Mathematics

Open-ended Challenging Tasks

Challenging tasks are open-ended, thought-provoking mathematical problems which support all students to use their mathematical knowledge and adopt a variety of strategies to solve the problems. The tasks are challenging and engaging and encourage students to problem-solve and justify their thinking. 

Over the past few weeks, challenging tasks have been used to encourage the mathematical thinking of students, particularly in Year 3-6. 

Challenging tasks requires students to persist and show grit - they will generally take students more than 10 minutes to solve - especially if they are able to find more than one answer! 

In today's Newsletter, I have included two problems which you may like to investigate with your child. Remember the important part is to explain their thinking and strategies - not just the answer. The suggested year levels are a guide. 

*Credit to Russo & Russo for the ideas.

Football Fanatic

Foundation - Year 2: 

In the first quarter of the 2017 AFL Grand Final, Richmond scored 15 points and Adelaide scored 26 points. What are the possible combinations of goals and behinds? Remember a goal is worth 6 points and a behind is worth 1 point. 

Dustin Martin won the Norm Smith medal for the best player on the ground. He had 29 disposals. How many kicks and handpasses might he have had? 

Year 3 and 4

Mrs.Sbizzirri watched a re-run of an AFL match. In the game, Richmond won by 48 points. 

What are some of the possible totals that each team may have scored? Find as many possibilities as you can. 

The actual total number of points for both teams combined was 168. 

Can you work out how many points each team scored? 

Both teams scored 12 behinds, how many goals did each team score?

Year 5 and 6

I went to support Richmond on Grand Final day - along with 100,020 other football fans. However, not everyone wanted Richmond to win. One-fifth were pure footy fans - they were neutrals who weren't supporting one side or the other. Of the remaining fans, there were three times as many Richmond supporters as Adelaide supporters. How many Richmond fans were there?

Harry Potter-inspired Mathematics!

Foundation - Year 2

Professor McGonagall, who is in charge of Gryffindor House, thinks that students make too much noise when lining up for lessons. To cut down the chatter, she lines up students boy-girl-boy-girl (and so on). If Hermione (who is a girl) is the 1st student in line for lessons, will the 6th student be a boy or a girl? Will the 11th student be a boy or girl? What about the 20th student? 

What would happen if Professor McGonagall changed her pattern? 

Year 3/4:

In a game of Quidditch, a team scores 10 points when they score a goal with the quaffle and 150 points when the Seeker catches the snitch. 

Despite scoring 17 goals with the quaffle and Harry catching the snitch, Gryffindor still lost the match to Slytherin by more than 100 points. 

How many quaffle goals might Slytherin have scored? What might have been the score in the game?

Year 5/6:

The Weasley family includes 7 siblings separated by a total of 11 years. In order of their ages, 6 boys (Bill, Charlie, Percy, Fred, George and Ron) are followed by 1 girl (Ginny). Fred and George are twins. All the boys are at least 2 years apart (except of course, the twins). If the ages of all the boys added to 32 in the year that Ginny was born, how old were each of the children? How old is each when Ron graduates from Hogwarts at the age of 18?