This blog aims to record and reflect on ways I demonstrate knowledge and application of Our Code, Our Standards as outlined by the New Zealand Education Council. This blog was created in 2018 and the intention is for it to continue to be used in years to follow.
Manaiakalani Mathematics Practice Intensive - Day#4
I almost didn't make it to today's session, so I am really pleased that I did. One look at the agenda and I was sold. I was particularly interested in fractions and place value.
Matauranga Site - Have a look at this site to get ideas for create and share opportunities. Google Vid - I need to use this more in class. Ensure that ākonga are using their own voice to share what they have learned.
We need to ensure that online apps are not just 'playing'.
Choral Counting
Talk is so important in learning. We can use Ground Rules for Talk and Talk Moves. Talk Moves is probably something I need to include more.
Choral counting is about recognising patterns and explain reasoning.
Choral Counting Key Concepts
Make sure you have space to record noticing and wonderings. I like "Let's prove it". The video shared was of Elena is a Class On Air clip, which would be good to look at again.
Prompts for Choral Counting
What do you notice? What do you wonder?
What do you think will come next? How do you know?
Can you predict a number further along in the count? Can you prove it to us?
Can you describe a rule for this count or pattern?
What do you notice about the digits in each place value as we count?
How is this count similar to or different from the last one we did?
What would happen if we started at a different number?
What if we counted backwards? What would the pattern look like?
Is there a number we will never say in this count? Why or why not?
How could you tell if a number belongs in this count or not?
If a number is covered, can you figure out what it is? How?
Do you see any diagonal, vertical, or horizontal patterns?
Are there any repeating groups?
Choral Counting Tasks
Place Value
We need multiple opportunities to use words to help it become part of our vocabulary.
Having a visual of the definition would be great for learners to gain a better understanding of key vocabulary.
Math Dictionary is a helpful tool as there is a lot of mathematical vocabulary.
There is quite a demand on our ākonga, so we need to gap fill and also teach to their level.
The place value materials are important to have and use with our ākonga.
Zero
Zero is a very unique number because it serves both as a number and as a placeholder in our place value system.
Zero as a Placeholder indicates that a particular place (such as tens or hundreds) has no value. For example, in the number 306, the zero shows that there are no tens. Introducing this concept early when teaching place value helps students understand the structure of our number system and is essential for reading and writing numbers correctly. Use manipulatives and clear language to teach this!
Zero as a Number represents a quantity of ‘nothing’ and is fundamental in mathematics, used in various operations and calculations. While introducing zero as a number can be abstract, especially for very young children, research suggests that children can start to understand zero by around age 4 or 5. This understanding deepens with more mathematical experience. It’s important to introduce zero in contexts that make sense to children and to use concrete examples and manipulatives.
Important to use concrete manipulatives and language to explain and represent Zero as a number and as a placeholder!
- Counting Blocks or Cubes and Dot Cards (subitising in the new curriculum), include a card representing ‘zero’
- Number Line, Ten Frames, PV blocks and PV houses and charts
Make sure we show zero as a number and a place holder.
Concrete, Pictorial, Abstract
This slide, which I made a copy of, will be so helpful for my teaching and for my team.
I love the Canva board, particularly because it is the digital tool that my class are going to become experts in using.
My next step is to make a copy of the place value task board and have this available for my kids. (I wish I done this in Term One when my focus was on Place Value. I think I would do a much better job now).
Rational Numbers
A sub strand within number. When getting students to use the math dictionary, make sure they are writing things in their own words, so actual understanding can be shown.
Effective Teaching of Fractions
Link fractions in real life contexts.
Critical thinking around the idea of 'bigger half'. Relate to sports, telling the time, baking etc.
By the end of Phase 2:
Fractions represent parts of a whole (division of numbers) Convert between mixed numbers and improper fractions Simplified fractions have no common factors Decimals and percentages are special types of fractions (denominators of 10 and 100).
Instead of using 'out of', use 'of'.
Be explicit when naming the parts of a fraction. Start with the denominator.
Teaching and learning about fractions can be difficult. There are misconceptions and difficulties in understanding. I noticed this when we did iKan.
Again, some fantastic content that I want to come back to.
Fractions as Operators
I like the term Mathematising. With any problem, mathematise it. What is the equation and what is it asking me to work out. Use addition, multiplication and division.
When getting ākonga to work independently, make sure they have good foundational understanding of the concepts and that misconceptions have been clarified.
Decimals and Percentages
Relates to number structure, relations. Read the whole number part first and then the fraction. Once the students have good understanding of the decimal place value.
Decimals, fractions and percentages are closely related.
Learners need to know key fraction-decimal-percentage equivalents to use as benchmarks.
Where did out decipipes get to? Make and compare decimal numbers.
Integers
An integer is a number with no decimal parts. Includes numbers including zero and negative numbers.
A big takeaway for me today is to use models and more visual representations as well as using materials.
I feel like I need to dedicate some time to go through slides and catch up on my mahi. I would also like to explore some of the sites that I have been introduced to.
I am so grateful to have a student teacher with me and I will work with her this week on our planning for the next fortnight. It will be good to be able to talk through the content that we have covered.
