When I am tutoring a learner in math, I always encourage them to use materials to help them visualize or model a problem. Learners from kindergarteners through middle school benefit from math experiences that are visual and concrete.
According to Jo Boaler (2019) in Mindeset Mathematics: Visualizing and Investigating Big Ideas Grade 6, “students need to physically create, draw, and construct mathematics to build deep understanding of what concepts represent and mean”. I use a variety of math materials with the students I tutor. Below you will find descriptions of the math materials I use most as well as resource links for printables, free virtual math tools, and comprehensive lessons.
Kids delight in playing math games with dice or dot cubes. The photo above shows large dot cubes, regular dice, multisided dice, number cubes, double dice, and place value dice. Building number fluency and computation practice can easily be achieved through fun games rather than flashcards and worksheets. I use math games as a warm-up activity in my sessions before diving into more focused problem-solving guided instruction. Below are some resources for games you can play at home with dice (most of the games are for 1st – 5th grade students).
- Dice Games can be found at Zeno
- Multiplication Practice & How Many Rows? from YouCubed.org
- More Games from Newark City Schools
Unifix Cubes were invented by Charles Tacey in 1953 to replace counting beads. The Tacey family was involved in the production of Froebel and Montessori educational materials in Europe and brought Unifix Cubes to the US through Didax Inc. Unfix cubes are versatile and easy to handle. They can be used to make patterns, record data, count, model fractions and compute. The Didax company makes companion guides for Unifix cubes. I use these cubes often because they are so easy for children to handle. The students use them to represent numbers and equations, to compare quantities and learn addition facts to ten.
Linking Cubes and Snap Cubes
For multiplication, area and spatial reasoning, my go to materials are Math Link Cubes from Learning Resources. These are a lot like Snap Cubes which are made by other educational companies. Like, Unfix Cubes, these cubes can be used to model operations, problem solve and create patterns but because they can be connected on six sides I use them to explore volume and surface area with upper elementary and middle school students. There are lots of Snap Cube activities for younger kids that help them explore shapes and help them visualize 2-D and 3-D shapes and solids.
Pattern Blocks are my favorite math manipulative. My kids and former classroom students loved to play with pattern blocks. They are great for open ended play. Pattern Blocks were designed in the 1960’s at EDC. They can be used by young kids in early childhood settings and kids through upper elementary grades. Below are some resources for using patterns blocks and how they help learners develop spatial skills, compose geometric shapes, and explore angles and fractions.
- Animal Puzzles from The Games for Young Mathematicians program at EDC, for 3- 6 year-olds.
- Pattern Block Lessons for Grade K-2 from The Math Learning Center
- Pattern Block Lessons for Grades 3-5 from The Math Learning Center
- Free Pattern Block Printables from The Stem Laboratory & Fairy Poppins Pattern Activity
Base Ten Blocks
Base Ten Blocks, also called Dienes Blocks, were develop by a Hungarian mathematician and math education enthusiast. He promoted learning math through games, hands-on materials and songs to bring joy to math learning. Base Ten Blocks are used by elementary aged students to model place value, operations, decimals, and percents. The Math Coach’s Corner is a great resource for understanding how children learn math in grades K – 5 and develop ideas about pace value.
- Virtual Base Ten Blocks model at Cool Math 4 Kids
- Models for Decimal Place Value by The Math Coach’s Corner
- Using Base Ten Blocks to Develop A Deeper Understanding of subtraction
Ten frames are great way to help young kids learn to organize individual objects, count, and develop a visual of 10 as 5 + 5. Ten frames also help children develop instant number recognition, and can help them learn addition and subtraction facts through 10. Using multiple ten frames encourages children to count by 10’s and develop number recognition and number facts beyond 10. I use ten frames with the young students I tutor to help them visualize numbers and number combinations which helps them build number sense.
- Getting Started with Ten Frames Video
- Back-to-School Make 10 Addition from The Stem Laboratory
- Online Ten Frame from the National Council of Teachers of Mathematics
- Online Ten Frame from Cool Math 4 Kids (make your own frame)
There are lots of math manipulatives available to help students model and visualize math concepts but mini erasers are the most fun. I use mini erasers with young students to tell story problems, act out word problems, sort and classify, model the four operations and solve computation problems. I like using mini erasers because of their versatility and because students get fine motor skills practice when handling them. They are an inexpensive and a fun way to practice math skills.
I hope you’ve found this list of math resources useful. Helping students develop number sense and become confident mathematical thinkers is very rewarding. Using materials to model mathematical concepts requires that learners be involved in the learning process and that helps them see themselves as capable math learners.