## 11 Teacher-Recommended Math Apps and Online Tools

Before the epidemic, some math teachers were already using digital tools to assist pupils to visualize math ideas, such as Desmos, or websites that foster mathematical debate, such as Fraction Talks, to help students learn about fractions. Other teachers, on the other hand, were motivated by remote learning to experiment with math apps and online tools for the first time.

More than 500 comments were combed through after we spoke with hundreds of educators about the math tools they found useful and unhelpful during remote learning this spring, and which ones were cut to be used in the next school year.

### PRACTICE YOUR MATH SKILLS

According to math experts, a variety of math applications and online tools can assist kids in developing the necessary core understanding of arithmetic operations that they will need as a baseline for more demanding math problems later on in their education.

Ashley Blackwelder, an elementary STEAM coordinator in South Carolina, recommends Moose Math, free software for iPhones and iPads, to assist younger students in practice skills such as counting, addition, and subtraction. Moose Math is available for download on the App Store. In Moose Math, students participate in math games that earn them points that they can use to assist in the construction of a town. According to Blackwelder, the format is simple for children to explore and is ideal for those with short attention spans.

According to Cassie Tabrizi, an instructional designer and curriculum developer, Happy Numbers (pre-K–grade 5) is an online resource ($14.50 per student or $1,450 per site for first-time schools) that breaks down mathematical equations to help students gain a better understanding of higher-order math concepts. Students must turn into a dinosaur figure and answer arithmetic problems to hatch dinosaur eggs to use it. While Tabrizi acknowledges that the website is beneficial, she advises that it be used in moderation: If pupils practice for more than 10 minutes every day, it can become monotonous for them to do so.

Students take on the role of a wizard to battle monsters in Prodigy (grades 1–8), a free game-based website for grades 1–8. (also available as an app for iPhone, iPad, iPod Touch, and Android). Prodigy is well-liked by children, but it is less popular with instructors because it is more play-based. Brittney Paige, a fifth-grade teacher in Seattle, says that, although it is more of a game, she appreciates the fact that it automatically targets math concepts that students struggled with in its preassessment and tracks how much progress they make on target areas as they progress through the game. When students finish an assignment early, most teachers give them the option of using Prodigy to complete the task.

### A duel between prodigies in mathematics

Prodigy provided the image.

A spell is cast in combat by a student’s pet after he or she has correctly answered a math problem.

Using Zearn (grades 1–5), a free, self-paced, web-based software that is integrated with Eureka Math—a free pre-K through 12 math curriculum—teachers can begin a normal lesson with engaging warm-up tasks, such as counting the number of apples eaten by a cartoon fox, to engage pupils. The application requires students to perform timed arithmetic problems, see instructional films on new ideas, and solve practice problems as they go through the levels. Even though Zearn is good for “high-level, conceptual practice” and provides good feedback for both teachers and students, Shannon McGrath, an instructional coach in Western Springs, Illinois, believes that the program can sometimes progress too slowly for students who master concepts quickly.

### TASKS IN MATH ARE AVAILABLE

According to math educators we spoke with, open math tasks (problems that typically have more than one correct answer) help students develop a conceptual understanding of mathematics rather than becoming hung up on memorizing facts. They all mentioned three free websites to use for open math tasks as examples of this.

An equation in Open Middle (pre-K–grade 12) is left with portions of it blank, and students are asked to fill them in to make it true. According to McGrath, “I like Open Middle for remote learning, especially when it’s combined with a Google Jamboard.” “The difficulties elicit inquisitive thinking, gamelike play, inventiveness, and perseverance,” says the professor.

Which of these graphs does not belong? is a collection of four graphs from the website Which One Doesn’t Belong?

Thanks to Mary Bourassa/Which One Doesn’t Belong? for the image.

“Which One Doesn’t Belong?” is a question that can be answered. Students in Mary Bourassa’s calculus class construct a mathematical justification for why each graph is the odd one out.

Would You Rather Math (pre-K–grade 12) is another game that McGrath enjoys for community development. When students use the site, they must choose between two real-life examples—for example, a box of chocolates with five rows and 14 columns or a box of chocolates with seven rows and nine columns—and then develop a mathematical argument to support their selection.

Which one doesn’t belong in this group? Students are asked to define which of four objects, numbers, or graphs does not belong to the group using math language on a similar website (pre-K–grade 12). “Because it is considered a low-floor, high-ceiling assignment, it is ideal for kicking off asynchronous debate,” explains Joseph Manfre, a math specialist for the Hawaii Department of Education. High school math teacher Mary Bourassa instructs her calculus students to identify reasons why each graph in a set of four does not belong by indicating graph characteristics such as asymptotes and non-differentiable points and then has her students create their own WODB sets using the information they have gathered.

### TASKS IN RICH MATH

Math educators have identified a couple of websites that provide rich math tasks—tasks that encourage rigor, teamwork, and conceptual thinking—for students.

There are many different forms included within a square.

Thanks to Bryan Penfound/Fraction Talks for their assistance.

When students are practicing fraction addition and multiplication, they might refer to this graphic from Fraction Talks. The bottom corner part is represented by the numbers 12 x 14 = 18.

Fraction Talks (grades 1–12) is a website that has graphics of geometric forms (triangles within triangles, for example) that are intended to inspire arithmetic discussions among students. The question “What do you observe?” can drive children to express what and how many shapes they notice, whereas the question “How many shapes are red or shaded?” enables students to discover and grasp fractions via exploration and understanding. Once students have a fundamental understanding of fractions, they can go on to more difficult concepts and problems. Bryan Penfound’s seventh- and eighth-grade pupils were able to visualize adding and multiplying fractions when he asked them to look at subsections of a form and what fractions they created when they were combined.

Visual Patterns (K–12) provides the beginning of a pattern, such as multiple boxes in a grid, and then asks students to work out the equation that best fits the pattern they have seen. Although there is only one correct solution, adds Manfre, “you may pose deeper questions with these kinds of exercises, and children can connect with mathematics in a more natural, visual manner.”

Three sets of blocks, each with an increasing number of pieces

Thanks to Visual Patterns for their assistance.

The students must figure out what the equation is for this pattern.

### TOOLS FOR SIMULATION

According to math teachers, simulations, such as altering an expression and observing a change in a graph, are excellent tools for assisting pupils in visualizing mathematical concepts.

Desmos was used to check in on an SEL graphing assignment.

Thanks to Ashley Taplin for her contribution.

Ashley Taplin, a secondary math specialist, assigned her pupils the task of graphing their emotions throughout the first week of online study.

Applets, which are simple pieces of code with a defined goal, were mentioned as a useful resource by a few professors. As an example, statistics students in Emma Chiappetta’s statistics class use applets from RossmanChance.com to edit and find sampling distribution patterns in graphs, among other things. A simple guide on how to use the applet and which settings to alter is created, and questions are asked to have students thinking critically about the patterns they’ve discovered are then asked. Her linear algebra pupils also benefit from the use of applets developed by the Massachusetts Institute of Technology (MIT).

A third free tool, Desmos (for grades 6–12), a website with interactive math lessons and a graphing calculator (also accessible as an app for the iPhone, iPad, iPod Touch, and Android), has emerged as a popular choice among teachers, according to what we learned. While social and emotional learning (SEL) and mathematics may not appear to go hand in hand, teachers were able to incorporate SEL into math classes using Desmos and other educational software. Ashley Taplin, a secondary math expert in San Antonio, Texas, assigned her pupils to graph how they were feeling throughout the first week of remote learning, for example. Taplin expresses special delight in the fact that teachers can create their activities, such as this one about parabolas and this card sort, in which students match cards with the name, related equation, and right graphical representation of a function to complete a task.

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