren't ready to write sentence-based summaries, the strategy can be done by drawing pictures, arranging pictures, or even participating verbally ("First, the text said this. Then, the text said this..."). Readers can also break the summary down into three parts: beginning, middle, and end.

Nonfiction strategy: noticing patterns, numbers, and facts

Teach students to pick up on patterns in a text. If a text mentions photosynthesis a bunch of times, chances are that's an important topic of the piece. Students can get into the habit of noticing and highlighting words and concepts that repeat. Additionally, teach students to notice and make note of numbers, statistics, and facts in nonfiction. See a number? Make a note! See a fact? Circle it!

How to do it: Determine a system of symbols for annotation and students can use these symbols to quickly make note of patterns, numbers/statistics, and facts they find in a text.

For young readers: Ask students to find what repeats and explore why. For example: If the text uses the word triangle a lot, it's logical that triangles are important in the text.

Strategy: Funneling topics

Once students know how to look for patterns, they can learn how to funnel down topics. This strategy teaches students to find the larger topic, the subtopics, and the supporting details in a nonfiction text.

How to do it: This can be done by simply writing notes on paper or you can provide students with a graphic organizer with an image of a funnel. Tell students to look for word patterns and clues within the title, captions, and display text. For example, a text uses the term NBA draft a lot, so it is likely that the overarching topic is basketball. Then, it's time to zoom in and look for subtopics and the supporting details in the text.

Main topic: Basketball

Subtopic 1: NBA Draft Rules

Supporting details: New salary rules will influence the NBA draft this year as they pick players.

For young readers: Teach students to pull out the big topic and then shrink it down to a detail or two. This can be done visually, in writing, verbally, or kinesthetically by using manipulatives. Gradually increase the level of detail the students look for.

Big idea: Koalas

Shrink it down: Koalas are from Australia

Shrink it down even more: Koalas only eat plants.

Strategy: Pile it on

How to do it: This idea comes from Serravallo's incredibly useful reading strategies book. Using sticky notes, readers jot down notes as they read. One sticky note per jot. After they're done, they "collect all the jots that have to do with one idea. Look across them, to pile the ideas together." This helps readers categorize what they've read, organize important topics, and pull out ideas as they're reading.

For young readers: Have students draw pictures on sticky notes, copying important words and phrases from the text or visually looking at and discussing this together as a class.

Continuing education and professional development

There are many ways to help your students - whether they are beginning their journey as readers or are independent teen readers. Continuing to advance your practice will benefit both them and you. One way to do that is by earning a MEd with a concentration in adolescent literacy or choosing a concentration that focuses on reading intervention strategies. "My MEd with a Reading Interventionist concentration helped me focus on the reading process of my students, especially my homeless students," says educator and Concordia graduate Casmore Shaw. "[My students] understand: if they can't read, they can't do the math. If they can't read, they can't understand anything about literature. If they can't read, they will not be able to progress."
Jennifer L.M. Gunn spent 10 years in newspaper and magazine publishing before moving to public education. She is a curriculum designer, a teaching coach, and high school educator in New York City. She is also co-founder of the annual EDxEDNYC Education Conference for teacher-led innovation and regularly presents at conferences on the topics of adolescent literacy, leadership, and education innovation.
Tags: Adolescent Literacy, Language Arts, Literacy, Reading Interventionist

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Help Students Determine Importance in Non-Fiction Reading Passages

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The skill of determining importance in a nonfiction text is an area in which students of all ages often struggle. For emerging readers, it can require so much attention to merely get through reading a nonfiction text, that it's easy not to process what the text actually says, much less pull out the important details and overall meaning.

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As I've discussed before, the point of skimming is not simply to read everything fast, but rather to read many things fast in order to identify the handful of places you need to slowly.

While this is generally true for the ACT, there are also some quirks particular to the Reading Comprehension section that make it necessary to approach skimming a bit differently.
1) Initial read-through
One of the particular challenges that ACT passages pose is that they can either focus primarily on a single argument and its supporting and/or contradicting evidence, or on a collection of facts and details that revolve around a particular topic. In the case of the former, you need to focus on the key places in the argument, the places where supporting and/or contradicting information is introduced.

These key places may only occur every other paragraph or even every third paragraph, but if you focus on topic sentences and keep an eye out for transitions such as therefore and for example, and punctuation such as dashes and colons (which signal explanations) you should be able to pick them out pretty easily. In case of the latter (especially Prose Fiction), you do actually need to read everything quickly in order to get a general impression of what's going on - there's just no other way to do it. As you skim, however, circle major transitions, explanations, and words like important to help you when you:
2) Go back to the passage in order to answer specific questions
Since the ACT does not usually give line numbers, Reading Comprehension can feel like some sort of twisted scavenger hunt. The trick is to identify one or two key words in the question and look only for them. If a question asks about the architectural significance of Frank Gehry's Stata Center, for (real) example, look only for the words S tata Center and ignore everything else. If you have no idea where those words could possibly be, don't just start reading random bits of the passage - chances are you'll just get lost and miss important information when it does appear. Instead, focus on reading topic sentences to figure out which paragraph is most likely to contain those words.
As your eye moves down the page, draw your index finger along with it
Establishing a physical connection with the passage helps to focus you and makes it easier to spot the words you're looking for.

Then, when you've found them, read the full sentences in which they appear, thoroughly, from beginning to end, and without skipping over anything. If you have to, put your finger on the page in order to make sure that you don't miss a single word. Pay particular attention to any major transitions you've circled in or near those sentences because there's a good chance the necessary information will be located near them. If you can't answer the question from the information in that sentence, read the sentence before AND the sentence after it. There's a good chance you'll find what you're looking for.

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How to skim ACT Reading passages effectively | The Critical Reader

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As I've discussed before, the point of skimming is not simply to read everything fast, but rather to read many things fast in order to identify the handful of places you need to slowly. While this is generally true for the ACT, there are also some quirks particular to the Reading Comprehension section that make...

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ACT Reading | 6 ESSENTIAL Tips and Strategies

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Test Packet # 5 - 8

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Test Packet # 1 - 4

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Subject Verb Agreement Rules (and Tricky Scenarios) - English Grammar Lesson

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In this article, we shall delve into the fun-filled world of subject-verb agreement on the ACT. Subject-verb agreement questions on ACT English are less common than punctuation questions; however, you can count on having at least a couple of subject-verb agreement on your ACT English section, so understanding this grammatical rule can easily help you improve your ACT English score.

While the grammar rule itself is relatively simple, the questions related to it can be challenging and a bit tricky. In this article, I'll teach you strategies and tips to become a master of all things subject-verb agreement on the ACT.

In this post, I'll do the following:

Give you a clear understanding of subject-verb agreement.

Explain why and how subject-verb agreement questions on ACT English can be tricky.

Offer general strategies that can help you correctly answer subject-verb agreement questions.

Provide you with practice questions so you can test what you've learned.

Review: Definition of a Subject

The subject of a sentence is the noun that corresponds with the verb in the sentence. In a sentence where there is an action, the subject is the noun that does the action. Doer of action=subject. Here's an example sentence:

Justin rescued a kitten from a burning building.

What is the subject? Justin. Why? Well, he is the hero who did the rescuing.

Similarly, in a sentence with a description, typically using a form of the verb "to be," the subject is the noun that is being described. See:

Justin is not funny.

Once again, "Justin" is the subject because he is the person who is not funny.

Now that we understand the concept of a subject, I'll define and explain subject-verb agreeement for you.

Explanation of Subject-Verb Agreement

Subject-verb agreement is a rule that states that all subjects must agree with their verbs in number. If a subject is singular, then you must use a singular verb. If a subject is plural, then you must use a plural verb.

On the ACT, most subject-verb agreement questions deal with verb forms in the third-person singular (he/she/it/one) and third-person plural (they). In the present and present perfect verb tenses, third-person singular verb forms end in an "s." Third-person plural verb forms do not. Look at this incorrectly written sentence in the present tense:

The reality television star read books.

This is the corrected version of the sentence:

The reality television star reads books.

While you may have intuitively known how to correct this sentence, and you could have relied on what "sounds right," you should understand why the original sentence was incorrect. The subject of the sentence is "the reality television star." She is the person who does the reading. Furthermore, since we're referring to one reality star, the subject is singular. Because our subject is singular, the verb needs to be in the singular form. In the present tense, "read" is plural. Therefore, we need to change the verb to the singular form "reads."

Let's look at another example with a plural subject. This is our incorrect sentence:

The singers performs bad cover songs.

How do we correct the sentence? Like this:

The singers perform bad cover songs.

The subject is "singers" because they are doing the performing. "Singers" is plural, so the verb should be in the plural form. The plural form of the verb is "perform."

This rule may seem rather simple; however, of course, the ACT doesn't want to make life too simple for you. Subject-verb agreement questions on the ACT can be challenging. The sentences will be more complex than the ones above, and the subject-verb agreement errors will not be as obvious.

How Are These Questions Challenging?

Typically, when you encounter subject-verb agreement questions on the ACT, the subject will not be placed directly in front of the verb. The subject will either be separated from the verb by an interrupting phrase or, in rare cases, the sentence will be inverted and the subject will follow the verb. Here are ACT English tips you can use to identify the traps students fall for.

Trap #1: Interrupting Phrases

Interrupting phrases are phrases that separate the subject from the verb. These phrases make identifying the subject and determining whether the verb should be singular or plural more challenging. We'll take a look at a couple of types of interrupting phrases. You don't need to know all of the specific grammar terms, but you should understand and recognize the effect they have on subject-verb agreement questions.

Prepositional Phrases

The most common interrupting phrase that appears on the ACT is the prepositional phrase. Simply, a prepositional phrase is a phrase that begins with a preposition. What are prepositions? Prepositions provide additional details about nouns and often answer the questions "Where?", "When?", or provide descriptive information. Take a look at some examples of commonly used prepositions:

http://study.com/academy/lesson/what-is-a-preposition-definition-uses-exa mples.html

On the ACT, prepositional phrases tend to be inserted between subjects and verbs to distract from errors in subject-verb agreement. Here's an example of an incorrectly written sentence using a prepositional phrase as an interrupting phrase:

Changes for the new and improved ACT Writing section is going to be implemented soon.

First, let's identify the subject. What is going to be implemented? Changes. The phrase "for the new and improved ACT Writing section" is a prepositional phrase that begins with the preposition "for." The prepositional phrase describes the changes that will be implemented. See how the ACT can trick you by putting a singular noun, "section," right before the verb.

However, because "changes" is plural, the verb should be in the plural form. Unfortunately, "is" is singular. Here's how the sentence should look:

Changes for the new and improved ACT Writing section are going to be implemented soon.

So how do you avoid falling for this common ACT trap?

Strategy

Cross out the prepositonal phrase and the sentence should still be grammatically correct. Additionally, using this strategy will enable you to more easily identify the subject and determine whether there's an error in subject-verb agreement. Always remember that the subject will never be contained within a prepositional phrase. Let's employ this strategy with the incorrectly written sentence above:

Changes for the new and improved ACT Writing section is going to be implemented soon.

Now that the subject is right in front of the verb, the subject-verb agreement error is much more obvious. The strategy involves three steps:

1. Cross out the prepositional phrase.

2. Identify the subject.

3. Determine if there's an error in subject-verb agreement.

Use this strategy and you'll be much less likely to miss a subject-verb agreement question on the ACT. You're welcome.

Actual ACT English Example Question

Let's use this strategy with an example taken from an actual ACT:

First, let's cross out the prepositional phrase. Equipment for both types of kayaks are similar. We're left with "Equipment are similar." Even if the answer is obvious to you at this point, let's go through the remaining steps. The subject is "equipment," which is singular. The verb is "are," which is plural; therefore, there's an error in subject-verb agreement and the correct answer is G. Based on the context of the passage, the verb should be in the present tense.

The other types of interrupting phrases on the ACT serve the same function as the prepositional phrase in subject-verb agreement questions. They separate the subject from the verb. Let's take a look at another common type of interrupting phrase on the ACT.

Non-Essential Clauses and Appositives

Non-essential clauses describe a noun, often the subject of a sentence. They are surrounded by commas and can be removed without creating grammatical errors or changes in the meaning of a sentence. Here's a sentence with the non-essential clause in bold:

My sister, who is very social, was elected class president.

The non-essential clause is separated by commas and serves to provide descriptive information about my sister. Removing the clause doesn't result in a grammatical error or change in the meaning of the sentence. Check it out:

My sister, who is very social, was elected class president.

One additional note about non-essential clauses is that a subject-verb agreement error can be contained within the clause itself. Take this sentence, for example:

Carbonated beverages, which is delicious, are not good for your health.

The verb in the non-essential clause, "is," corresponds with the subject "carbonated beverages." Because the subject is plural, the verb should be in the plural form as well. The sentence should read:

Carbonated beverages, which are delicious, are not good for your health.

While a non-essential clause usually starts with a relative pronoun (which, who, whose, or where), it doesn't in a phrase known as an appositive. An appositive serves the same purpose as a non-essential clause, but an appositive doesn't contain a verb. Here's a sentence with the appositive in bold:

My sister, a very social person, was elected class president.

The appositive provides descriptive information about my sister, but the phrase can be removed without changing the meaning of the sentence or creating a grammatical error.

How will knowing about these phrases help you answer subject-verb agreement questions on the ACT? Read below to find out.

Non-Essential Clauses and Appositives on the ACT

Just like prepositional phrases, non-essential clauses and appositives will be placed between subjects and verbs to make it less clear if there's an error in subject-verb agreement. Here's a sentence with a non-essential clause. I've underlined the subject and bolded the verb:

My boss, who is extremely kind to his employees, give helpful advice.

The non-essential clause separates the subject from the verb. The subject is "boss," which is singular, and the verb is "give," which is plural. There's an obvious error in subject-agreement. The sentence should read:

My boss, who is extremely kind to his employees, gives helpful advice.

On the ACT, you may encounter a similar sentence. Many students will incorrectly assume that the subject is "employees" because that is the noun closest to the verb. While "employees" is plural, the actual subject "boss" is singular. By correctly identifying the subject, you can avoid being tricked by the interrupting phrase.

The method you should you use to avoid being tricked is the same one I taught you for prepositional phrases.

Strategy

In sentences with non-essential clauses or appositives, always cross out those phrases. Doing so makes it much easier to identify errors in subject-verb agreement. Let's use this strategy with the incorrectly written exmple sentence from above:

My boss, who is extremely kind to his employees, give helpful advice.

After we cross out the non-essential clause, we're left with "My boss give helpful advice." The singular subject is right next to the plural verb. The error in subject-verb agreement should be obvious. Nice!

Actual ACT English Example Question

Let's put our knowledge to use. Here's another example from a real ACT:

In this example, the non-essential clause is surrounded by dashes, which serve the same function as commas in this sentence. The ACT folks threw in that extra curve ball because they also really like testing your knowledge of punctuation. If we cross out the prepositional phrase "of letters" and the non-essential clause, we're left with "Dickinson's last twenty years reveals." The subject is "years," which is plural, so the verb should be in the plural form. The answer is B.

Let's briefly discuss one last type of interrupting phrase you may encounter on the ACT.

Essential Clauses with "That"

Occasionally, an error in subject-verb agreement will involve a clause beginning with "that." The clause will end right before the verb. For sentences with these clauses, simply use the same strategy we used with non-essential clauses. Take a look at this sentence:

A book that has an interesting plot and well-developed characters are fun to read.

The essential clause begins with "that" and ends right before the verb "are." Just like we did with non-essential clauses, let's cross out the clause. We're left with "A book are fun to read." The singular subject is now right next to the plural verb. Here's the corrected version of the sentence:

A book that has an interesting plot and well-developed characters is fun to read.

There's another tactic the ACT uses, though much less common, to complicate basic subject-verb agreement questions.

Trap #2: Sometimes the Subject Comes After the Verb

In rare instances, the typical word order of a sentence will be altered so that a prepositional phrase appears at the beginning of a sentence and the subject follows the verb. In these instances, it can be particularly challenging to identify the subject and determine if there's an error in subject-verb agreeement. In order to illustrate this point, let's look at an example sentence with the prepositional phrase underlined and the verb in bold:

In the trunk of my car resides fifteen empty water bottles.

We know that a subject can't be contained within a prepositional phrase. Also, we know that a subject is the noun that's doing the action. In the sentence, what's residing? The water bottles. The prepositional phrase provides information about where the water bottles are residing. Because the subject is "water bottles," the verb should be in the plural form. This is the correct version of the sentence:

In the trunk of my car reside fifteen empty water bottles.

The correctly written sentence may sound more awkward to you because the singular noun "car" is placed right next to the plural form of a verb. You should focus on the rules and strategies as opposed to just relying on what "sounds right."

In extremely rare situations, the subject follows the verb but is not preceded by a prepositional phrase. Check out this sentence:

Skipping school is fun, but less fun is its consequences.

In this sentence, what is less fun? The "consequences". Therefore, in the second clause, "consequences" is the subject. The verb "is" corresponds with the subject "consequences." Because we have a plural subject and a singular verb, there's an error in subject-verb agreement. This is the corrected version of the sentence:

Skipping school is fun, but less fun are its consequences.

Is there a way to simplify these types of sentences to help determine if there's an error in subject-verb agreement? Of course.

Strategy

In sentences in which the subject follows the verb, rearrange the sentence so that it follows the normal structure of subject then verb. Using this strategy will allow you to more easily spot any errors in subject-verb agreement.

If you utilize this method in the incorrectly written sentence above, you'd be left with "its consequences is less fun." The plural subject is now right next to the singular verb and the error should be immediately apparent.

Now, we'll cover one more unique situation that can complicate the most basic subject-verb agreement questions.

Trap #3: Compound Subjects

A compound subject is a subject in which two singular nouns are connected by "and." In a sentence with a compound subject, you should use the plural form of the verb. Here's a basic sentence demonstrating this rule:

Justin and the ACT are friends.

Because the subject is both "Justin" and the "ACT," the verb should be in the plural form.

This is a more complicated example in which a prepositional phrase is also placed at the beginning of the sentence:

In between the cushions of my couch is change and an old pen.

First, let's rearrange the sentence so that the subject comes before the verb. What's in between the cushions? Change and an old pen. So after doing our rearranging, the sentence should read "Change and an old pen is in between the cushions of my couch." The subject is both change and an old pen; therefore, the verb should be in the plural form. This is the corrected sentence:

In between the cushions of my couch are change and an old pen.

At this point, we're aware of the ways the ACT complicates basic subject-verb agreement questions. We've also learned specific strategies to use when faced with certain types of situations. Here are some general tips to follow to help you correctly answer any subject-verb agreement question you may encounter on the ACT.

General Strategies for ACT Subject-Verb Agreement

Look for Errors in Subject-Verb Agreement When a Verb Is Underlined

If a verb is underlined, make sure there are no errors in subject-verb agreement.

Singular and Plural Forms of the Same Verb in the Answer Choices Signal a Possible Error in Subject-Verb Agreement

On the ACT, you can often figure out what's being tested based on the underlined phrase and the answer choices. If you see that there are singular and plural forms of the same verb in the answer choices, determine if there's an error in subject-verb agreement.

Always Identify the Subject

Both subjects of sentences and subjects of clauses must agree with their verbs. For each underlined verb, find the noun that corresponds with that specific verb. Then, determine whether that subject is singular or plural and make sure that the subject and verb agree.

The Subject Is Never Part of a Prepositional Phrase

Be aware that a subject will not be part of a prepositional phrase. Most subject-verb agreement questions on the ACT separate a subject from a verb with a prepositional phrase. Remember the strategy of crossing out the phrase to aid in answering these questions.

Be Able to Recognize the Common Tricks

Knowing the common tricks the ACT English section uses on questions that test your knowledge of subject-verb agreement can be helpful. The better you know these tricks, the more quickly you'll be able to recognize them and use the appropriate strategies to correctly answer subject-verb agreement questions.

Additional Practice

Hopefully, by this point you thoroughly understand subject-verb agreement and how to correctly answer any subject-verb agreement question that may appear on the ACT. I've created some realistic ACT English practice problems to test you on what you've learned. Remember to use the general strategies I referenced above.

1. Beautifully written sentences composed by the prolific and talented author has been integral to his success.

2. The size and style of the dress is not to my liking.

3. The selfish man, who owns five cars and two houses, has been unwilling to give any money to charity.

4. Mastery of grammar rules are essential to doing well on ACT English.

5. Swimming pools that are above ground are often mocked by snobs.

Answers: 1. B., 2. D, 3. A, 4. C, 5. A

What's Next?

Now that you're comfortable with subject-verb agreement on the ACT, familiarize yourself with everything that's actually tested on ACT English. You'll probably want to read this article about commas, too.

For those overachievers out there, find out how to get a perfect score on ACT English from a perfect scorer.

Want to improve your ACT score by 4 points?
Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more.

Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this English lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next.
Check out our 5-day free trial:

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Subject-Verb Agreement for ACT English: Tips and Practice

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In this article, we shall delve into the fun-filled world of subject-verb agreement on the ACT. Subject-verb agreement questions on ACT English are less common than punctuation questions; however, you can count on having at least a couple of subject-verb agreement on your ACT English section, so understanding this grammatical rule can easily help you improve your ACT English score.

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ACT Subject Verb Agreement  - This Comes Up a Lot!

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Want to quickly improve your ACT Reading score? The keys to the ACT Reading test are strategy and pacing. You'll need to have a plan for HOW you will read each passage, tackle the questions, and finish in the allotted time; otherwise it'll be hard to achieve your desired score. For example, you'll want to focus on the author's point of view, mark up the passage as you go, and spend no more than 3 minutes per passage on an initial read (9 minutes on a passage and its questions).

Ready for some more specific tips for ACT Reading success? Let's get to it.

1. Find the author's point of view as you read

Do you find yourself getting lost in the details, or reading too quickly and missing some of the important information? For the ACT Reading Test, you've got to strike a balance between reading for the author's point of view and for the function of each paragraph, while also noting the location of important details in case you need to come back later. How do you do all of this at the same time?

2. Make sure you underline anything that seems significant to you

Look for words and phrases that reveal the author's opinion, or give the main idea of each paragraph. The test booklet is basically one large piece of scratch paper, so it doesn't matter if you write all over it. In fact, it's better if you do! Underline, circle, write 3-5 word summaries of each paragraph...whatever works for you. Just don't get so carried away with the note taking that you run out of time...

3. Time yourself as you practice

If you are spending more than 3 minutes reading and marking passages, you are risking not being able to finish all of the questions on test day. As you become more and more confident with your accuracy, try to get as precise as possible with the timing of your note taking.

4. Do at least ten ACT Reading practice tests

Full-length practice tests are available in ACT practice books at local bookstores, at your local library, and are even downloadable online. Find a quiet place where you can take the practice ACT, and clear off the table or desk. Try and eliminate any distractions and do the best you can to mimic your test-day environment. Keep a clock or timer in front of you so you can periodically check and see how you are doing. You may want to set the timer to go off every 9-10 minutes. Don't rush, but make sure you can move confidently from one passage to the next and answer ALL questions in the time allotted.

5. For Vocabulary in Context questions, go back to the passage

A commonly used vocab word often takes on a secondary definition within ACT passages. Do not assume that the common meaning is the correct answer; there may be several meanings you do not know. Go back to the passage and see how the word is being used in context.

6. Always pre-phrase an answer

Before you look at the answer choices, use the passage to predict your own answer. Then match your prediction to the answer choices. This will save you time. Don't get stuck weighing answer choices. Cross out all answer choices that don't match your prediction, pick the best available answer, and move on!

7. Dumb down complicated questions

If you read a question and it is confusing or unclear to you, rephrase it in simpler terms. Think of it as though you were going to explain the question to a small child. What is it really asking?

8. After 9 minutes, move on to the next passage

The ACT Reading Test is 35 minutes long and contains 40 questions (10 questions oin each passage). This means you'll have slightly less than 9 minutes to spend on each of the 4 passages, so pacing yourself is essential.

9. Do the passages in any order

You will always see 4 passages and you must always answer all 40 questions (even if you just guess - the ACT does not penalize you for wrong answers!) But that doesn't mean you have to approach the passages in the order in which they are presented on the test. As you practice, you will start to realize which passages are easier and which are more challenging for you. For example, if Prose Fiction is your strong point but Natural Science passages make you nervous, it may make sense for you to do the Prose Fiction passage first and save the Natural Science passage for last. Just make sure you're bubbling in the write question number on your answer sheet...

10. Bubble your answer carefully

If you do decide to skip around, make sure you are still bubbling your answers into the corresponding numbers on the answer grid. You don't want to lose points because you bubbled incorrectly!

In need of more tips? Check out the video below!

Want to learn more about how to improve your ACT reading score? Check out Magoosh test prep!

Happy studying!

About Rita Neumann

Rita creates fun, inspiring, and educational resources that introduce students to Magoosh and help them prep for their exams. She earned both her BA and Master of Pacific International Affairs from UC San Diego, where she also studied Spanish, French, and Portuguese. Rita loves education and marketing, just as much as she loves vinyasa yoga and baking chocolate chip cookies.

Magoosh blog comment policy: To create the best experience for our readers, we will approve and respond to comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! :) If your comment was not approved, it likely did not adhere to these guidelines. If you are a Premium Magoosh student and would like more personalized service, you can use the Help tab on the Magoosh dashboard. Thanks!

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Ten Tips to Quickly Improve Your ACT Reading Score

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Want to quickly improve your ACT Reading score? The keys to the ACT Reading test are strategy and pacing. You'll need to have a plan for HOW you will read each passage, tackle the questions, and finish in the allotted time; otherwise it'll be hard to achieve your desired score.

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Test Packet # 9-12, 24

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ACT Practice Test - Free ACT Exam | 4Tests.com

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Take a free, ACT Practice Test exam now. This is a practice exam will help you prepare for the brand new ACT exam. 100% free and no registration required.

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What exactly are vocab in context questions, and what are the best ways to approach answering them? In this article, I'll start by going over the basics of what vocab in context questions are, then segue into an in-depth discussion of each of the two types (complete with examples). Finally, I'll wrap it up by suggesting strategies to use when tackling these types of questions.

feature image credit: 7dc_b188407-zuleikha-reading by Wolfgang Lonien used under CC BY-SA 2.0/Cropped from original.

What Are Vocab In Context Questions?

Vocabulary in context questions are the questions on ACT Reading that question you directly about vocabulary in the context of a paragraph. While having vocab knowledge can help you with other types of questions, for the purposes of this article I've focused on the types of questions where knowing vocabulary is essential to being able to get the right answer.

From my reviewing of dozens of official ACT practice tests, I've come to the conclusion that there are two types of ways the ACT Reading will question you on vocabulary:

1. Based on how the word is used in the passage, what does that word mean?

2. How would you sum up the meaning of a few lines or a paragraph, using one word as your answer?

Read on for a more in-depth look at each of these types of vocab in context questions.

Question Type 1: What's The Meaning Of The Word In Context?

These questions are probably among the most straightforward of all the ACT Reading questions. I like to think of them as asking "Here's the word - what's the definition?"

Just because the questions are straightforward doesn't mean that they can't be tricky, but the way the questions are phrased themselves are pretty simple. In fact, they are almost always asked in the following way:

As it is used in line [number], the word [X] most nearly means...

Or, to give a concrete example:

As it is used in line 42, the word howled most nearly means...

Why does the ACT always use the phrase "most nearly," rather than just straight up asking "what does this word mean?" I believe there are two reasons:

1. the phrase is designed to trick you into picking an answer that kind of works (after all, howled only has to NEARLY mean the answer choice, right?)

2. it's the ACT's way of covering its butt (nope, you can't just pick AN answer that works, you have to pick the BEST answer out of the available choices).

Most often, these "Here's the word, what's the definition?" questions are about words that have multiple meanings. Since the ACT wants to trick you into rushing into thinking you know the answer, the test often will include an answer choice that is accurate for SOME definition of the word, just not the way it's used in the passage. Here's an example, taken verbatim from an official ACT practice test.

Off the top of my head, the word read can be used to mean any of the answers, with the possible exception of choice C. In order to figure out which way read is being used in line 45, you'll have to go back to the passage. The source sentence is as follows:

"Scientists determine an eel's age using a microscope to read the growth rings of its otolith - a small, hard calcium deposit at the base of its skull." (lines 44-47; italics mine)

So how would you solve this question? First, rephrase the word or phrase in question to make answering the question easier: "Scientists figure out how old an eel is using a microscope to look at and decipher the growth rings on the thing." As you can see, the rephrasing does not have to be super elegant, just accurate.

Next, substitute answers into your rephrased sentence - for this question, only "observe" makes sense (Scientists figure out how old an eel is using a microscope to observe the growth rings on the thing).

Want another example? Not a problem! Here's a trickier example I've modified from an ACTual ACT (I could only hold out on that wordplay for so long).

Practice Example A:
"The lycanthropic virus story is really nailed down," says Giles. "The epicenters that have been mapped over thousands of years are likely the spots where werewolves are concentrated."

As it is used in this line, concentrated most nearly means...

(A) extracted

(B) paid attention to

(C) gathered together

(D) directed to one topic

If you replaced the word "concentrated" with any of the answer choices, it COULD make thematic sense. After all, werewolves could be extracted from a place, or be paid attention to (although it seems unlikely that the ACT would have you pick an answer choice that means ending a sentence with a preposition). Also, doesn't "concentrated" sometimes have something to do with things being directed to one topic?

Danger! Danger! This is all part of the ACT's Cunning Plan™ (NB: not actually trademarked) to trap you!

It's a trap by Mike Knell, used under CC BY-SA 2.0/Cropped from original.
Do NOT answer the question based on things that "could be right," depending on information you do not know.
Imagine you're a cranky English teacher, grading student interpretations of a book read for class. You're not a generous teacher who's looking for reason to give a student points any way you can because she argued the point. No, you're looking for reasons to mark answers as WRONG.

Take that mindset into the ACT Reading with you: Only the answer that is directly supported by the context of the passage is acceptable. In the case of example A above, the answer is (C) gathered together: the centers of the lycanthropic virus infection are likely the spots where werewolves are gathered together.

None of the answer choices come even close to fitting into context of this sentence.

On occasion, rather than asking about specific words, ACT Reading will instead ask about multiple words, making the question more like "Here's the phrase, what's the meaning?" See example B:

Example taken from ACT website.

In either case, these questions should be approached in the same way: always, always go back to the line in which the word or phrase appears - don't let the ACT fool you into answering without checking!

Question Type 2: What Word Is Defined By The Passage?

These questions ask you to recognize the definition in the passage and relate it to the answer choice that matches it. In contrast to the previous question type of vocab-in-context questions, I think of these as asking "Here's the definition, what's the word?"

The ACT has more varied ways of asking these questions than the "here's the word, what's the meaning?" questions. I've listed below just a few examples that I came across in my reviewing of ACT practice tests. Disclaimer: I have edited the questions so that they all refer to the same subject matter; these are not how the questions appeared on the actual ACT.

Sample "Here's the definition, what's the word?" questions:

Which of the following words best describes the narrator's father working as he prepares for the full moon?

Which of the following best describes how the victim referred to in the fifth paragraph (lines 58-71) is said to have started to transform into a werewolf?

Lines 42-53 suggest that, prior to W. Rosenberg's research, medical researchers had thought of the werewolf as...

Answer to the last question: Apparently as round, yellow, and half-wolf, half...duck in a shirt?
"What word is defined by the passage?" questions can actually be easier than the "here's the word, what's the definition?" questions. Why? Because since the definitions are in paragraph form, you may be able to gather more information to help answer the question. Here's another actual ACT sample question:

If you know the definition of the word "discernment," you have an easy shortcut to the answer: "The problem with reevaluating and devaluing men poets is that it's difficult to be sure you have good judgment when you're doing it. How SHOULD you do it? With caution, or by being cautious."

Even if you don't know exactly what discernment means, however, the author goes on to explain further in the rest of the paragraph: "The author thinks that taking men poets down a peg too immediately, or quickly, is a problem...that means that people who do it should be cautious."

Using that clue, you could solve the question, even if you didn't know what "discernment" meant.

Strategies To Master Vocabulary In Context Questions

So what strategies can you use to master these two types of ACT Reading questions? I've put together a 3-step strategy guide below.

Strategy 1: Rephrase the information given

For questions that ask about words in context, define the word first in your head (or on scrap paper, whichever is easier) in the context of the sentence or paragraph, without looking at the answer choices. Remember, your rephrasing does not have to be elegant as long as it conveys the meaning. For instance, take a look at example C:

"She thinks I have a power that she doesn't have and this brings out her envy and bad humor."

In this line, humor most nearly means...

My thought process: Let me replace the word with one that keeps the meaning of the sentence. "She thinks I have a power that she doesn't have and this brings out her envy and bad state of mind." Okay, that makes sense and is what the original passage said.

For questions that ask you to take a paragraph and choose the best answer that describes it, answer the question in your own words before looking at the answer choices. See example D:

My thought process: Question is asking about what researchers thought about the brain. Okay, what does the paragraph say? We need a "new view of the brain" that includes the idea that the brain is "dynamic", "active", and "adaptive," NOT "programmed and static." So medical researchers used to think the brain didn't change, but now they think it does. Okay, got it, now what're my answer choices?

Strategy 2: Cross out answers that clearly don't fit

Sometimes, you can get to the right answer just by knowing what the wrong answers are. This is an especially useful strategy if there's an answer choice with a word that you don't know the meaning of. If you know that the other three answers are definitely wrong, it doesn't matter that you don't know what the meaning of the fourth answer is; by process of elimination, it must the correct choice. Let's take a look at this strategy in the context of example C, from before:

My thought process: Choices are personality, whim, mood, and comedy. I rephrased the sentence as "She thinks I have a power that she doesn't have and this brings out her envy and bad state of mind." Which choice is closest to "state of mind?" Personality: not really. Whim: No. Mood: yes. Comedy: no. The answer must be C. mood.

This strategy still works if you are trying to sum up the meaning of a paragraph in one word. I'll copy and paste example D again, so you don't have to scroll back up:

My thought process: The choices are dynamic, unchanging, paradoxical, or creative. My rephrasing of the paragraph was that medical researchers used to think the brain didn't change, but now they think it does. Which of the choices are closest to meaning "didn't change" or "not changing"? Well, unchanging, obviously. What about the others? Dynamic is what they say the NEW view should be, so no. Paradoxical: there's nothing about that in the text. Creative: nothing about that in the text. Answer must be B. unchanging.

Strategy 3: (Optional) Plug the definition back in

This strategy works best for the "here's the word, what's the meaning?" questions, because word-for-word substitutions are a lot simpler than word-to-sum-up-entire-paragraphs-of-information substitutions. Let's take one more look at example C, a "here's the word, what's the meaning?" question:

"She thinks I have a power that she doesn't have and this brings out her envy and bad humor."

In this line, humor most nearly means...

My thought process: "She thinks I have a power that she doesn't have and this brings out her envy and bad mood." Yeah, that seems right. But I'll double check:

"She thinks I have a power that she doesn't have and this brings out her envy and bad personality." That doesn't really make sense - why would your personality need to be brought out? No. Especially when "mood" works better in this sentence.

Get Plugged In by Rennett Stowe, used under CC BY 2.0.

Whew. Where Do I Go From Here?

Are these strategies fine in theory, but you always run out of time on real ACT Reading sections? Discover how to avoid that terrible fate here.

Want more in depth guides like this? Read our other guides on Big Picture, Detail, Function, and Inference ACT Reading questions, as well as our deep dive into ACT Reading paired passages. And subscribe to this blog on the upper right.

What are the other types of questions you'll find on the ACT, and what's the best way to read the passage to answer them? We have strategies for reading passages effectively.

Want a breakdown of all the skills you'll need to excel on the ACT Reading? Read about what's actually tested on ACT Reading.

Want to improve your ACT score by 4 points?
Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more.

Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Reading lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next.
Check out our 5-day free trial:

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Vocab In Context Questions and Strategies for ACT Reading

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What exactly are vocab in context questions, and what are the best ways to approach answering them? In this article, I'll start by going over the basics of what vocab in context questions are, then segue into an in-depth discussion of each of the two types (complete with examples).

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Detail Questions

Detail questions on the ACT ask you about a specific word, line or detail in the passage. They don't talk about the passage as a whole.

That makes them good questions to tackle first, because you don't need to understand the entire passage to hit the detail questions effectively. You can use these questions to score points while you're getting a sense for the passage, which saves you precious minutes of reading time.

That doesn't mean detail questions are easy, though. In fact, they can be quite difficult, especially because the answer choices are often designed to trick you. In this lesson, you'll learn a method that you can repeat on all detail or word meaning questions to help you avoid tricky answer choices and answer the questions as efficiently as possible. Then we'll walk through a real practice question using the steps so you can see how they work in action.

Step-by-Step

To answer questions about details or specific words on the ACT, here's a 3-step plan of attack:

1. Read the question. Read it slowly, at a speaking pace, so that you really understand what it's asking. Don't read the answer choices; only read the question. Cover the answers with your hand if you have to.

2. Go straight to the passage, and answer in your own words. Again, don't read the answer choices! Find the part of the passage that the question is referring to and read enough to get a little context. Then come up with an answer to the question in your own words, without so much as a peep at the answer choices.

3. Pick the answer choice that matches your answer. Now you finally get to look at your answer choice options. Pick the one that corresponds most closely to the answer you came up with.

Example Question

To help you put this into practice, next we'll look at an example question and go through it using the 3-step process.

Step one is to read the question but not the answer choices. In this example, our question is: 'In the context of the passage, mentioning the 'dehydrated meals and signal flares' serves to characterize Smith as...'

So, we're trying to find out what the 'dehydrated meals and signal flares' say about Smith.

Now we'll move on to step two, finding the relevant part of the passage and answering the question without looking at the answers. Here's the passage:

'Smith once brought a full survival kit complete with dehydrated meals and signal flares to a barbecue party in the park. He kept cold-weather emergency go bags in his car year-round, even in August when the heat was smothering and everyone broke a sweat walking outside for the newspaper.'

Reading this excerpt, what do you think the dehydrated meals and signal flares say about Smith? What kind of person does he sound like?

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act reading: detail and word meaning questions - video & lesson transcript | study.com

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ACT Reading: Detail and Word Meaning Questions - Video & Lesson Transcript | Study.com

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Detail questions on the ACT ask you about a specific word, line or detail in the passage. They don't talk about the passage as a whole. That makes them good questions to tackle first, because you don't need to understand the entire passage to hit the detail questions effectively.

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Finding the Slope of a Line from the Equation 1 | Coolmath.com

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This is going to be a lot like what we just did at the end of the last section. So far, I've shown you how to find the slope from the graph and when you have two points... But, what if you just have the equation?

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Now we mixed up things a little bit more: on the left side of the scale, not only do we have these identical unknown masses with mass X, these three blue things, we also have some of the 1kg masses over here, actually, we have two of them. Now, we are going to figure out what X is. But before we even do that, I want you to think about a mathematical equation that can represent what is going on; that equates what we have on the left hand, with what we have on the right side of the scale. I will give you a few seconds to think about it... So let's think about what we have on the left side: we have 3 masses with mass X, so you can say we have 3x and then we have 2 masses of 1 kilogram, so in total we have 2 kg. So + 2. So one way to think about the total mass on the left-hand side is 3x + 2. Three masses with mass X, plus two kilograms. That is what we have on the left-hand side. Now, let us think about what we have on the right-hand side. We can simply count them: [counts to 14] Fourteen blocks, each has a mass of 1 kg, so the total mass will be 14 kg. And we see that the scale is balanced, not tilting down or upwards. So this mass over here must be equal to this total mass. The scale is balanced, so we can write an 'equal'-sign. (let me do that in a white coulour, I do not like that brown) Now, what I want you to think about, and you can think about it either through the symbols or through the scales, is: how would you go about -- let us think about a few things: how would you first go about at least getting rid of these little 1kg blocks? I will give you a second to think about that... Well, the simplest thing is: you can take these 1kg blocks off of the left-hand side, but remember, if you just took these blocks off of the left-hand side, and it was balanced before, now the left-hand side will be lighter and it will move up. But we want to keep it balanced so we can keep saying 'equal'. That this mass is equal to that mass. So, if we remove 2 block from the left-hand side, we need to remove 2 from the right-hand side. So, we can remove two there, and then we can remove two over there. Mathematically, what we are doing is: we are subtracting 2 kilograms from each side. We are subtracting 2 from this side, So on the left-hand side we now have 3x + 2, minus 2 we are left with just 3x, and on the right-hand side we had 14 and we took away 2 (let me write this:) we took away 2, so we are going to be left with 12 blocks. And you see that there, the ones that I have not crossed out, there are 12 left, and here you have 3 of those X-blocks. Since we removed the same amount from both sides, our scale is still balanced. And our equation: 3x is now equal to 12. Now, this turns into a problem very similar to what we saw in the last video, so now I ask you: what can we do to isolate one x, to only have one 'X' on the left-hand side of the scale, while keeping the scale balanced? The easiest way to think about it is: If I want one X on this left-hand side, that is a third of the total X's here. So what if I were to multiply the left-hand side by one-third -- -- but if I want to keep the scale balanced, I have to multiply the right-hand side by one-third. If we can do that mathematically, Over here I can multiply the left-hand side by 1/3, and if I want to keep my scale balanced I also have to multiply the right-hand side by 1/3. Multiplying it physically literally means: just keeping a third of what we had originally We would get rid of two of these. If we want to keep a third of what we had here originally, -- there are 12 blocks left over after removing those first two -- so, 1/3 of 12: we are only going to have four of these little 1kg boxes left. Let me remove all but four. (so, remove those, and those...) And I have left [counts them] 4 here. And so, what you are left with, the only thing you have left, is this 'X' - I will shade it in to show this is the one we actually have left - and then we have these 1 kilogram boxes. You see it mathematically over here: 1/3 * 3x -- or you could have said 3x divided by 3 -- either way, that gives us -- these threes cancel out, so that would give you an 'X' and on the right-hand side: 12 * 1/3 - which is the same as 12/3, is equal to 4. And, since we did the same thing to both sides, the scale is still balanced. So you see that the mass of this thing must be the same as the mass of these 4 left-over blocks. x must be equal to 4 kilograms.

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Intro to two-step equations | Algebra (video) | Khan Academy

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Now we mixed up things a little bit more: on the left side of the scale, not only do we have these identical unknown masses with mass X, these three blue things, we also have some of the 1kg masses over here, actually, we have two of them.

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Equations and Inequalities - Two-step equations and inequalities - First Glance

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To view, open in new window

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To view, open in new window

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This is the practice packet provided by LOSFA.  It is modeled after the pre and post test questions, so it should be the primary focus for sample questions.

The sample questions listed for each standard are from this packet.

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Coordinate Graph
x and y axis
origin
plot a point
slope (basic understanding including visually determining if positive or negative.)

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Slope Intercept Form (they may have had this for one year, so not mastered)
*What is it?
*Find slope
*Find y
intercept
*Graph
*Rearrange an      equation into
slope
intercept form
Standard Form (most likely first introduction to this for most)
More complex steps to transform into slope intercept form OR test points starting with (ex) x = 0 to find out y.  Either way, an easier option to at least begin with is listing possible answers (a, b, c) and show them how to place the answer in the equation to see if it makes a true statement.

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Numbers squared
Square Root

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Cube roots (might have had this skill before)

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Variables
One step equations

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Two Step Equation
You could first show them how to find the correct answer via plug a possible answer (from multiple choice)

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This padlet is an OPTIONAL set of resources to aid during ACT Prep time at the summer camps.

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Finding the subject and verb of a sentence.
Simple S/V agreement
Prepositions
Prepositional phrases

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More complex s/v agreement sentences including those with collective nouns and those with a prepositional phrase between the actual subject and verb for the sentence.