Maths Mind Reading

How to use these cards!!!   For the classroom please make them large enough for all to see

  (Dont forget to put your magic Clock and hat on)

1.    Have your child or student to choose a number from 1 to 31, but keep it secret, or write it on paper and keep hidden

2.    Now ask them to point to the cards that their number appears on, still keeping their number secret.

3.    With a flourish of your magic Wand and "Abracadabra" Add, in your head, the first numbers on each card and give the answer to the child.
        If they chose 23 you will find 23 on Cards 1, 2, 3, 5.  
        The first numbers on each card are, 1 + 2 + 4 + 16 which add to 23!!!

4.     Repeat with another child or student!!!!

Please DO NOT tell them what you are doing.  The real joy for the children is to investigate and discover what you are doing.  They could also make their own cards.

For Older Children/Students:     Use these cards

Teachers/parents have you worked out how these cards are made?  If you can not work it out message me and I will give you some hints.  Again please dont TELL the kids, let them work it out for themselves.   A Hint: it is based on a number system smaller than our usual groups of 10!!

Palindromes

02 02 2020

0202 02 02

A palindrome reads the same forward or backwards. The second of February 2020 as written above was a Palindrome.

We usually look for palindromes in words: MUM, DAD, LEVEL etc but we can also explore them in numbers.

99 is a Palindrome as are 1, 2, 3, 4, 5, 6, 7, 8, 9, but we have a problem when we reach 10. In reverse this is 01.

But wait:  if we take 10 and then add its reverse 01  (10 + 01 = 11) we get 11 a Palindrome.

We call 10 a 1 step palindrome as it takes just one step to turn it into a palindrome

37 is not a palindrome so lets see what happens when we reverse and add:

37 + 73 = 110

110 + 011 = 121

WOW a two step palindrome

 

Most of the numbers from 1 to 100 can be turned into palindromes by reversing adding and continuing until a palindrome is reached.  Each time we reverse and add it is called a step.

Find all the 1 step palindromes, 2 step palindromes, 3 step palindromes and colour accordingly on the 10 chart below.  

Can you find any numbers that don't seem to be able to be converted into a palindrome?

Find palindromes for some larger numbers, what is the largest number of steps you can find for one number?

Write a sentence or phrase that is a palindrome

Read ROBERT TREBOR by Marilyn Burns in the book: Good Times: Every Kid's Book of Things to Do   ISBN-10: 0553011626    or ISBN-13: 978-0553011623

Teachers check out this link N-Rich Maths  a maths website from Cambridge University England. Great ideas for all  ages

Meaningful Contexts

The NZ Maths Curriculum states:  
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to: (then lists the Achievement Objectives)

What are Meaningful Contexts? 
Is the usual Maths Text (work sheet) activities meaningful for most students? whether it be 4 + 5 =  ? or use Pythagoras to find the length of the 3rd side of the triangle.  Apart from doing as they are told or pleasing me the teacher, is there a real reason for the students to answer?

To me a meaningful context is something that appeals to students whether it be cultural, imaginative, a challenge, a real life situation, something that really engages the learning and they see a reason for finding the answer/solution.

In a previous post "TwentyOne" I suggest the "Challenge to beat me" was a meaningful contect for many of the students I worked with.

Over the years I have seen so much "busy work' in maths that no wonder we produce so many people who dislike or "cant do Maths"

At one mini conference I attended the Manager of a large printing company, welcomed us and said "I admire you people with your interest in maths and science...  I just cant do maths!!"  At morning tea I challenged him and asked why he said that. In the discussion he revealed that he was an accountant and did budgets and kept records etc.  HE DID NOT EQUATE ACCOUNTANCY TO MATHEMATICS.  I suggest that is because he did not explore maths through meaningful or real life contexts!!!

I suggest that many of the measurement activities that we get students to do are often not motivating for them and they therefore do not learn the required objectives we had hoped.

    Is there a need for students to be measuring the netball court, when it is already marked out?

    Why do we ask students to measure the height of the door to the classroom?

I suggest that we need to look for activities that have a “realness” to them so that the students can see a reason for investigating and completing the activity and hence developing the skills of measurement.

Perhaps we need to rephrase the netball court in a different way,

    “There is a limited budget available for spending on court markings. 
    To help the BOT decide how much money is available we need to know how much it will      cost to repaint the netball court lines”

We now have a situation where there is richness to the activity rather than just taking the trundle wheel and measuring the lengths of the lines.

As a School Committee member, before ‘Tomorrows Schools’ I was asked to estimate the cost of repainting the school swimming pool.  
I felt that this was better done by the senior children as a ‘practical measuring activity.  
We, the School Committee, told the students the cost of the paint was and what area a litre could be expected to cover.  
The students had to work out the surface area and then decide on how many litres of paint and consequently the cost.  
The important outcome was that their maths was used to assist the Committee and the students actual saw the pool being painted!!!!!

The challenge for each of us is to find, WITH THE HELP OF OUR STUDENTS, interesting tasks that will help them achieve the desired learning outcomes.

Have you considered reading books like "Counting on Frank"   as a starting point for a maths investigation:  (Is Frank's investigation about Ball Point Pens still true?)



How many students in the class have attached ear lobes? and how many have unattached?



In Gulliver's Travels Gulliver's thumb was measured and from this one measurement the Little People made him a coat.  Would this be true today, How could we find out?


How much pocket money does each child get in the class?

What can you tell me about Kowhaiwhai Patterns?


In the Bible Goliath was described as being "6 cubits and a span". Would he fit through the classroom door without banging his head?

In the song "Twelve Days of Christmas" many things are mentioned.  How much would all these things costs?  check out this link 12 Days of Christmas

New class in 2020  (Year 4+) check in with me for an interesting "Trait" investigation with a Circular Graph

We Learn Maths By DOING

I often wonder if we play lip service to the way children learn.  If we spend time with pre-schoolers we see them constantly playing and through their play and questioning and interaction with the teachers the learn various skills and concepts.

Yet when we look at primary maths' learning there is often an emphasis on numbers and numerals. Yet these are quite abstract concepts.  I am sure we would not just a put a book of words in front of students and expect them to learn.

As a Maths Adviser to schools/teachers and then as a private consultant I encouraged teachers to use the following:

Do

Say

Write

When fluent with "Do" ask the students to explain what they were "Doing", When fluent with "Doing" then "Write" about what you said and did!!  This then leads to mastery of the concepts.


A couple of years ago I saw a FB post in response to  request for feedback about a Measurement Activity created by a Canadian Maths Teacher.  The response:
"This is a great measurement activity but we are an iPad school so it would be great if it could be created for the iPad"
To suggest that I saw RED was a bit of an under statement !  How does a children learn what a metre a cm, a gram, a kilogram, a litre etc through manipulating abstract concepts of electronic screens. They need to measure length, estimate mass if they are going to understand the concepts of measurement.


You probably are thinking, what brought this on Len?  This post on FB originally from Jo Boaler
It could be a great poster in every maths class and teachers staffroom

 

Some activities to get you started.

These could be arranged as Stations around the room for students to explore and complete.

Twenty One

Another Nim activity.

As an adviser/consultant I had this activity at hand(in my head as it does not need counters or pens and pencils)

Objective:     To be the last person to take away either 3 or 2 or 1 to leave zero

Players:         Two or two teams.  (when introducing the activity I would always play the "Class" or Group, so I was one team and the class was the other. This of course made it easier for me to win as a class would try numbers at random, with no clear strategy)

How:             First player starts by verbalising ("I will take away 1 and leave 20")
                      Second player takes away 1, 2, or 3  ("I will take away 2 leaving 18)
                      First player takes away 1, 2, or 3 verbalising and leaving the remainder
                      Continue until one player takes away 1, 2, or 3 to leave zero

Encourage:  The students(and yourself to find a strategy that will allow you to always win.
                            Does the first player always win?
                            Does the second player always win?
                            What is the last number that you must leave to always win?

Adaptation:  Start at Zero and be the first to reach 21
                       Take away a different set of numbers, e.g. 1, 2, 3, or 4?

Please Dont: Share your strategy, encourage the students to come up with their own.  This is the basis of Creativity, Investigations, Becoming Stuck and moving through, Problem Solving. 
                      As soon as two players know a strategy then whoever starts will control the game this is whn you use an adaptation.

When I was working in classes and schools as an adviser/consultant/teacher I would often use this activity as by doing it mentally as explained above helps mental agility with students.
At any break time of the next visit there would be queues of students wanting to play against me so that they "could win"  It often took a number of days before I came a cross a student who knew the strategy.

Yes:               We could show the working on the board, but this takes away the mental aspects and the strategy is much easier to see!
                      We could use a pile of 21 counters

Encourage Creativity and Investigations: STOP USING WALTS etc

This photo is self explanatory.  Whoever thought we should write WALT's,  Specific Objectives on the board, screen, before students working, must have been more interested in Test results than student's real learning.

See below for another post about Writing Objectives before a lesson:

Thanks to the person who shared this on FaceBook.

Writing Objectives A waste of time

Struggle/Being Stuck with Maths

I can remember seeing in a lecture room, at Auckland College of Education some years back, a wall poster along the lines of: STUCK, congratulations.  I just wish I could remember the rest but it nwas along the lines of "this is when the learning starts"

When I read the article below, by Jo Boaler, I thought I should share, because often as teachers we often try and make everything so easy we break math's learning into small steps, each step taking us towards the big goal. Is this really the way children learn best? (Most Text Books and Programs do just this!)

In the real world, outside the classroom, most of us learn best when we become STUCK, figure a way through and achieve what we wanted.

I would like to encourage all teachers to have activities available for all students to become STUCK and perhaps FRUSTRATED, so that REAL Learning can take place, and the student can feel real achievement in what they have done.

Feel free to share this article and perhaps join Jo Boaler's You Cubed email list.

                          Why Struggle Is Essential for the Brain — and Our Lives  
 
As parents and teachers, we do just about everything we can to make sure that children don’t struggle. It turns out we are making a terrible mistake. Research shows that struggling is absolutely critical to mastery and that the highest achieving people in the world are those who have struggled the most. The more I communicate this message to parents and teachers the more stories I hear of complete personal transformation.
Neuroscientists have found that mistakes are helpful for brain growth and connectivity and if we are not struggling, we are not learning. Not only is struggle good for our brains but people who know about the value of struggle improve their learning potential. This knowledge would not be earth shattering if it was not for the fact that we in the Western world are trained to jump in and prevent learners from experiencing struggle. 
 
“When students look at me and say: “This is hard,” I say, “That is fantastic.”
 
An international study of mathematics teaching found that teachers in Japan put their students in places of struggle 44 percent of the time in classrooms—they saw this less than 1 percent of the time in U.S. classrooms. What do we parents and teachers do instead? We jump in and show the way, offering steps to a solution to help save our students from struggle. This is in large part because this new science is not widely available and we are culturally trained to feel bad, and to rush in and help, when this is probably the last thing we should do.
The research on the impact of struggle turns out to help adults too—in all sorts of jobs. I interviewed sixty-two people for my new book, “Limitless Mind.” Many of them shared similar accounts of how they used to go into meetings afraid they would be found out for not knowing something. After learning about the importance of not knowing and of engaging in struggle they now proudly show up and say “I don’t know, but I will find out.” They display a mindset of discovery and curiosity, which has helped their lives in many ways.
Once we stop the charade of knowing everything, and embrace knowing less, with a willingness to sit with uncertainty, unexpected things happen.

When I was teaching middle schoolers in a research math camp a few years ago one girl stood out to me; she was nearly always wrong in her thinking, but she was always engaged, arguing her case, pushing to understand better. An observer of the class would have described her as a low achiever, but she improved more than any other of the 84 students we taught that summer. Her standardized test score in mathematics improved by 450 percent after 18 struggle filled lessons. Our messages to the students—that struggle would be valued and mistakes are productive—had helped her feel good about struggle and embrace it.
When I tell young learners that struggle and mistakes are the best times for our brains it is freeing. Students no longer give up on problems when they find them hard—they push through the struggle to the wonderful places on the other side. When students look at me with a puppy dog face and say: “This is hard,” I say, “That is fantastic. That feeling of ‘hard’ is the feeling of your brain developing, strengthening and growing”.
 
“We cannot achieve anything creative without being comfortable with mistakes and struggle”
 
In 2016, two young computer scientists rocked the world of mathematics by solving a previously unsolved math problem, an event that many described as audacious. The two young men reflected that it was knowing less that allowed them to solve the difficult problem. It freed their mind to think in better ways.
I am not arguing that knowledge is bad or knowing answers is not helpful. What I am saying is that knowledge is less important than a mindset of discovery and curiosity. We cannot achieve anything creative without being comfortable with mistakes and struggle—and we should all embrace times of struggle, knowing they are helping our brains. When we adopt a limitless perspective, approaching different jobs and conversations with a comfort with uncertainty and struggle, with a willingness to learn from others and with a flexible approach to problems, outcomes improve—in learning and in life.
Millions of students start the school year each year excited for all they will learn, but as soon as they struggle or see someone solve a problem with ease, they start to doubt themselves and mentally shut down. This starts a less productive learning pathway for them. Instead they should value the time of struggle and know that they are on their way to being better, wiser and equipped with a stronger brain. Getting answers right is OK, being stuck and finding them hard is fantastic.
 
Jo Boaler is the Nomellini-Olivier Professor of Education at Stanford, co-founder of youcubed.org and author of the new book “Limitless Mind: Learn, Lead & Live without Barriers.”