For students who are experiencing difficulties in maths, hands-on, physical manipulatives should be the go-to, as they help make abstract maths concrete. However, some of these physical objects can be expensive, hard to source or consist of small pieces that are easily lost.

This is where virtual manipulatives come in.

“*Virtual manipulatives are … a dynamic visual representation of physical manipulatives which can be operated through a computer mouse (or a finger on a tablet) to slide, flip, and turn just like a three-dimensional object. Virtual manipulatives give learners the same opportunity to make meaning and see relationships as the result of their actions, just like a physical manipulative*” https://www.dreambox.com/resources/blogs/benefits-virtual-manipulatives.

Here are some of our favourite manipulatives that are free and do not require the installation of an app.

## Ten frame

These ten frames help students represent quantities and model addition and subtraction equations. Use them to help your child learn one-to-one correspondence, recognise quantities to ten without counting, learn number bonds to ten, and visualise smaller numbers inside bigger numbers. With two of these tens frames, children can practice bridging to ten (e.g. that 9 + 5 is the same as 10 + 4).

## Number line

Number lines help with representing and comparing numbers and finding the relationship between numbers. Number lines are also beneficial to use when adding and subtracting.

Using a number line efficiently is a precursor to visualising number lines. Visualising number lines is an important skill as it speeds up calculating and frees up the working memory so it can focus on mathematical procedures.

## Fraction number line

Many students find fractions difficult, and many don’t fully understand the rules and concepts around fractions because they are abstract. This fraction number line helps children visualise fractions. It can be used to help students understand the relationship between fractions (e.g. that 1/2 if bigger than 1/3), get to grips with equivalent fractions (e.g. that 1/2 is the same as 2 lots of 1/4 or 2/4), understand the relationship between mixed numbers and improper fractions, and count in fractions.

## Place value discs

Place value discs help students connect the place of each digit in a number to their value. Students can practise making numbers with the discs, then recording this mathematically. For example, 4,352 is made of (4 x 1000) + (3 x 100) + (5 x 10) + (2 x 1).

These discs also help students visualise addition, subtraction, multiplication and division problems.

## Manipulative clock

Teach students how to tell the time with a manipulative maths clock. Have your child move the hands of the clock to show a time. Move the hands and have your child tell *you* the time.

You can choose which hand(s) you want to show, add in fraction lines so that students can connect a fraction of a shape to a fraction of a number (e.g. connecting 1/4 of the circle with 1/4 of an hour), and show a digital clock alongside, so that students learn to connect analogue to digital time.

If your child isn’t ready to tell the time yet, focus on these early measure concepts first.

## Decimal strips

Decimal strips help students visualise decimals and their relationship to each other. Use these strips to compare the size of decimals, add, subtract, multiply and divide decimals, and count in decimals.

## Place value cards

Place value cards give students practice with place value. Overlap the cards to build a number, then pull them apart to partition the number into parts. Children will be able to see the value of each digit in a number and can practise writing numbers in expanded form.

## Base ten blocks

Base ten blocks also help students understand place value and the value of ten in our base ten system. Use them to model numbers or equations.

This manipulative also helps children understand how to move value from one place to another (regrouping, carrying, borrowing). Draw a ring with your mouse around 10 x ones then press the ‘join’ button. The selected pieces will join together to make 1 x ten.

## Area perimeter explorer

Area perimeter explorer allows children to have fun creating their own shapes, and exploring the difference between area and perimeter. You can hide the perimeter and/or totals if you want to concentrate on just one or the other.

If your child isn’t ready to learn area and perimeter yet, focus on these early geometry concepts first.

## Online maths manipulatives: The benefits

Virtual manipulatives are engaging, motivating, open-ended, and help make maths visual. They help with problem-solving, communicating, reasoning, making connections, and estimation. Manipulatives help students make sense of, and understand the symbolic language of maths.

For students who have maths learning difficulties, however, hands on, concrete resources should always be used in conjunction with virtual manipulatives.

Want to make sure your child or student is getting the right support? Would you like someone to accurately pinpoint where the difficulties lie in your child and the steps needed to address them? We offer targeted one-to-one maths tuition. All sessions are delivered by a maths specialist.

Do you or your child find maths challenging? What online manipulatives do you use to help? Comment below or on our facebook page. We’d love to hear from you.