It’s been a short while since I’ve posted one of these, so let’s hop right in. For this post, I will be using a slightly different format to highlight some of the resources that I found to be interesting, as well as add my thoughts and some suggestions.
Stage 4: Fractions
Get to 10 or Get to 100 by Clio Stearns
- Requires dice with mixed numeral faces. In pairs, students take turns rolling 2 (or more) dice and record the sum on a sheet. The goal of the game is to get as close to a total of 10 (or 100) without going over.
- The key focus of this activity is developing students’ skills in adding together mixed numerals. I think this would work well as an orientation activity.
- It would require a lot of effort, but I think the dice with mixed numerals should be different to each other (to ensure there’s enough variety in the sums); you could also design ‘challenging’ dice that use uncommon denominators (e.g. 1 5/11).
- If all the students use the same dice, it may be interesting to collect results from everybody and process the data via Excel.
BONUS TOOL: Roll The Dice
- Roll the Dice allows you to virtually roll any regular dice (including d4, d6, d8, d10, d12 and d20), as well as browse any of the custom dice made by the RTD community (be careful about browsing the custom dice list in class).
- You can also create your own custom dice that you can pair with activities or games that you have found or created for your students.
- For example, in the Get to 10 (or 100) game, you can create custom dice with mixed numeral faces, such as the one I’ve made here.
- I would recommend using improper fractions instead of mixed numerals as they are easier to read and require students to do extra processing; additionally, you’re not restricted to only 6 faces, you can add as many as you want.
BONUS ACTIVITY: How Close to 100? by YouCubed
- A game similar to the one above; this one makes use of dice and arrays.
- Students are given a pair of dice and a grid of 10 x 10 squares. In pairs, students take turns rolling the dice, then draw a rectangle using the numbers that come up as the dimensions.
- For example, students who roll a 3 and 5 are instructed to draw a 3 x 5 rectangle in the grid, then afterwards record their results as a number sentence.
- You could get students to keep a running total of the fraction of the grid their arrays have covered (requires basic summing).
Multiplying Fraction Array by John Ulbright
- This GeoGebra file also makes use of an array approach to visually demonstrate how two fractions are multiplied together.
- It works pretty well for simple fractions (small denominators), but becomes impractical to use for complex fractions.
- More specifically, the grid doesn’t scale up when the denominators become large, so the grid lines increase in density (I would not use any denominators larger than 25).
- The other included GeoGebra file works for mixed numerals, however I think this only works well with narration or teacher explanation to accompany each step.
Stage 4: Decimals
Fraction Decimal Percentages from NRICH
- Basic game where students pair together the equivalent fractions, decimals or percentages.
- There’s a tiny trick in the activity where students have to recognise the difference between recurring and terminating decimals, and how that connects to equivalent fractions and percentages.
- This activity would also make a great orientation game, or something to do at the conclusion of a lesson.
- Make sure you also give students the opportunity to create their own set of cards for their peers to solve (you could give them blank paper or small whiteboards to write on).
Decimal Ropes from Maths300 (requires login)
- Another simple activity that includes students using pegs to (approximately) mark out decimals (e.g. tenths) on a length of rope, then folding the rope in different ways to create fractions.
- For further details about the activity, visit the Maths300 website; there’s a whole lesson plan available using the rope, as well as computer simulations.
- A key strength of this activity is its hands-on nature and its testing of students’ estimation skills (e.g. roughly how far along this rope is a quarter.
Place Your Orders from NRICH
- Note: This is more of a transition activity rather than one solely focused on teaching about decimals.
- This warm-up activity is intended to re-introduce students to different orders of magnitude and types of quantities, such as distance, time and speed.
- What I like about this activity is that it requires students to use their estimation skills; if students don’t have a frame of reference for any of the options, then that creates an opportunity for the class to do experiments or research (or for the teacher to provide additional information).
- Students could also be tasked with designing their own challenges (that students can feasibly estimate or otherwise research).
Woolworths Problem by Matthias Sender
- This is included as an example of what I think should be used more often in Mathematics lessons: real-world examples with accompanying images of teachers (or others).
- In this example, an individual wants to determine the cost of purchasing less than a kilogram of lemons, where the cost is $3 per kilogram.
- What might be interesting: creating a video of yourself purchasing items (that are $x/kg) at a grocery store, and pausing the video before getting to self-checkout. Get students to work together in groups to determine the cost before playing the rest of the video.
- You could also throw students off by adding last-minute items (like an additional fruit or vegetable), and get students to adapt their working out to accommodate the new item.
Stage 4: Percentages
Ordering Percentages by Stefan Sender
- This activity requires simple setup: write down a series of fractions, decimals and percentages (between 0 and 1) on sticky notes or small pieces of paper.
- Provide students with the set of numbers and instruct them to arrange them from smallest to largest (similar to a number line).
- Use different coloured sticky notes to differentiate between fractions, decimals and percentages (e.g. red, orange and white as seen in the example).
- Optionally, you could provide students with sticky notes for them to write equivalent fractions, decimals or percentages to ones that are already sorted (e.g. 0.8 and 0.80).
Real-World Examples collected by Stefan Sender (see below)
- For this final section, I will be focusing on examples of percentages that can be found in the real-world or online.
- This website contains examples of everyday percentages, including those about discounts, nutritional information and battery life.
- Here are another set of statistics and infographics, many of which contain percentages that students can use for interpretation and processing.
- Included on Sender’s website are examples of nutrition panels (Weet-Bix, Chicken Stock, Protein Powder), as well as statistics related to the environment and global energy usage.
- Similar to what Sender has done, consider taking photographs of household products if they have percentages listed, and encourage your students to do the same.
- Percentages can also be found in the Financial Mathematics substrand, for example: interest rates, profits, commissions and appreciation/depreciation.
BONUS: Choose Your Own Statistics by Splash ABC
- This website allows you to view and create infographics of different statistics, such as demographics, life expectancy and weekly wages.
- You could use this to create sets of information for students to interpret and process (combining the Percentages topic with Data Collection and Representation).
STEM Vault 