Bar Viz
Bar Viz A is the first of what will be a series of apps that use the Bar Model to represent a mathematical structure. The learner is asked to enter the missing value shown by a question mark (?) in both the diagram and the number equation.
Like all mathematical practice the learner should be at an appropriate level to access this and if in doubt parents should consult their child's teacher however because the app offers puzzles with smaller and larger values it could be appropriate from early Key Stage 2 (UK) to later Key Stage 3 depending on the confidence and prior attainment of the learner.
The simplest structure used is the additive, part-part-whole structure. The missing value could be either part or the whole and the diagram and number sentence are shown together to help the learner see the lnik between the two. It is also worth noting that the size of the bars correspond to their value as would be expected in a number line representation.
The second mathematical structure represented is a two-part-part style number sentence. This provides an extra challenge for the learner as they may choose to solve the puzzle by adding to find the total and then subtracting to discover the missing value. However it is worth exploring different strategies as some puzzles reveal alternative methods that may give the learner an extra "string to their bow" when solving other similar puzzles and more generally gain a deeper understanding of arithmetic as a result.
The multiplicative structure is also represented and the learners are again asked to enter the missing value which could be either the content of a bar or the number of bars, which distinguish between the multiplier or the multiplicand if you want to introduce the correct terminology. Alternatively, they may be asked to find the value of the complete bar or product of the multiplication.
At first glance this could be thought of a essentially a times table practice puzzle, however as before the bar diagram representation is shown alongside the number sentence. As such, the learner may develop a better understanding of the mathematical structure behind the number equation. Especially as a prelude to the next puzzle structure which combines both the additive and multiplicative in one.
This final structure is a useful pre-cursor to the simple linear equation format the learner will no doubt meet in Key Stage 3. And while the app uses a question mark (?) for the missing value rather than the usual algebraic letters, learners who are familiar with this kind of puzzle and the underlying structure should find the step to solving algebraic equations relatively straightforward.
As is often the case, practice and familiarity will develop confidence which in turn helps towards self-motivation and a desire to learn and practice more.
Further Bar Model Apps within the series will be produced soon.