Problem Solving - How old are we?

      How Old Are We?

I am twice my brother's age and one-fifth my mother's age.

My dad is older than mum by half my brother's age. All our ages are whole numbers.
  

I go to school but my brother doesn't, yet.


How old are we?

Is there more than one solution?

Extension:

Can you create your own ‘How old are we?’ question for your class maths mate, your parents, or your teacher?

Problem Solving - Vehicles in the Car Park

Vehicles in the Carpark

In the staff carpark there were only 12 vehicles, but 40 wheels.

What type of vehicles, and how many of them, might have been in the carpark?

Are there other possible solutions using different vehicles?

Problem Solving - Tug of War

Tug of War

Five oxen are as strong as eight donkeys

 

An elephant is as strong as one ox and four donkeys

  

Who will win if an elephant and four donkeys verses 5 oxen?

SHARING YOUR MATHS THINKING

Is there another way you could solve this problem?

Share your maths thinking with a partner. Were you able to explain your strategy clearly, so they could understand?

Record your thinking, so others can understand.

Problem Solving - Cups of Tea

Mrs Brockie's Tea Cups

Mrs Brockie bought some new cups and saucers.

There are four sets: a set of white, a set of red, a set of blue and a set of green. In each set there are four cups and four saucers. So there are sixteen cups and sixteen saucers altogether.

Just for the fun of it, you decide to mix them around a bit so that there are sixteen different-looking cup/saucer combinations laid out on the table in a very long line.

There are these sixteen different cup/saucer combinations on the table and you think about arranging them in a big square. Because there are sixteen, you realise that there are going to be four rows with four in each row (or if you like, four rows and four columns).

Place these sixteen different combinations of cup/saucer in this four by four arrangement with the following rules:

1. In any row there must only be one cup of each colour;
2. In any row there must only be one saucer of each colour;
3. In any column there must only be one cup of each colour
4. In any column there must be only one saucer of each colour.

There are a lot of different ways of approaching this challenge.

Track the patterns:  Draw coloured lines to track the same coloured cups (or saucers). What patterns are you noticing? How could this help solve similar problems with larger numbers, e.g. 5 sets of 5 cups and saucers, etc.

Extension

What if there were coloured teaspoons to add - same rules!

What if there were coloured cupcake as well as the teaspoon. Is it still possible?

The Power of the Words 'Not Yet'

Carol Dweck is a Professor of Psychology at Stanford University. Her main research interest is in motivation, personality and development. Her research looks at how our mindsets, and the way we view events in our lives, impacts on our intelligence.

"In a fixed mindset students believe their basic abilities, their intelligence, their talents, are just fixed traits. They have a certain amount and that's that, and then their goal becomes to look smart all the time and never look dumb. In a growth mindset students understand that their talents and abilities can be developed through effort, good teaching and persistence," (Dweck, C., 2012).

Carol Dweck researches “growth mindset” — the idea that we can grow our brain's capacity to learn and to solve problems. In this talk, she describes two ways to think about a problem that’s slightly too hard for you to solve. Are you not smart enough to solve it … or have you just not solved it yet?

Struggle is Good

When you struggle with maths you are growing your brain!  Research has shown that when people struggle, think hard, problem solve, etc., their brain neurons make stronger connections.  That is, your brain muscle grows!  Just like other muscles in your body, if you work out, practice, and train hard - your muscle will grow. So, next time something seems hard - persist and grow your brain!