Head of Preparatory School
Prep Maths Week
It has been a momentous week full of number games, problem-solving and lots of exciting talk about Mathematics. There has been an animated buzz around the classrooms as students played tug of war on number beads, ordered two- and three-digit numbers on number snakes and solved daily problems inside and outside the classroom. You can read a message from Ciara Harding, Junior Campus Numeracy Specialist at the bottom of this article.
Ysafety Workshop
Thank you to families who came to the Junior campus ysafe workshop this week. David shared important and relevant information on keeping our children safe on the internet. This message was then shared with Years 1 and 2 later in the day using age appropriate language and examples.
Please click on the link to access the Redlands Cybersafety Hub.
Redlands Cybersafety Hub
Jeans for Genes Day
Friday 5 August
Jeans for Genes Day is an annual fundraising campaign which is aimed at supporting families and individuals affected by genetic disorders. The campaign raises money through a variety of activities in order to provide grants to organisations which transform the lives of children living with genetic disorders. This year the Prep School and Redlands House students can support this cause by wearing their jeans or mufti attire to school on 5 August. Those who do participate are asked to donate a gold coin.
Term 4 Departure Notice
The final date for giving notice of depature during or at the end of Term 4 was last Friday 22 July. Families who are planning on leaving the School during or at the end of Term 4 and haven’t yet given notice should email registrar@redlands.nsw.edu.au by 4pm tomorrow, Friday 29 July, to avoid fees in lieu.
Reduce, Reuse, Recycle, Rethink
This term, Kindergarten is inquiring into the unit titled ‘Reduce, Reuse, Recycle, Rethink’. The children are exploring the material world, focusing on the observable properties of materials and how they can determine a product’s use.
Throughout the unit the children will be designing and building various items. This commenced last week with Kindergarten being provoked to design and build their own pair of binoculars. The children brought in old cereal boxes, tissue boxes etc and got making. We then used our binoculars to go on a scavenger hunt and look for different types of materials around the school.
In the coming weeks, Kindergarten will continue to be challenged to think responsibly about our environment and how we can repurpose old materials. We would like the children to recognise the power of our community and we are asking for families to donate any old materials that can be repurposed. This could include off cuts of fabrics, wool, bottle lids/tops, thin plastics, buttons, CD’s, cork products, egg cartons etc. There will be a tub placed in Prep Reception from Friday 29 July until Friday 12 August for you to drop off any items.
We thank you for your assistance and look forward to sharing our creations with you.
Jump Rope for Heart
We are excited to announce that Redlands Prep are participating in Jump Rope for Heart this year. This is a fantastic physical activity program and fundraiser by the Heart Foundation.
By participating in Jump Rope for Heart this term, we’re expecting to get our students moving. We’ll have ropes available at the Friendship bench during break times and will be encouraging everyone to help raise funds for lifesaving research and support programs.
Over the coming weeks your child will learn new skills, increase their physical activity, and learn about heart health. Before school, as well as during recess and lunch, the students will have time to practice, have fun and show off their new skipping skills to their friends.
When you register your child online you’ll gain access to additional skipping resources to help give your child a great reason to get away from the screens and get outdoors. If you choose to register your child online you and your child can:
- Track skipping skills progress and earn virtual badges along the way
- Access additional skipping resources
- Post updates to your page so family and friends can follow their progress
- Easily raise funds online
Please know that there is no pressure to register and every child in Prep will still have access to skipping ropes and the physical fun they bring at school.
Prep Maths Week: Ciara Harding, Junior Campus Numeracy Specialist
During Maths Week, I thought it would be an excellent opportunity to share some research about an important area of mathematics – 21st-century addition and subtraction. I reflect on my experiences as a primary school student, sitting on the floor watching my teacher recite how to set up, organise and solve addition algorithms (figure 1) on the chalkboard. Copious amounts of practice followed to ensure the algorithm was drilled into my brain. Despite this experience not being too long ago, research into addition and subtraction has considerably changed over the past few decades.
Figure 1: Standard Written Algorithm for Addition
Addition and subtraction are an important part of the primary mathematics curriculum. To help students become successful and competent 21st-century citizens, students need to have a flexible understanding of numbers and a range of addition and subtraction strategies. In essence, rote teaching the written algorithm is not the best practice to help students as they move through higher levels of mathematics education.
The Australian curriculum (and new NSW K-2 Mathematics curriculum) states that students should engage in solving addition and subtraction questions/problems with numbers appropriate to their age and year level. In Kindergarten, numbers focus between 0 and 10 and require lots of concrete materials and modelling. In Year 1, students continue modelling addition and subtraction situations and develop various strategies to solve problems between 0 and 30. In Year 2, students progress to hone both written and mental strategies to solve two-digit addition and subtraction problems effectively. I cannot express enough the importance of not moving too quickly to increase numbers. Kindergarten students should focus on understanding number bonds (addition pairs) for all numbers between 0 and 10. Similarly, Year 1 students should aim for mastery of addition and subtraction between 0 and 30 rather than try to work with all two-digit numbers.
Flexible addition and subtraction methods involve separating (decomposing) and combining (putting together) numbers in a variety of ways. Flexibility requires a strong understanding of place value (the base-ten structure of our number system) and the various properties of addition and subtraction (e.g., the commutative and associative property). Whilst the standard algorithm is an elegant strategy (please note I am not saying to completely abandon the use of the algorithm, rather I encourage students to build a repertoire of strategies), research has shown that students view the algorithm as a procedure rather than think mathematically about the numbers and the operation.
In many situations, alternative strategies (also referred to as invented strategies) are easier and faster than the standard algorithm. Think about the following subtraction 100 – 25.
Some students may resort to the algorithm, but an inaccurate understanding of the algorithm structure or the procedure can lead to common errors, including:
Reversing the subtraction: In this example, the student struggled with the digit 0 being at the top of the algorithm. They reversed the order and subtracted 0 from 5 (instead of 5 from 0).
Errors regrouping: In this example, the student started to regroup but did not link place value to change 10 tens to 9 tens.
In both examples there were limited connections to place value. If a student approached this problem without using the algorithm, they could have employed several different strategies including
– Jumping back 2 tens then 5 ones.
– Subtraction in 2 parts. 100 – 20 = 80. 80 – 5 = 75 or 100 – 5 = 95. 95 – 20 = 75
– Overshoot subtraction, then come back. 100 – 30 = 70. 70 + 5 = 75
Some strategies to help students develop a broad understanding of addition and subtraction include:
Single-digit addition: 58 + 6
- Using decade numbers as benchmarks. To effectively solve 58 + 6, students can use 60 (the nearest decade) as a benchmark to make the addition easier.
58 + 6. Add 2 to 58 to make it 60 then subtract 2 at the end (to avoid changing the numbers). Flexibility means students can mentally manipulate the numbers without changing the overall quantity in the equation – if 2 is added at the start, then 2 must be subtracted at the end.
58 + 6 = 60 + 6 – 2 = 64
- Using number facts. To quickly solve 58 + 6, students can separate the two-digit numbers into its place value and add the numbers separately.
58 + 6. Split 58 into 5 tens and 8 ones. Add 8 ones and 6 ones (14 ones = 1 ten and 4 ones) back with 5 tens. Place value understanding is an easy way to partition (split) numbers and add according to their place value. Flexible transitioning between place value, e.g., 14 ones is the same as 1 tens and 4 ones, helps students group numbers to and thus add quickly.
58 + 6. 8 + 6 = 14. 14 + 50 = 64
Adding two-digit numbers: Some students went on an excursion. There were 46 girls and 38 boys. How many students on the trip?
- Place value split strategy addition: Split the number into its place value. Add tens, add-ones then combine.
46 + 38. 40 + 30 = 70. 8 + 6 = 14. 70 + 14 = 84.
- Place value two step addition: This time, rather than split both numbers. Use the first number as the starting point. Split the 38 into 3 tens and 8 ones. Add on tens. Then add ones.
46 + 38. 46 + 30 = 76. 76 + 4 + 4 = 84.
Students may jump three tens rather than add 30 in one go. Another important idea is splitting + 8 into + 4 + 4. This is effective because 76 + 4 = 80 means students can connect their combinations to 10 number facts.
- Add an easy number (move some to make tens): Take 2 away from the 46 and put it with the 38 to make 40. Adding 40 is easier than adding 38!
46 + 38 = 44 + 40 = 84.
- Add an easy number then compensate: 38 is close to 40. Add 40 then compensate back by subtracting 2 at the end.
46 + 38 = 46 + 40 = 86 – 2 = 84.
Subtracting two-digit numbers: Jessica counted all of the teacher’s pencils. Some were sharpened and some were not. She counted 73 pencils in all; 46 pencils were not sharpened. How many were sharpened?
* Before exploring different strategies for two-digit subtraction, I wanted to share the think-addition strategy. A powerful way to understand subtraction is for students to make the connection to addition (think-addition). For 38 – 19, the idea is to think, ‘How much do I need to add to 19 to get to 38?’. Below are some ways to use addition to solve the above problem.
- Add tens to get close, then ones: 46 and 20 make 66 (30 is too much). Then 4 more is 70 and 3 is 73. That’s 20 and 7 = 27
73 – 46. 46 + 20 = 66. 66 + 4 = 70. 70 + 3 = 73. The total added is 27.
- Add tens to overshoot, then come back:Adding 30 to 46 then coming back to 73.
46 + 30 = 76. 76 – 3 = 76. 30 – 3 = 27. Added 27.
- Add ones to make a ten, then add tens and ones: 46 and 4 is 50. 50 and 20 is 70 and 3 more is 73.
46 + 4 = 50. 50 + 20 = 70. 70 + 3 = 73. Total added is 27.
Take away strategies can also be employed to solve two-digit subtraction.
- Take away tens, then subtract ones. It is important students do not just take away from the ones place value then take away from the tens place value because sometimes more ones need to be taken away. In this example, if a student looked exclusively at the ones place value, they cannot take away 6 ones from 3 ones. To avoid this, encourage students to subtract using two steps. First, subtract the tens, then take away the ones.
73 – 46. 73 – 40 = 33. 33 – 3 = 30. 30 – 3 = 27.
To avoid errors, students should always bridge to 10 (stop at the decade). Rather than complete 33 – 6. Students should subtract 3 first to arrive at 30. Then subtract the remaining 3 to get to 27.
Something I have found highly successful when teaching addition and subtraction is encouraging students to use more than one strategy. If a student accurately answers a question, before moving on, I always say, ‘Is there another way you could have solved this? Show me?’ Asking students to find multiple solution pathways means they have to think flexibly about numbers and manipulate them (partition) in different ways to add/subtract.
Before concluding my commentary, these strategies (and the subsequent conversations about addition and subtraction) can grow organically from real-world situations. If you are at the shops and you buy an item for $6 and pay for it with a $20 (in a pre-COVID world), stop and ask your child what the change would be. You could time the commute home from school. It took 16 minutes on Monday afternoon but on Tuesday, there were roadworks so it took 38 minutes to get to school. What was the difference between these times? Making mathematics meaningful, relevant and purposeful is the best way to help students engage in deep thinking. Maths is entrenched in our world – organising a budget, planning holiday expenses, making sure the beautiful new couch fits into the space and even ensuring money is left on opal cards. Talking about numbers with children is a great way to help them see mathematics as a powerful tool for creative thinking, problem-solving, global understanding, and communication.
Don’t forget to come and join us after drop off on Friday morning to play some maths games with your children in classrooms!
Mrs Ainslie Breckenridge
Head of Preparatory School
abreckenridge@redlands.nsw.edu.au
9968 9848
