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April 2024’s New Teacher Tools

It’s April and there’s no fooling anyone: spring is in full bloom! We are in the homestretch of the school year and are getting ready to finish up our courses and begin reviewing for end-of-year assessments. We still have some new materials to make teaching easier for teachers, so let’s get at them in our latest blog post:

• Unit 10 (Solids) – Practice with the Volume of Right Rectangular Prisms. This is a nice set of problems that gives students a lot of practice calculating volumes, especially of prisms that have sides with fractional lengths.
• Unit 11 (Statistics) – Mid-Unit Quiz – Form B.
• Unit 11 (Statistics) – Practice Creating Histograms. In this worksheet, students summarize data sets visually using histograms. In some problems, students decide if the x-axis needs and axis break and an appropriate scale for the x-axis.
• Spanish Language Versions of the Unit 11 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 10 (Geometric Measurement)Mid-Unit Quiz – Form B.
• Unit 10 (Geometric Measurement) – Practice with Volumes of Prisms. This worksheet gives students practice with calculating the volumes of right prisms. Bases have shapes of both parallelograms and right triangles.
• Spanish Language Versions of the Unit 10 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 10 (Scientific Notation) – Mid-Unit Quiz – Form B.
• Unit 10 (Scientific Notation) – Practice with Applying Scientific Notation. This is a wonderful worksheet full of problems that ask students to use scientific notation in real-world situations. Examples include the number of people worldwide that have green eyes and the unit rate of donuts consumed in the United States.
• Unit 11 (Systems of Equations)Mid-Unit Quiz – Form B.
• Spanish Language Versions of the Unit 10 and Unit 11 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 10 (Functions and Their Transformations) – Unit Assessment – Form B.
• Unit 10 (Functions and Their Transformations) – Mid-Unit Quiz – Form A.
• Unit 9 (Circle Geometry) – Unit Assessment – Form A.
• Unit 9 (Circle Geometry) – Exit Tickets
• Unit 9 (Circle Geometry) Tangent Circles Exploration. In this exploration, students see how for every triangle, there are three mutually tangent circles that can be constructed. This activity not only illustrates another remarkable connection between triangles and circles, but also reinforces the construction of the incircle for any triangle.
• Unit 12 (Probability) – Practice with Adding Probabilities. This worksheet gives students a plethora of problems to reinforce how probabilities add in “or” probability/counting scenarios. Through various applied problems, students solve for all parts of the addition probability rule.

Thanks for checking out April 2024’s New Teacher Tools — we hope they help!

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February 2024’s New Teacher Tools

Winter is still holding on here in New York (barely), but eMATHinstruction is heating up with new add-ons and new courses. We are excited to release our updated version of Algebra II (N-Gen Math Algebra II) in the late spring and will, of course, continue to release new materials for each of our active courses through May of this year. Here are this month’s new resources — have at ’em!

• Unit 8 (Percent) – Mid-Unit Quiz – Form B
• Unit 8 (Percent) – Practice with Everyday Percent Problems. This worksheet gives students great practice calculating percentages based on finding 10% of a number and then scaling up (for 20%, 30%, etc.) or scaling down (for 5%). Practical application problems are emphasized.
• Unit 9 (Area) – Mid-Unit Quiz – Form B
• *Spanish Language Versions of the Unit 8 and Unit 9 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 8cc (Common Core Probability)Mid-Unit Quiz – Form B
• Unit 8cc (Common Core Probability) – Practice with Simulating a Compound Event. In this worksheet, students use random number generators to simulate the probability of getting a certain number of good night sleeps in a workweek.
• *Spanish Language Versions of the Unit 8cc Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 6cc (Common Core Functions) – Practice with Linear Functions. In this worksheet, students get practice creating linear functions, working with linear functions, and interpreting linear functions. All exercises are applied.
• Unit 7 (Exponents and Roots) – Mid-Unit Quiz – Form B
• Unit 7 (Exponents and Roots) – Practice with Exponent Properties. This worksheet gives students ample practice with negative exponents, the zero exponent, and the three basic exponent properties.
• *Spanish Language Versions of the Unit 7 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 8 (Quadratic Functions) – Unit Assessment – Form B
• Unit 8 (Quadratic Functions) – Mid-Unit Quiz – Form A
• Unit 7 (Dilations and Similarity) – Unit Assessment – Form A
• Unit 7 (Dilations and Similarity) – Exit Tickets
• Unit 7 (Dilations and Similarity) Partitioning a Side with an Angle Bisector. In this extended activity, students explore what happens when a side of a triangle is partitioned by an angle bisector. This activity gets kids to make conjectures based on measurement, use their knowledge of constructions, and finally has students prove their conjecture by the use of a similarity proof.
• Unit 9 (Complex Numbers) – Practice with Complex Number Arithmetic. In this worksheet, students get ample practice adding, subtracting, and multiplying complex numbers. They also get reinforcement that sometimes these calculations result in purely real or purely imaginary numbers.
• Unit 10 (Polynomial and Rational Functions) – Practice with the Factored Form of a Polynomial. This worksheet gives students great practice forming equations of polynomials based on their zeros and an additional point. Some work with double zeros is also included.

CHECK BACK HERE EACH MONTH OF THE SCHOOL YEAR FOR NEW TEACHER TOOLS TO MAKE TEACHING EASIER!

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January 2024’s New Teacher Tools

A new (calendar) year is here. Happy beginning to 2024!!! We are deep into the winter and even deeper into the school year. We’ve been busy over the holidays creating new materials for you hardworking teachers to use in your classrooms — enjoy!

• Unit 7 (Ratios and Rates) – Mid-Unit Quiz – Form B
• Unit 7 (Ratios and Rates) – Practice with Unit Rates. This worksheet gives students valuable practice with taking information given about two variables and producing unit rates. Work with both fractions and decimals is included.
• *Spanish Language Versions of the Unit 7 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 7cc (Common Core Statistics) – Practice with Mean as a Balancing Point. In this worksheet, students use the fact that the mean must balance distances that the data are above and below it to solve a variety of problems.
• Unit 8 (Probability)Mid-Unit Quiz – Form B
• Unit 8 (Probability) – Practice with Simulating a Compound Event. In this worksheet, students use random number generators to simulate the probability of getting a certain number of good night sleeps in a workweek.
• *Spanish Language Versions of the Unit 8 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 6 (Functions) – Practice with Linear Functions. In this worksheet, students get practice creating linear functions, working with linear functions, and interpreting linear functions. All exercises are applied.
• Unit 6cc (Common Core Functions) – Mid-Unit Quiz – Form B
• *Spanish Language Versions of the Unit 6cc Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 7 (Polynomials) – Unit Assessment – Form B
• Unit 7 (Polynomials) – Mid-Unit Quiz – Form A
• Unit 6 (Quadrilaterals) – Unit Assessment – Form A
• Unit 6 (Quadrilaterals) – Exit Tickets
• Unit 6 (Quadrilaterals) – Constructing Quadrilaterals. In this extended activity, students combine their knowledge of constructions with the sufficient conditions for a variety of special quadrilaterals to construct them. Although these constructions are not required, they give students a great chance to reinforce important skills from constructions and essential knowledge from quadrilaterals.
• Unit 8 (Quadratic Functions and Their Algebra) – Practice with Completing the Square Versus the Quadratic Formula. In this worksheet, students solve quadratic equations using both completing the square and the quadratic formula. By comparing the two solution methods, students get better and identifying when one technique is easier than the other to solve a quadratic equation.
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December 2023’s New Teacher Tools

Happy Holidays to all of our teachers and students out there! As the days get shorter and the nights longer (which is well modeled using trigonometric functions), here at eMATHinstruction we are sending out some end-of-the-calendar-year additions to our courses to make the season bright!

• Unit 6 (Equations and Inequalities) – Mid-Unit Quiz – Form B
• Unit 6 (Equations and Inequalities) – One-Step Equation Practice. Equation solving is new to sixth grade students. This worksheet gives them additional practice in both multiple choice and free response problems to solve one-step equations using inverse operations.
• *Spanish Language Versions of the Unit 6 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 7 (Statistics) – Practice with Statistical Measures. In this worksheet, students take unsorted data lists, sort them, and then find various statistical measures for the sorted list.
• Unit 7 (Statistics)Mid-Unit Quiz – Form B
• Unit 7cc (Statistics) – Mid-Unit Quiz – Form B
• *Spanish Language Versions of the Unit 7 and Unit 7cc Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 5 (Equations of Lines) – Mid-Unit Quiz – Form B
• Unit 5 (Equations of Lines) – Finding the Equation of a Line Given Two Points. This worksheet walks students through the process of finding the equation of a line if two points on the line are known.
• Unit 6 (Functions) – Mid-Unit Quiz – Form B
• *Spanish Language Versions of the Unit 5 and Unit 6 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 6 (Exponential Algebra and Functions) – Unit Assessment – Form B
• Unit 6 (Exponential Algebra and Functions) – Mid-Unit Quiz – Form A
• Unit 5 (Coordinate Geometry) – Unit Assessment – Form A
• Unit 5 (Coordinate Geometry) – Exit Tickets
• Unit 5 (Coordinate Geometry) – Finding the Circumcenter. In this extended activity, students find the circumcenter of a triangle using coordinate geometry.
• Unit 7 (Transformation of Functions) – Practice Finding Formulas for Transformed Functions. This worksheet gives students practice taking a parent function and finding its equation after being put through the various types of transformations that we’ve studied in Common Core Algebra II.

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October 2023’s New Teacher Tools

Happy Fall, y’all! The weather is getting colder and the colors more spectacular, at least here in the Northeast. We have lots of new resources to share — as always, we hope they help make teaching math a little easier. (Btw, the new Geometry course and new Spanish language versions of some of our middle school materials are indicated by *** below).

• Unit 3 (Decimals) – Practice with Decimal Word Problems. This is a good set of problems that gives students practice using various operations with decimals to solve real-world problems.
• Unit 4 (Negative Numbers) – Mid-Unit Quiz – Form B
• Unit 4 (Negative Numbers) – Practice with Ordering Signed Numbers. This worksheet has students think about where various negative and positive numbers fall on number lines. Students also compare various signed numbers using greater than or less than symbols.
• ***Spanish Language Versions of the Unit 4 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 4 (Percent) – Practice Finding Percent, Part, and Whole. In this worksheet, students get additional practice both in standard and applied problems calculating percent, finding a part, and finding a whole in the standard percentage relationship.
• Unit 4 (Percent) – Mid-Unit Quiz – Form B
• Unit 5 (Linear Expressions) – Mid-Unit Quiz – Form B
• ***Spanish Language Versions of the Unit 4 and Unit 5 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 3 (Transformations) – Mid-Unit Quiz – Form B
• Unit 3 (Transformations) – Practice with Angles of a Triangle. This worksheet is a nice collection of numerical and algebraic problems that rely on the relationships between the interior and exterior angles of a triangle.
• ***Spanish Language Versions of the Unit 3 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 4 (Linear Functions) – Unit Assessment – Form B
• Unit 4 (Linear Functions) – Mid-Unit Quiz – Form A
• Unit 3 (Euclidean Triangle Geometry) – Unit Assessment – Form A
• Unit 3 (Euclidean Triangle Geometry) – Exit Tickets
• Unit 3 (Euclidean Triangle Geometry) – Triangle Inequality Exploration Activity. In this extended exploratory activity, students try to predict the number of integer lengths that the third side of a triangle can have based on two integer sides given.
• Unit 4 (Exponential and Logarithmic Functions) – General Logarithm Practice. This set of problems gives students more practice with various aspects of logarithms, including their inverse nature with exponential functions and the basic log laws.
• Unit 5 (Sequences and Series) – Arithmetic and Geometric Sequence Practice. This worksheet is a nice collection of problems that only deals with arithmetic and geometric sequences (not series). Students translate between explicit and recursive definitions of these two types of sequences as well as predicting a given term of the sequence given various pieces of information.
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August 2023’s New Teacher Tools

Happy August!!! As the summer sun starts to set, a new school year is on the horizon for many (it’s even started for some!). While we’ve had a great summer (and hope you have too), we are genuinely excited for school to begin and have been creating new materials for all of our teacher members to use, including a new Geometry course and new Spanish language versions of some of our middle school materials (see the ***items below).

NEW MATERIALS FOR TEACHERS

Here are the new teacher tools to use in the classroom for each of our courses:

• Unit 1 (The Whole Numbers) – Mid-Unit Quiz – Form B
• Unit 1 (The Whole Numbers) – Practice with Multidigit Multiplication and Division. This is a great practice sheet for students to work on their fundamental ability to multiply and divide numbers that have multiple digits.
• Unit 2 (Fractions) – Mid-Unit Quiz – Form B
• ***Spanish Language Versions of the Unit 1 and Unit 2 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 1 (Essential Review) – Mid-Unit Quiz – Form B
• Unit 1 (Essential Review) – Practice Converting Between Fractions and Decimals. This worksheet gives students extra practice moving from fractions to decimals and from decimals to fractions. It is intended to be for non-calculator use.
• Unit 2 (Operations with Signed Numbers) – Mid-Unit Quiz – Form B
• ***Spanish Language Versions of the Unit1 and Unit 2 Mid-Unit Quiz (Form A only) and Exit Tickets
• Unit 1 (The Algebra of One Variable) – Mid-Unit Quiz – Form B
• Unit 1 (The Algebra of One Variable) – Practice with Combining Like Terms. This worksheet is a collection of good problems that challenge students to combine expressions by combining like terms.
• ***Spanish Language Versions of the Unit 1 Mid-Unit Quiz (Form A only) and Exit Tickets.
• Unit 1 (The Building Blocks of Algebra) – Unit Assessment – Form B
• Unit 1 (The Building Blocks of Algebra) – Mid-Unit Quiz – Form A
• Unit 2 (Linear Equations and Inequalities) – Unit Assessment – Form B
• Unit 2 (Linear Equations and Inequalities) – Mid-Unit Quiz – Form A
• Unit 1 (Beginning Concepts) – Unit Assessment – Form A
• Unit 1 (Beginning Concepts) – Exit Tickets
• Unit 1 (Beginning Concepts) – Sides Versus Angles in a Triangle. In this extended exploratory activity, students make and test conjectures about the relationships between the side lengths of a triangle and the angle measures.
• Unit 1 (Algebraic Essentials Review) – Practice Multiplying Polynomials. This worksheet gives students practice in this essential skill.
• Unit 2 (Functions as the Cornerstones of Algebra II) – Practice with Domain and Range. This worksheet gives students practice with identifying the domain and range of a function using various function representations. Limitations on the domain, such as division by zero, are also stressed.
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The end of the school year is near and so is end-of-the-year testing. Here at eMATHinstruction, we are wrapping up our new additions for the year and getting into test prep mode. Without further delay, let’s get into our final new resources for the year.

NEW MATERIALS FOR TEACHERS

Here are the new teacher tools to use in the classroom for each of our courses:

• Unit 11cc (Common Core Statistics) – Form B Unit Assessment.
• Unit 11cc (Common Core Statistics) – Practice with Mean, Median, and Mode. This is a great worksheet to give your students some extra practice with these measures of center.
• Unit 12 (Probability) – Form B Unit Assessment
• Unit 12 (Probability) – Practice with Probability and Expected Outcomes. This is a good sheet of practice problems on both finding simple probabilities and calculating expected outcomes given probabilities.
• No new additions this month.
• Unit 11 (Systems of Equations) – Form B Unit Assessment.
• Unit 12cc (Common Core Statistics of Two Variables) – Form B Unit Assessment.
• Unit 12cc (Common Core Statistics of Two Variables) – Practice with Two-Way Frequency Charts. In this practice sheet, students work with two-way frequency charts and look at associations that can be inferred from these charts.
• Unit 11 (Statistics) – Form A Unit Assessment.
• Unit 11 (Statistics) – Exit Tickets.
• Unit 11 (Statistics) – Family Size – Extended Statistical Modeling Problem. This is a great problem where students look at whether people had more siblings in the past. Students analyze two data sets and try to determine if the variations they see are due to the groups or just due to chance.
• Unit 10 (Measurement and Modeling) – Form D Mid-Unit Quiz.
• Unit 10 (Measurement and Modeling) – Practice with Sectors of Circles. In this practice sheet, students work with finding the arc length, area, or central angle of a sector of a circle given other quantities.
• Unit 12 (Probability) – Practice Using Products to Calculate Probabilities. This worksheet gives students lots of practice with probability problems that involve products (AND probability problems). Some of these are quite challenging.
• Unit 13 (Statistics) – Form D Mid-Unit Quiz.
• Unit 13 (Statistics) – Practice with Margin of Error. In this practice set of problems, students work with margin of error both for means and proportions.

WOOHOO! eMATH’s N-GEN MATH GEOMETRY IS HERE!

ALL LESSONS & HOMEWORK FILES for N-Gen Math Geometry can be found on our website here for FREE.

ALL KIRK WEILER VIDEOS on N-Gen Geometry can be found on eMATH’s YouTube channel here for FREE.

All Common Core Geometry paid MEMBERSHIPS automatically have INSTANT ACCESS to all the paid resources for N-Gen Geometry (and vice versa)!

• And N-Gen Geometry WORKBOOKS will be available to order THIS SUMMER for your high school Geometry classes starting in the fall!

You’ll see that eMATH’s N-Gen Math Geometry resources designed by Kirk Weiler are like triangles with a 90-degree angle, BECAUSE THEY’RE ALWAYS RIGHT!

Let eMATHinstruction’s teacher extraordinaire, Kirk Weiler, give you or your students a helpful review of the skills they’ll need to master regents.

ALGEBRA I
Review: Tuesday, June 13, 6:00pm
The 2023 Test Date: Thursday, June 15

GEOMETRY
Review: Sunday, June 18, 6:00pm
The 2023 Test Date: Tuesday, June 20

ALGEBRA II
Review: Monday, June 19, 6:00pm
The 2023 Test Date: Wednesday, June 21

All live reviews (and their recordings) will be accessible in the “Live” section of eMATH’s YouTube Channel HERE.

Thanks for checking out our May 2023 Newsletter! We hope you had a lovely Mother’s Day (if you celebrated), are honoring Asian American & Pacific Islander Heritage Month in some way, and are looking forward to a nice long Memorial Day weekend.

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Spring has fully sprung here in upstate New York as we head into the last part of the school year: the trees are bursting with color, the daffodils have already had their heyday, and the ticks are out in full force! We here at eMATH are fighting allergies to finish up the newest edition to our catalogue, our N-Gen Math Geometry videos and workbooks. And we’re always creating new materials for all of our existing courses — April’s new teacher tools to use in the classroom for each of our courses linked to below are below. But first! An important request…

For a better eMATH experience, members should update their info, especially because we’ve added new helpful fields. Plus, it’s always a good idea to occasionally make sure all your info is up to date. CLICK HERE to update. And thanks!

NEW MATERIALS FOR TEACHERS

Here are the new teacher tools to use in the classroom for each of our courses:

• Unit 10 (Solids) – Form B Unit Assessment
• Unit 11 (Statistics) – Practice with the Mean, Median, and Mode. This great little worksheet gives your sixth grader some additional work with the three major measures of central tendency.
• Unit 11 (Statistics) – Form B Unit Assessment
• Unit 10 (Geometric Measurement) – Practice with the Circumference and Area Formulas of a Circle. This worksheet has students work with both fundamental formulas and express their answers both in terms of pi and in decimal form.
• Unit 10 (Geometric Measurement) – Form B Unit Assessment

***Note: These are the final add-ons for Math 7 for the school year!***
• Unit 10 (Scientific Notation) – Practice with Scientific Notation. In this worksheet, students gain additional practice with converting between the standard representation of a number and expressing the number in scientific notation.
• Unit 10 (Scientific Notation) – Form B Unit Assessment
• Unit 11 (Systems of Equations) – Practice with Solving Systems Using Substitution. This worksheet gives students lots of extra problems where they solve simple linear systems using the method of substitution. Some word problems are included.
• Unit 10 (Functions and Their Transformations) – Form A Unit Assessment
• Unit 10 (Functions and Their Transformations) – Exit Tickets
• Unit 10 (Functions and Their Transformations) – The Gateway Arch Extended Modeling Problem. In this extended problem, students have a chance to model the shape of the Gateway (St. Louis) Arch using the vertex form of a parabola.
• Unit 9 (Circle Geometry) – Form D Mid-Unit Quiz
• Unit 9 (Circle Geometry) – Practice with the Equation of a Circle. This worksheet gives students opportunities to practice identifying the center and radius of a circle given the circle in center-radius form. It also has problems that force students to complete the square to place the circle in center-radius form.
• Unit 11 (The Circular Functions) – Practice Calculating the Values of the Trigonometric Functions. In this practice set of problems, students calculate the value of each of the six trigonometric functions if given the value of the sine or cosine function and the quadrant of the angle.
• Unit 12 (Probability) – Form D Mid-Unit Quiz

GET KIRK’S VIDS IN ANY LANGUAGE!

DID YOU KNOW that all of eMATHinstruction’s YouTube videos led by Kirk Weiler are available in multiple languages? Math may be a universal language, but if any students don’t speak Kirk’s native tongue (English) or don’t speak it fluently, they can get automatically generated closed captions of the lessons in their own mother tongue. You can watch this tutorial or follow these instructions:

1. While watching an eMATH YouTube video, hit the pause button.
2. Click on the [CC] icon to turn Closed Captioning ON.
3. If the settings aren’t already set to your preferred language, click the gear icon to access Settings.
4. Click on the “[CC] Subtitles” link in the pop-up list.
5. In the next pop-up that appears, click on “Auto-translate.”
6. Then select your preferred language!

Voila! Listo! Där!

Regents Exams are just under two months away! As usual, Kirk will be hosting live review sessions before each math exam. Stay tuned for exact dates and times!

We hope you got a refund on Tax Day, took eco-action on Earth Day, and enjoyed Math & Statistics Awareness Month this April! Thanks for reading our April 2023 Newsletter. 🙂

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Spring has finally arrived, at least on the calendar. Of course, we hope you all had a great Pi Day on March 14th (check out these fun pi facts that may just blow your mind). We’re excited to be moving through the second half of the school year and can see the end approaching. We’ve got a few more new resources to post before the year is over, so let’s get right into our new additions.

NEW MATERIALS FOR TEACHERS

Here are the new teacher tools to use in the classroom for each of our courses:

• Unit 9 (Area) – Form B Unit Assessment
• Unit 10 (Solids) – Practice with Surface Area. This is a great set of problems to give students practice on drawing surface area nets and calculating the surface area of prisms.
• Unit 9 (The Geometry of Angles and Triangles) – Form B Unit Assessment
• Unit 9 (The Geometry of Angles and Triangles) – Practice with Supplementary and Complementary Angle Pairs. In this worksheet, students get a chance to reinforce their understanding of supplementary and complementary angle pairs through both numerical work and some algebraic work.
• Unit 7 (Exponents and Roots) – Solving Equations Using Square Roots and Cube Roots (Enrichment). This worksheets gives your students who need more of a challenge a chance to solve multistep equations where they must take either a square root or cube root to solve.
• Unit 8 (The Pythagorean Theorem) – Form B Unit Assessment
• Unit 9 (Volume and Surface Area of Solids) – Form B Unit Assessment
• Unit 9 (Volume and Surface Area of Solids) – Basic Volume Practice. In this worksheet, students get practice calculating the volume of all of the solids they saw in Unit 9, including leaving some answers in terms of pi.
• Unit 9 (Roots and Irrational Numbers) – Form A Unit Assessment
• Unit 9 (Roots and Irrational Numbers) – Exit Tickets
• Unit 9 (Roots and Irrational Number) – Designing a Fenced in Area – Modeling Problem. In this extended modeling problem, students determine the dimensions of a fenced in area based on the amount of fencing and the area enclosed. Solutions are irrational and force the students to use the quadratic formula or completing the square.
• Unit 8 (Right Triangle Trigonometry) – Form D Mid-Unit Quiz
• Unit 8 (Right Triangle Trigonometry) – Multistep Right Triangle Trigonometry Practice. In this worksheet, students are given the chance to solve trigonometry problems that require more than one trigonometric ratio.
• Unit 10 (Polynomial and Rational Functions) – Practice Finding the Zeros of a Polynomial Algebraically. In this lesson, students find the zeros of quadratic, cubic, and quartic polynomials by factoring, including factoring by grouping.
• Unit 11 (The Circular Functions) – Form D Mid-Unit Quiz

THE PEN(CIL) IS MIGHTIER THAN THE SCREEN

In case you missed our latest blog post, read HERE about why it’s so important for math to be written out. Hint: it’s not just because Good Will Hunting wouldn’t have won an Oscar if Matt Damon had done his calculations on a smartphone.

Have You Heard of Any of These Mathematicians?

Well, you should have! They’re some of the most important mathematicians in the history of math, and not just because they’re women. Learn more about Hypatia, Ada Lovelace, Mary Cartwright, Katherine Johnson, and more HERE. Happy Women’s History Month, y’all!

Oh, and by the way, Regents Reviews are coming in June!

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The Pen(cil) Is Mightier Than the Screen: Math Must Be Written Out

This might sound counterintuitive coming from a company that has literally hundreds of online math lessons available on YouTube, but for math to be learned well, students must practice on paper.

Study after study has shown as much:

A 2020 study by the Reboot Foundation found that of students using an online math tool, those who were encouraged to do their calculations using pencil and paper did an average of 13 points better than those who weren’t.

A 2014 series of studies published in Psychological Science found that those students who take notes by hand (which allows them to summarize, paraphrase, and concept map) perform better than students who type notes quickly verbatim on a laptop.

A 2017 review of research done since 1992 found that students were able to better comprehend information in print for texts that were more than a page in length, which is apparently related to the disruptive effect that scrolling has on comprehension.

– The same authors as the 2017 review conducted their own three studies on college students and found that comprehension was better for print reading than it was for digital reading.

A 2021 Tokyo study shows stronger brain activity after writing on paper than on a tablet or smartphone, suggesting that unique, complex information in analog methods likely gives the brain more details to trigger memory.

And let’s not forget the importance of “showing your work” to help students grasp concepts and avoid guessing while allowing teachers to troubleshoot incomprehension and pinpoint mistakes in calculatory processes.

All of the above is why eMATHinstruction sells workbooks to school districts and offers free print-outs to teachers — so that students can work out problems on paper

All this is not to say that there aren’t effective uses for digital technology when it comes to teaching and learning math. For example, the interactivity and dynamics of digital tools can be particularly helpful in geometry education, where comprehending visual and dynamic geometrical objects and relations is necessary. And tech certainly has its benefits: with more and more communities gaining access to internet infrastructure, kids can use and reuse infinite online learning tools, making learning more equitable; education can happen across borders; online files can’t be damaged the way physical textbooks can; and relying on less paper is more sustainable. The digital tools currently available haven’t yet reached their full potential: the features of digital resources — e.g. dynamics, feedback, personalization, and cooperation — can and should be improved upon. The sky’s the limit! Or should we say, the potential is unbounded by any finite number.

As with most things in life, a balanced approach is best: use and improve upon technology to aid in the teaching and learning of math, but don’t give up on the tried-and-true method of pencil on paper. Good Will Hunting would not have won an Oscar had Matt Damon done his calculations on a computer instead of a chalkboard. Plus, pencil sharpeners are just plain fun!