Virtual Manipulatives
The Returning to School Curriculum Guidance for Primary School Leaders and Teachers document, which can be accessed by clicking on the image, explains that "while the use of physical manipulatives may be more restricted owing to health and safety and hygiene requirements, alternative versions of resources including notation boards, hundred-squares, Dienes cut-outs and virtual manipulatives could be utilised in supporting children’s mathematical understanding in the 2020/21 school year" (DES 2020, p.23).
To support teachers, this section of STEM Smaointe will spotlight some virtual manipulatives* and associated activities to aid teaching, learning and assessment in Mathematics.
*Virtual manipulatives below are suggestions and do not represent an exhaustive list. Please note, they were freely available for use as of Oct. 15th 2020.
Five - frames and ten - frames are models which help pupils anchor to 5 and 10. A five - frame is a 1 X 5 array and a ten - frame is a 2 X 5 array. The virtual manipulative allows you to adjust accordingly. It is recommended that pupils work with a five - frame before progressing to a ten - frame.
Five/Ten Frame Flash: Flash a five/ten frame to the pupils and ask them how many dots they saw. How many dots did you see? How many empty boxes did you see? Where were the dots? How many were on the top row and how many were on the bottom row? Did you have time to count? How did you get your answer?
One More/Less Challenge: Flash a five/ten frame and ask the pupils to place one more/one less counter on their frame. E.g. Teacher flashes 3 and asks pupils to place one more counter on their frame. Pupils place 4 dots on the frame. Question the pupils as to how many empty boxes there are and how many more they would need to make 5/10.
Build a Set:
Five - Frame: Teacher calls out a number to the pupils e.g. 3 and they show that amount on the five - frame. Ask them to place the counters in a different way and ask questions about their arrangement. It has a space in the middle. It is 2 and 1.
Ten - Frame: For numbers greater than 5, encourage pupils to fill the first row first. E.g. Place 7 counters on your frame. Question the pupils about their arrangements. How many empty boxes have you got? What does this tell us about 10? I have 3 empty boxes so that tells me that 7+3=10. Turn the tablet upside down, what does this tell us about 10 now? 3+7=10
Guess What? One player secretly arranges some counters on a ten-frame. The other player asks questions that can be answered yes or no, trying to gain enough clues to work out the arrangement of counters, e.g. Is the top row full? Is it an odd/even number? Is there an empty box in the bottom row?
Image taken from Mathsbot.com
Dienes blocks are base ten materials that help pupils to represent numbers in expanded form. Two examples of virtual versions of Dienes blocks are linked above. Here are some suggested activities that could be explored using these virtual manipulatives:
Show me: Pupils use the Dienes blocks to visually represent some of the following numbers: numbers with the same digit in a different place (7, 70, 700 etc.), two/three/four digit numbers and numbers with 0 as a placeholder (307, 7,089 etc.). The following questions may be used to reflect on this activity: Show me 67. How did you build your number using the blocks? Did anyone do it a different way? Can we think of another way to say the number 67? If we put 0 in front of the two digits, in between the two digits or at the end of the two digits, would this change the number? Show me that number
More or Less: As an extension of the previous activity, pupils are once again asked to visually represent a number using the virtual manipulatives. Next, encourage pupils to show what this number would look like if it had 1 more or 1 less, 10 more/less, 100 more/less, 1000 more/less. Pupils then reflect on how this changed both the visual representation of the number and the number in standard form e.g. 67 changed to 77.
Place Mat (Notation board): A virtual place mat/notation board can be used for organising Dienes blocks into thousands, hundreds, tens and ones. This enables pupils to understand the links between the visual representation of a number and the number written in standard form. Pupils can represent a number by placing the appropriate digits into the correct columns and then record the number using words and symbols. This way, pupils are using the base ten name as well as the standard name for any number. For example, the number 546 in base ten language is five hundreds, four tens and six ones or 500 + 40 + 6.
Place Mat Activity:
The teacher chooses a number and displays an arrangement of base ten materials to the class using this virtual manipulative.
Pupils write this number down in base ten language (words and numbers) and in standard form. For example a pupil may write the following: The number teacher showed using Dienes blocks has three hundreds, two tens and 4 ones, this is 300 + 20 + 4 which is 324.
The teacher then changes one piece (the hundred, the ten or one), for example, change 546 to 576. Pupils then write this new number in base ten language (words and numbers) and in standard form.
This activity can be repeated in pairs/pods/bubble whereby one pupil completes the teacher’s role.
Rekenrek
Image taken from https://apps.mathlearningcenter.org/number-rack/
"The Rekenrek provides a visual model that encourages young learners to build numbers in groups of five and ten, to use doubling and halving strategies, and to count-on from known relationships to solve addition and subtraction problems" (Frykholm, 2008). Below are some suggested activities for using the Rekenrek. For further guidance and support in developing your pupils’ number sense, apply for school support at the contact us tab above.
Introducing the tool: Show the pupils a sample Rekenrek and ask them what they notice. Elicit that there are two rows of 10 beads and the colour of the beads change at 5.
Show Me(one row only): Invite the pupils to show you a certain number on the Rekenrek – “Show me 6 on the Rekenrek.” How did you find the 6? What do you notice about how far it is from 10, from 5, etc.
Show Me (using both rows): As above but this time they must use both rows to show 6. This creates an opportunity to discuss the different ways to make 6, 4+2, 3+3, etc.
See and Slide: Teacher displays a number of beads on the Rekenrek and challenges the pupils to display the same number using one or two moves. Question the pupils as to how they did it. E.g. 15 - I moved ten on the top row and 5 on the bottom - 2 moves!
Hundred Square
Image taken from https://www.abcya.com/games/interactive_100_number_chart
Once pupils have engaged in building the 100 square gradually, the following activities can be used to develop pupils knowledge of number relationships and positioning of numbers whilst encouraging the use of Mathematical language.
Missing Number: Remove some numbers from the 100 square. Pupils replace them and explain why they chose that particular number. You can remove random numbers, sequences of numbers or even all numbers.
Neighbours Number: Begin with a blank virtual 100 square. Highlight a number and ask pupils to identify the neighbouring numbers. Pupils should try several of these activities. Teacher questioning is very important for this activity. The questions posed should enable pupils to identify and discuss the relationships and patterns between numbers. Teacher: What do you notice about the number to the left/right/above/below/on the diagonal?
Guess My Number: Pupils use the virtual 100 square. Explain to pupils that you have written down a number between 1 and 100 and that they are going to try to work out what number it is by asking questions about it. As each pupil asks a question, the pupils can remove any numbers that they now know are not the correct number. Pupils should be encouraged to ask questions that reflect a range of understanding of numbers, for example, “Is it in the twenties?”; “Is it an even number?”; “Is it greater than 50?” This could also be played in pods or pairs.
Squares: Highlight a square on the hundred square (2 boxes by 2 boxes). What do you notice about the numbers that you have highlighted? Add the numbers in the opposite corners, what do you notice? Highlight another 2x2 square and investigate if the same pattern holds. What would happen if you highlighted squares of larger sizes? For another, more challenging version of this problem see Diagonal Sums at NRich Maths.