Learn by Doing

Mathematics Lessons for Remote Learning

Teacher Resource

Target: Y7, 8, 9, 10 –NZC Level 3/4

Topic: FAT LESSONS – For Teachers

Starter – Odd One Out

logical

strategic

critical

creative

The idea here is to select the odd one .

I choose __________ because _____________________

Learn by Doing

THE DEEP UNDERSTANDING OF TEACHING

· Enabling others to know and understand, to connect concepts logically, to be creative and critical, and to communicate effectively in order to make sense of the world around us and solve problems encountered.

FAT LESSONS

Overview

Creating an engaging lesson for a selection of students is the daily problem for every teacher. There will be better descriptions of Deep Understanding than the above but I can work with that one. Too many lessons are driven by a worksheet or a textbook. These things are what someone else thinks is how and what to learn. There is a better way to create learning that is more satisfying and purposeful to both student and teacher. This is what I call “FAT LESSONS”.

The Starter

Teachers are usually informed of a topic or part of a topic, idea, skill or knowledge that is deemed to be important or seen as a need for a student. This can happen by reading the curriculum or a scheme, or by observing and noticing gaps and need. Iprefer a more designed approach and in my learning area mathematics I am blessed by a logical mind and a logical system of knowledge. I also notice and listen and from that information deduce need that may not be in any logical order or even in the curriculum.

What ever happens a teacher decides that a lesson will be about a particular idea, knowledge or skill.

For example, I notice most of my students are not very consistent plotting points and get coordinates mixed up, do not see patterns, use incorrect mathematical language, do not use mathematical equipment appropriately and are not very good problem solvers. They prefer to be told what to do and are quite happy to do almost nothing and/or listen to music.

The Entree

The idea then forms that I will design a series of lessons that involve points on a Cartesian Plane, patterns of points, some fun activities with points, some problems that can be solved using this knowledge. My lessons are for a Year 9 class of mixed gender and ability who have 5x60 minutes class periods in a day at school and a series of maths classes every week. I start with a mind-map sketch of concepts.

I am not thinking of what or how at this stage. I am just tapping into my curriculum knowledge, my mathematical knowledge, my previous experiences of what works with young minds, a desire to make students think and create some fun. I am playing. I am playing with ideas. This is the creative brain working.

The Main

A logical seqence of development starts to form in my mind as I engage with the problem. I am constructing knowledge and logical thought at first, then adding some patterning and colour. I want to explore relationships and shapes. I can challenge a mind here. A game is needed to steady the ship and have fun. Can angle be introduced or reviewed as well?

1. Revise Number Lines and the sets of numbers N, W, I and R as starters. I need to make sure getting bigger and smaller is known and that is less than , and is greater than . Signed numbers and where to put the sign. [the signs here should all be superscripts before the number]. Practise drawing a numberline and placing a variety of numbers on it. Include zero. Should be very straightforward!

2. A little chat about Rene Descarte. https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes

Rene was a deep thinker and in 1637 published the idea of crossing two number lines at right angles and so creating what became known as the Cartesian Plane. This allowed pictures or graphs of relationships to be visualised and is a widely used tool by every mathematician today. Hence it’s importance in learning mathematics. Point out the modern language names of x-axis, y-axis, origin, linear scales and increasing up and right. It could be homework to search for the historical names and read more about this amazing person and life when he was alive.

3. Practice drawing a Cartesian Plane like the one shown here.

Notice the numbers are numbering the lines not the gap! 0 marks the origin for both number lines. The arrow shows increasing x and increasing y. We can skip number the axes (plural) and count in 2’s or 5’s or even 10’s. When we have all drawn 2 or 3 perfect examples we move on!

4. Point plotting. All points have the order (x, y). They are called ordered pairs. We locate the point (2, 3) on the plane by moving across 2 on the x-axis and moving up 3 on the y axis.

Now locate (-3, 1), (-1.5, -2.5) and (0, 0). Toss a dice to generate the numbers. Give the students a red die and a white die. Red could be x and White could be y. A coin could be used to get +ve and -ve. Plot 20 points!

5. What Shape is This?

(a) Plot these points and join them with a line. (2, 1), (5, 1), (5, 6), (2, 6). What shape am I?

(b) Plot (12, 0), (4, 5), (-4, 5) and what shape am I?

(c) (-2,2), (-2, -2), (-1,-2), (-1, 1), (1, -2), (2, -2), (2, 2), (1, 2), (1, -1), (-1,2) and back to (-2, 2). What am I?

(d) Draw the rest of the logo above and record the list of points in order!

(e) Give your list to a buddy and have them, check your points!

(f) Code this cat!

and draw your own!

6. Battle Ships

Cut out the two boards. The idea here is to label the squares (battle theatre) with letters to show where you put your fleet of ships. Your buddy does the same. Do not show each other!

Turns to name squares on the enemy battle theatre. “B5”. This is like dropping a bomb on that square and anything under it is destroyed. You have to say what has been hit! “You just hit my aircraft carrier!”. Ships can be vertical or horizontal. Person who annilates the other person’s fleet wins. It is a good idea to keep a list of what you have called.

Extensions. You can use diagonals, add some mines, move your subs, use a nuclear bomb that wipes out a 3x3 grid.

Notice the difference in naming used here. The gaps are named and letters are used.

The Dessert!

And I think that will do for now. I will leave the “relationship is a set of ordered pairs” idea for another day. This is where we make a table, use an equation, draw a graph and play with these three ideas making connections in any way. There are straight lines, bent lines and graphical solutions, less than and greater than to explore. Another day!

The Meta-Cognitive Overview

The creative brain needs no shackles and at first ideas flow steadily. For the Starter and Entree really good advice is to do this with a buddy and have some fun bouncing and recording ideas. Use colour. Use pictures. Make a mess! It will all congeal.

Starter – Odd One Out

logical

strategic

critical

creative

The idea here is to select the odd one .

I choose __________ because _____________________

Any answer here! I would always choose creative because it is where I get ideas.

Journalling

Today I learned ________________________________________________________________

And I would like to know about ___________________________________________________

Comments

Make any comment you feel like making here.

Math Language: List all the math words you can find in this document and write what you think it means beside the word. Eg subtraction means to take away or to find the difference. Keeping a list of these words is a very good idea.

Students and teachers are welcome to email jimhogan2@icloud.com with comments. This was a starter lesson that could be given to a NZC Level 2 or 3 student for some placevalue learning and revision. Students should select a set time each day and perhaps using the timer on a cell phone set 45 minutes or so to learn and practice mathematics. Keep trying on problems and expect to struggle. Persevering and struggling are great competencies to develop. You can learn more about these from https://www.youcubed.org/resource/growth-mindset/. We have a great math website in Nzwith a special resource called e-AKO https://nzmaths.co.nz/information-about-e-ako-pld-360 .

Teaching is an artform