When we talk about math and tools for elementary students, we often use manipulative materials and real-world applications. What I like to do is present students with the opportunity to explore the numbers in their world, and map them to actual numbers on a number line. I’ll also expose them to some of the notation we use when we figure out math problems, such as putting parentheses around groups of numbers or putting an equals sign between things that are the same (this makes it look like you multiplied!). Then I’ll lead them into engaging activities that allow me to check their understanding of the concepts introduced.
Adapt to Student Needs
Innovative combo of live instruction and adaptive online math lessons
Excellent adaptive math for flipped or blended classrooms
Individualized, game-based math adapts to kids’ needs
Build Fundamental Skills
Numbers-and-quantity game has precise focus and superb scaffolding
Bottom line: Super approach to teaching a very specific topic: Help kids develop an easy familiarity with quantities under five.Grades: Pre-K–K Price: FreeGet it now See full review
Original videos and activities a treasure trove for teachers and students
Engaging supplemental resource encourages conceptual understanding
Engage with Gaming
Playful collection of games reinforces a diversity of skills
Bottom line: A great add-on to any classroom as a treat for students or as a way to get students to practice taught concepts to mastery.Grades: K–7 Price: Free to try, Paid Visit website See full review
Brilliant, wacky adventure game seamlessly integrates geometry
Bottom line: This captivating game is a great way to introduce or reinforce early geometry concepts.Grades: 1–4 Price: $2.99 Get it now See full review
Fun virtual world builds deep understanding of fractions
Bottom line: A 3D world that uses adaptive computer manipulatives and multiple representations to help students retain important fractions concepts.Grades: 3–6 Price: Free, Paid Visit website See full review
Innovative game-based approach to teaching geometry
Bottom line: Kids build fundamental geometry skills as they play, but connections to classroom math will require teacher support.Grades: 3–8 Price: $4.99
MATH SKILLS PRACTICE
A number of math apps and online tools can help students develop the necessary foundational understanding of arithmetic operations they’ll need as a baseline for more challenging math problems later on, math teachers told us.
To help younger students practice skills like counting, addition, and subtraction, Ashley Blackwelder, an elementary STEAM coordinator in South Carolina, highly recommends Moose Math, a free app for iPhones and iPads. In Moose Math, students play math games that earn them points to help build a town. Blackwelder says the format is easy for kids to navigate and great for short attention spans.
Curriculum and instructional designer Cassie Tabrizi recommended Happy Numbers (pre-K–grade 5), a subscription-based website ($14.50 per student or $1,450 per site for first-time schools) that breaks down mathematical equations to help students build understanding of higher-order math concepts. To use it, students transform into a dinosaur character and solve math problems to hatch dinosaur eggs. Tabrizi said that the website is helpful, but she recommends using it in moderation: It can feel tedious for students if they practice longer than 10 minutes a day.
Students fight monsters in the persona of a wizard in Prodigy (grades 1–8), a free game-based website (also available as an app for iPhone, iPad, iPod Touch, and Android). Prodigy is loved by kids, but less so by educators because it is more play based. Brittney Paige, a fifth-grade teacher in Seattle, says that even though it is more of a game, she likes that it automatically targets math concepts that students struggled with in its preassessment and tracks how much progress they make on target areas. Most teachers offer Prodigy as an option for students if they finish an assignment early.
Courtesy of ProdigyAfter successfully answering a math problem, a student’s pet casts a spell in a battle.
Zearn (grades 1–5), a free, self-paced, web-based program aligned with Eureka Math—a free pre-K through 12 math curriculum—starts a typical lesson with fun warm-up activities, like adding up how many apples a cartoon fox eats, to engage students. As they work through the program, students complete timed arithmetic problems, watch instructional videos on new concepts, and solve practice problems. Shannon McGrath, an instructional coach in Western Springs, Illinois, says that Zearn is good “high-level, conceptual practice” and gives good feedback for both teachers and students, but can sometimes progress too slowly for kids who master concepts quickly.
OPEN MATH TASKS
Open math tasks—problems that typically have more than one answer—help students develop a conceptual understanding of math rather than get hung up on memorizing facts, said math educators we talked to, who consistently mentioned three free websites to use for open math tasks.
Open Middle (pre-K–grade 12) leaves parts of an equation blank and asks students to fill them in to make it true. “I love Open Middle for remote learning, especially paired with a Google Jamboard,” says McGrath. “The problems inspire inquiry thinking, gamelike play, creativity, and perseverance.”
Courtesy of Mary Bourassa/Which One Doesn’t BelongUsing “Which One Doesn’t Belong?” Mary Bourassa’s calculus students make a mathematical argument why each graph is the odd one out.
McGrath also likes Would You Rather Math (pre-K–grade 12) for community building. When using the site, students choose between two real-life examples—like a box of chocolates with five rows and 14 columns or a box of chocolates with seven rows and nine columns—and have to make a mathematical argument to validate their choice.
Which One Doesn’t Belong? (pre-K–grade 12), a similar site, showcases four shapes, numbers, or graphs and asks students to describe which one doesn’t belong, using math vocabulary. “This is great for opening a synchronous discussion, as it is considered a low-floor, high-ceiling task,” says Joseph Manfre, a math specialist for the Hawaii Department of Education. High school math teacher Mary Bourassa has her calculus students identify reasons why each graph in a set of four doesn’t belong by indicating graph characteristics like asymptotes and non-differentiable points, and later has her students create their own WODB sets.
RICH MATH TASKS
For rich math tasks—tasks that lend themselves to rigor, collaboration, and conceptual thinking—math educators noted a couple of websites.
Courtesy of Bryan Penfound/Fraction TalksStudents use this image from Fraction Talks to practice adding and multiplying fractions. The bottom corner section represents ½ x ¼ = ⅛.
Fraction Talks (grades 1–12) is a website filled with images of shapes—triangles within triangles, for example—that encourages math discussions. Simply asking students, “What do you observe?” can prompt them to share what and how many shapes they notice, while asking “How many shapes are red or shaded?” encourages students to explore and understand fractions. Once students have a basic understanding of fractions, they can start to explore more complex concepts. By prompting students to look at subsections of a shape—and what fractions they created when combined—Bryan Penfound helped his seventh- and eighth-grade students to visualize adding and multiplying fractions.
Visual Patterns (K–grade 12) shows the beginning of a pattern—like several boxes in a grid—then asks students to figure out the equation to fit the pattern. “Even though there is only one answer,” says Manfre, “you can ask deeper questions with these kinds of tasks, and engage students with mathematics in its more natural, visual form.”
Courtesy of Visual PatternsStudents need to identify the equation for this pattern.
According to math teachers, simulations, like manipulating an expression and seeing a change in a graph, are great tools to help students visualize math concepts.
Courtesy of Ashley TaplinAshley Taplin, a secondary math specialist, had her students graph how they felt during the first week of distance learning.
Applets—a simple code with a specific objective—were mentioned by a few teachers as a good resource. Emma Chiappetta’s statistics students use applets from RossmanChance.com to manipulate and identify sampling distribution patterns in graphs, for example. She creates a basic guide on how to use the applet with which values to change, and then asks questions to get students thinking critically about those patterns. Chiappetta also uses applets from the Massachusetts Institute of Technology for her linear algebra students.
Desmos (grades 6–12), a website with interactive math activities and a graphing calculator (also available as an app on iPhone, iPad, iPod Touch, and Android), is another free tool and a favorite among teachers, we heard. While social and emotional learning (SEL) and math may not seem to go hand in hand, teachers integrated SEL into math lessons using Desmos. In the first week of distance learning, Ashley Taplin, a secondary math specialist in San Antonio, Texas, had her students graph how they were feeling, for example. Taplin says she particularly loves that teachers can make their own activities—like this one about parabolas and this card sort, where students match cards with the name, corresponding equation, and correct graphical representation of a function.
Base Ten Blocks
Number Pieces is a great free app that allows every student with an iPad to have an endless number of base ten blocks at their fingertips. Whether they are learning basic place value, modeling how to add decimals, or exploring expanded notation, this app is worth looking into. Children can write all over the iPad screen and demonstrate their thought process as they manipulate the virtual base ten blocks.
Even on an iPad, a protractor can be used as a tool to measure angles. Children can simply practice making acute and obtuse angles by moving the line on the screen, or they can measure the angles in objects placed on top of their iPad. Try putting traditional pattern blocks or cutout paper shapes on top of an iPad screen. There are even a few apps that let you use the camera on an iPad or an iPod Touch for measuring angles.
Geometry Pad lets children draw lines and shapes on graph paper. They can plot points on this coordinate grid and even add text to the screen. This app is easy to use and includes tons of functions to try out. Educreations also lets students change the background of their screen to graph paper before they start writing.
Say goodbye to rubber bands! This virtual tool is perfect for elementary and middle school classrooms. Kids can simply create polygons on their geoboard to show off different quadrilaterals and triangles. They can also find the perimeter and area of each shape.
Ruler is a neat app to try out on your iPad — it simply turns your screen into a ruler. Students can measure items placed on their screen in inches and centimeters. They can solve perimeter and area problems with the information they gather using this virtual measurement tool. There are also apps that help children learn how to use a ruler properly.
A neat alternative to traditional pattern blocks, Pattern Shapes from the Math Learning Center is a must-have for iPad math classrooms. In addition to moving each piece around the screen, kids can draw all over the screen to show their work. A virtually endless supply of pattern blocks at your fingertips can help students who need extra support or strategic intervention.
Whether you’re teaching elapsed time or just helping students monitor their pacing and stamina, the timer built into the clock that comes with the iPad (or one of the many comparable options) is a great addition to your classroom. It’s perfect for teachers with one iPad or for children working in small groups, as they can now calculate how much time has passed or learn how to read a clock with these virtual tools.
The Common Core State Standards stress the importance of having children use math vocabulary in written and spoken explanations of their thinking. MathTerms Glossary can help students learn definitions of different words so that they can use them appropriately. It’s a great reference tool for students in a one-to-one classroom and even has Spanish language entries.
There are lots of calculators that can be downloaded for iPads including ones that feature scientific functions. Two of my favorites include handwriting recognition technology so students can use their finger or a stylus to write a problem and see the correct answer. MyScript Calculator and MyScript MathPad are great virtual tools to have available to students who want to check their work.
Want to learn more? Here’s a webcast from APPitic, a site maintained by Apple Distinguished Educator that focuses on using the iPad to teach Common Core math.
A quick substitution of a traditional tool can be a great way to experiment with new technology. Have you tried out any virtual math tools in your classroom?
We all need math tools in our lives. Whether it’s mental math, estimation, or problem solving, everyone can benefit from having some great tools to help along the way.