Student Challenge Friday

Here is your Friday challenge:

A bag contains only red, yellow and blue lollies. The probability of picking a red lolly is 0.25 and the probability of picking a yellow lolly is 0.40. What is the least number of lollies that could be in the bag?

Extra:

What would be the probability of picking a blue lolly?

Write your answer in the comments with your name and class or ask your teacher to send me a photo of your work :-)

Below are photos of Room 6 working out the problem:

Room 6 found this a really challenging problem.  We decided that if red was 0.25 and yellow was 0.4, then the probability of a blue lolly was 0.35.  From there, we got a bit stuck – most of us turned these decimals into fractions and then didn’t know where to go from there.

With a bit of help from Mr Dawson, we figured out that in a bag of 100 lollies, there would be 25 red, 40 yellow and 35 blue.  We then decided to divide all those numbers by the highest common factor we could find, which was 5.  That reduced the numbers to 5 red, 8 yellow and 7 blue, which means the smallest amount of lollies in a bag was 20.

Missing the Whole

My new groups have been doing a lot of work on fractions in particular part to whole fractions as this is usually where there struggle. 

To start off with we have been looking at basic fractions in a variety of ways i.e. of sets, of shapes, of a number etc while always relating it back to the whole. When we started getting the hang of that we moved onto part to whole where students are given questions involving a part of a fraction and they need to work out the rest of the whole. 

The three level question I used was:

1) Miss Breen has baked chocolate chip cookies for her family.  Her son takes 6 of them when she isn't looking. Her son has taken one quarter (1/4) of the cookies. How many cookies does Miss Breen have left for the rest of the family?

2) Miss Breen has baked chocolate chip cookies for her family.  Her son takes 122 of them when she isn't looking. Her son has taken one sixth (1/6) of the cookies. How many cookies does Miss Breen have left for the rest of the family?

3) Miss Breen has baked chocolate chip cookies for her family.  Her son takes 1052 of them when she isn't looking. Her son has taken one eighth (1/8) of the cookies. How many cookies does Miss Breen have left for the rest of the family?

I wrote this question to consolidate their part to whole fractions work and also to focus on the big idea of 'Distributive Law' (how numbers can be split) to help work out problems more efficiently. These questions were somewhat challenging but I am intending on making them even harder next time.

Here are some pictures of what the students shared back after their problem solving session:

New Groups

Last term I had to say farewell to most of the students that I worked with in term 1 and 2. Now I have 4 new groups of year 4 to 8 students.

Introducing Group 6 & 9:

More group photos to come

MATHS WEEK 2015 - Final Day Problems

Here are your challenges for today:

Junior Problem:

Mr Cressey has lots of rubbish bins to clean. On Monday he cleans four bins. On Tuesday he cleans twelve bins. On Wednesday he cleans half the amount of bins that he did on Tuesday. On Thursday he had more to clean. By Friday morning he had cleaned 33 bins altogether. How many bins did he clean on Thursday?

Senior Problem:

Matua Dudley had a whole box of chocolate biscuits.  He was feeling very hungry, so he ate 2/8 of the biscuits.  That left only 27 chocolate biscuits. He then shared 3/9 of the remaining biscuits out to the staff. How many were left in the box?

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Students: Write your answer in the comment section with your name and class.

Teachers: If you have any photos of student thinking please email to Miss Breen 

That is all the problems for this week. Congratulations to all the students and classes who completed the challenges, you are awesome!

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Here is Room 6 once again showing their fantastic thinking on the senior problem:

Another great problem, Miss Breen!  We worked out that if Matua Dudley had eaten 2/8 of the biscuits, then 6/8 of the biscuits were left.  This totalled 27 biscuits.  We then divided 27 by six to tell us what 1/8 of all the biscuits was – this came to 4.5.  To find out the total number of biscuits, we did 4.5 x 8 (because 8/8 would equal the total amount of all the biscuits) = 36.

To find out how many were left, we divided 27 by nine in order to find 1/9.  This came to 3.  We knew that, since 3/9 had been shared, that 6/9 were left.  So we did 3 biscuits x 6 = 18, so 18 biscuits were left in the box.

We will miss these maths problems, they were really good for challenging our thinking!

Room 6.

MATHS WEEK 2015 - Day 4 Problems

Here are your challenges for today:

Junior Problem:

When Miss Breen teaches in Room 14 she promises to give stickers to the students who finish their homework. 14 students hand their homework into Miss Breen. She gives their teacher Whaea Donna 28 stickers to hand out fairly between the 14 students. How many stickers will each student get?

Senior Problem:

Whaea Oronsay is having trouble with the school bus on a trip to the snow. She notices that after the bus reaches a speed of 110km/hr, every hour after that the bus's speed automatically decreases by 10%. How many hours of driving would it take before the bus is only able to drive at a speed less than 30km/hr.

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Students: Write your answer in the comment section with your name and class.

Teachers: If you have any photos of student thinking please email to Miss Breen 

Come back tomorrow for new challenges!

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Here is Room 6's thinking:

Hi Miss Breen,

We thought today’s problem could be worked out a couple of ways.

Firstly, we knew that 10% of 110 was 11, so we kept subtracting 11 until we got below 30.  This means the bus would drop below 30kmh in the eighth hour.

The second way was a bit more complicated.  The first hour, the bus’ speed decreases by 11kmh (10% of 110kmh).  The bus is now going at 99kmh after one hour.  In the second hour, we figured out that 10% of 99kmh is 9.9kmh.  That means that the bus, after two hours, is now going 89.1kmh.  In the third hour, 10% of 89.1kmh is 8.91kmh, so we subtracted that…and so on.  The numbers got really hard to manage, so we ended up having to use a calculator!  J  Anyway, using this method, we worked out that the bus would drop below 30kmh in the 13^th hour.

MATHS WEEK 2015 - Day 3 Problems

Here are your challenges for Wednesday:

Junior Problem:

Sarah began earning pocket money by doing chores at home everyday. She was given $2 on her first day. Then she was given $3 every day after for a long time. How much money did she have after 2 weeks? If she spends half of that money on a toy how much will she have spent?

Senior Problem:

Mike aims to drink at least 3 litres of water a day to keep hydrated. On Monday he meets his goal, on Tuesday he drinks only half of this goal. On Wednesday he drinks 50% more than he did on Tuesday. How many litres of water did he drink on Wednesday?

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Students: Write your answer in the comment section with your name and class.

Teachers: If you have any photos of student thinking please email to Miss Breen 

Come back tomorrow for new challenges!
------------------------------------------------------ Here is some feedback and photos of Room 6 completing the senior question today:

Room 6 found the Senior problem very challenging – mainly due to the fact that a lot of us didn’t take the time to understand exactly what the question was asking us!

We figured out that half of 3 was 1.5, but a lot of us then doubled 1.5, because we thought 50% more meant two times as much!  One group decided that 50% of 1.5 was 0.75, so they added that to 1.5 to make 2.25, and we now think that is the correct answer.

Great problem, Miss Breen!

MATHS WEEK 2015 - Day 2 Problms

Here are your challenges for Tuesday:

Junior Problem

Miss Breen has baked chocolate chip cookies for her family.  Her son sneakily eats 5 of them when she isn't looking. Her son has eaten one quarter (1/4) of the cookies. How many cookies does Miss Breen have left for the rest of the family?

Senior Problem

Emma is making 2 pizzas. She cuts each of her pizzas into sixths.  She has 36 pieces of pineapple to spread evenly on her 2 pizzas.  How many pieces of pineapple will be on seven/sixths (7/6) of the pizzas?

Students: Write your answer in the comments area with your name/class

Teachers: please send photos of student thinking to Miss Breen :-)

Good Luck!

Come back tomorrow for new challenges!

Here is a photo of student thinking (senior problem) in Room 7 today:

Here are some photos of Room 18 working hard on the junior problem today:

MATHS WEEK 2015 - Day 1 Problems

Maths Problems for 2015 Maths Week

JUNIOR PROBLEM - Monday

A group of bees are out collecting nectar to make honey. 6 of the bees are on flowers and the other half return to the hive. How many bees return to the hive?

Write your answer with your name/class in the comments area :-)

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SENIOR PROBLEM - Monday

Our school has a practice fire drill, the bell continually rings. 25 students are still in class, the other seven eighths (7/8) of the school's students are already lined up on the courts. How many students are on the courts?

Write your answer with your name/class in the comments area :-)

GOOD LUCK!

COME BACK TOMORROW FOR NEW CHALLENGES!

ShowMe Some Learning

The other day I introduced some of my students to the ipad app 'ShowMe' which is an interactive whiteboard. As we have been focusing on patterns in algebra, this app gave my students the chance to share how they work out the continuing sequence of a pattern.

*The copy-master pattern in the video comes from the unit plan Letter Patterns on the NZmaths website.

In the video by Tyrell and Moengaroa (group 3), they are explaining the sequence of the pattern and they come up with a rule which they can use to work out larger numbers in the sequence. As this was their first time using the App they didn't explain as thoroughly as they normally do to their group but I think they did great!

Below is some problem solving work around patterning by Tyrell, Foloi and Katrina

Our teachers create and share within our school three level word problems, as we are currently involved in the Mathematical Inquiry Communities (MIC) with Bobbi Hunter and Massey University. This problem was originally created by Matua Tuiono, Mr Lysaght and Miss Tafa here at Clendon Park School though I have altered the numbers for my students.

1   1. At the first CPS Home School Partnership evening 7 people turned up. The second year 12 people turned up. The third year 17 people turned up. How many people turned up in the eighth year? (What is the pattern?/What is the rule?)

 .  2. How many people turned up in the seventeenth year?

    3. How many people turned up in the thirty second year?

*The first picture shows their workings for question 1 & 2 and the second picture shows their working for question 3. As you can see by coming up with a rule in the first question they were able to quickly find how many people would have turned up in the 17th and 32nd year.  The pattern was +5 and their rule was  x5 + 2. The +2 comes from the first number in the sequence which is the only number that isn't +5 (7-5 = 2) They also noticed that the numbers all ended in 2 and 7 so they could easily predict the next number.

What's the Pattern?

My students have just starting exploring the early stages of algebra and exploring algebraic thinking using colours, shapes, symbols, numbers, letters etc to begin to identify patterns and relationships, which is a key to being successful in mathematics.

Here are some links to pattern games for your child or students to practise: 

Click on the link:
Finish the Pattern
Pattern Farm

Pattern Match Numbers
Pattern Match Shapes

Extra for experts:
Algebra Function Machine - Find the rule

Here are some photos of my year 4 group (group 1) creating their own repeating patterns:

Working in a class

Each week I relieve in a year 2/3 class so for one day I get to practice problem solving with a class rather than with my small groups. 

This class was split into half and one half works independently in Maths while the other half works with me. They are given a word problem and are asked to read it and talk about what they can see in their heads and what the problem is asking them to do. Once they have had a think, pair, share with their buddy we come back as a group to talk about the problem and also the rules when working with a buddy. This is to ensure that all the students are clear about what the problem is and the expectations before they start trying to solve it. Once we have had a whole group discussion, the students are given a chance to try to work it out. At this stage most students generally choose to use materials such as beans, counters or ice block sticks to help them. 

Here are some photos of the students problem solving:

Measurement

Hello, it has been a while since my last post so I'm trying very hard to catch up on posting about my students. My groups have been working hard for the past couple of weeks learning about measurement using both non standard and standard units.

I have been using ideas from measurement units that can be found on http://nzmaths.co.nz/length-units-work I have found them very valuable and have been altering them or adapting them to suit my students and where they are at.

We have been mainly looking at length and width. 

Group 3 and 5 have been looking at estimations, length, width, benchmarks, surface area, distance, total distance, average, centrimetres and metres to name just some. They have made paper planes (see unit http://nzmaths.co.nz/resource/paper-planes-level-2) which they flew against each other and then were asked to measure the distance, work out total distance, average flight distance etc. They used measuring tapes for this which meant they had to convert metres into centimetres. 

Group 1, 2, 4 have been doing a lot of work around estimations, length, width, non standard units i.e. pencils, hand spans, blocks etc moving on to 1cm cubes, 10cm blocks and making their own rulers. 

Most of the activities have been very hands on which has helped to engage the children in the learning.

The next step will be problem solving with a measurement context.

Below are some photos of my various groups learning about measurement recently: