mag yr5 ps 5.2.22 - the curriculum place
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Australian Curriculum Year 5 Australian Code ACMNA291 -‐ Use efficient mental and wri:en strategies and apply appropriate digital technologies to solve problems. Key Idea-‐ It is important to explicitly teach thinking skills as a means of equipping all students with important tools that will assist students to be life-‐long learners.
By learning problem-‐solving in mathemaHcs, students should acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situaHons that will serve them well outside the mathemaHcs classroom.
In everyday life and in the workplace, being a good problem solver can lead to great advantages.” (NCTM principles and standards for school mathemaHcs page 200). Resources • FISH Strategy Cards • Learning Journal • FISH pockets (op:onal) • QR code reader
Introduc7on Ac7vity Process: Revise FISH (MAG 5.1.1) u Complete introductory ac:vity process u Complete what does the acronym mean ac:vity u Complete stages of FISH ac:vity
Ac7vity Process: FISH Strategies Using an iPad using Inspira:ons or interac:ve whiteboard create a concept map with a Red, Blue, Yellow and Green Symbol for the FISH. This map will con:nue to grow as the learners work with a variety of problems. Ask learners to start an ‘ I can’ strategies list in their learning journal as a two column guide. Explain that problem solving is at the heart of Mathema:cs and is an essen:al life skill that we use everyday intui:vely but not always efficiently. Explain that problem solving is higher level thinking when we do it well. Each strategy (yellow cards) is a category of strategies and an have a number of varia:ons.
Ask learners to think of Yellow FISH as reminders of possible strategies that they can use in different contexts for different purposes.
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ApplicaHon
Problem Solving includes formula:ng and solving authen:c problems using whole numbers and measurements and crea:ng financial plans
Reasoning includes inves:ga:ng strategies to perform calcula:ons efficiently, con:nuing paUerns involving frac:ons and decimals, interpre:ng results of chance experiments, posing appropriate ques:ons for data inves:ga:ons and interpre:ng data sets
Two proficiency strands are supported the FISH process.
Paraphrasing-‐Demonstrate ac:ve listening. Teacher pays close aUen:on to what is said and signaling that listening to others is important and providing a model of it helps you understand beUer, builds sense of being valued and capable. When learners feel that all are treated equally the risk of speaking up is reduced.
‘The Lollipop lady is very popular with students at the local school. Along with her usual morning smile, she has a daily riddle for students. Yesterday she asked. How do 5 and 9 more make 2?’
Use a two column guide Invite learners to think and except all ideas: • of all the things you can do with 5 and 9. • all the places you see 5 and 9
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Teaching problem solving has to be in sync with what is developmentally reasonable for learners. It is not enough to engage learners, the teachers’ aim needs to be to enable them. To capitalize on the natural ability of children to look, listen and talk to make sense of the world. To provide opportuni:es to use and widen their capacity to learn on their own. To enable this aim teachers need to understand that the FISH process ques:ons are essen:al. The ques:ons are consistently repeated ini:ally so that learners get used to them, recognise them and begin to incorporate them into their own process. The aim for the teacher is to pose ques:ons that lead to cogni:ve habits that s:ck.
The strategy ac:vi:es that follow should be modeled through the teachers facilita:on of discussion by poin:ng to the observed details in the text, responding to all learners comments. Paraphrasing each comment and linking one comment to another.
Poin7ng-‐What is observed in the text/problem For Example. The Lollipop lady is very popular with students at the local school. Along with her usual morning smile, she has a daily riddle for students. Yesterday she asked. How do 5 and 9 more make 2? In this problem the red fish ques:on is how and make is also located in text where the blue fish informa:on is located. It is important to point out that the red-‐what am I asked to find? and the blue-‐what informa:on do I have? Are not always stated at the beginning of the problem. This problem also provides the opportunity to talk about the kind of informa:on it involves-‐a riddle, which has an impact on the nature of the answer. Consider all possibili:es is an approach to start with.
Linking-‐Shows how ideas interact, by connec:ng literal and inferen:al ideas that agree and disagree. It also illustrates how ideas develop. Learners grow to understand how knowledge is created rather than simply delivered by a teacher. They learn to think things through on their own and to allow different ideas to be considered. Look at the ideas in the first column and ask What can’t you do with 5 and 9 more to make 2? A simple answer might be just add or subtract the numbers. Ask why is this not a strategy that will lead to a reasonable answer.
As this is a riddle ask learners to consider much they are influenced by the work ‘make’ Ask learners to consider the list and suggest how 5 and 9 more make 2. Move possible clues in the second column. As we have not found a simple opera:ons solu:on ask learners to carefully consider all the places you see 5 and 9? Reasonable solu7on is on a clock using 12 hour :me On the clock 5 plus 9 hours makes 2 o’clock. Extend the problem by asking learners to create a maths riddle of their own
Guess, Check and Improve Strategy Tired of riding the surf, playing catch and flying kites, Rory and Pablo are coun:ng birds at the beach. There are lots of birds, especially sea gulls and sandpipers. At one :me during the day the boys count 142 sea gulls and sandpipers altogether. There was 42 more sea gulls than sandpipers. How many sea gulls and how many sandpipers did they count? Extend it The boy sister counted 224 birds altogether. She counted 82 more sea gulls than sandpipers. How many sandpipers and how many sea gulls did she count.
Look and Find a PaSern Each winter Elephant Seals return to the Ano Nuevo State Park on the Californian coast. On the first day of their return, park rangers count 5 seals lying on the beach. On the second day, 6 more seals arrive. On the third day, 7 more seals arrive. Each day the number of seals that arrives increases by one more than the number of seals that arrived the day before. At this rate, how many seals will be on the beach at the end of the eighth day? Extend it If the number of seals increases by four each day, how many seals will be on the beach at the end of the eighth day?
Work Backwards Andrew’s soccer team is having a great season. The team is being coached by Andrew’s mother, who has divided the team into five groups. ½ the players are forwards, 1/6 are wings, 1/6 are halkacks, 1/12 are fullbacks, and two others are goalies. How many players are on Andrew’s team, and how many are in each group? Extend it On the opposing team ½ are forwards, ¼ are halkacks, 1/8 are wings, 1/16 are fullbacks and two are goalies. How many players are on this team?
Model-‐Draw a Picture, Model or Diagram It’s a wet weather day so the class must stay inside for lunch. Meagan and Monica are nearly finished with their checker game. Each player has one piece lem on the board. Begin at Megan’s red checker piece’s posi:on, and move two squares north towards the middle of the board. Now move east one square, then go south one square and turn east. Go east three squares and finally south one. Now place Monica’s black checker piece in this square. How far apart are the two pieces on the board? Extend it From Megan’s red piece go north 4 squares, east 5, south 2, west 4, and south 2. How far apart are the two checker pieces
Problem Solving Progression-‐learners with different experiences think differently through developmental stages
Begin to develop own ways of recording
Begin to look for paUerns in results as they work and use them to find other possible outcomes
Begin to organise their work and check results
Begin to understand and use formulae and symbols to represent problems
Begin to work in an organised way from the start
Break a several-‐step problem or inves:ga:on into simpler steps
Check answers and ensure solu:ons make sense
Check as they work, sponng and correc:ng errors and reviewing methods
Check their methods and jus:fy answers
Check their work and make appropriate correc:ons eg. decide that two numbers less than 100 cannot give a total more than 200 and correct the addi:on
Choose their own equipment appropriate to the task, including calculators
Consider appropriate units
Consider efficient methods, rela:ng problems to previous experiences
Decide how best to represent conclusions, using appropriate recording
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Use Concrete Materials Strategy Two adults and two children have been stranded on an island in a river. They must cross the wide river to safety, but they only have one canoe. The canoe can either take one adult or two children at a :me. How can they safely reach the other side? Extend it What if there were three children and two adults? Solve a Simpler Problem Strategy There were tulips of every colour and size on floats at the Tulip Bowl Parade in Amsterdam. There was nine marshals sta:oned every two blocks along the parade route to help control the crowd. The marshals will meet amer the parade to make a report. Because the marshals are not used to their wooden shoes, what is the fewest number of combined blocks they could walk for their mee:ng? Extend it If there was 11 marshals, what would be the fewest number of combined blocks they would have to walk amer the parade. Ac7ng it Out Strategy Sylvia Spider spins a web each morning that sparkles in the early morning dew. The web has three circles: an outer circle, a middle circle, and an inner circle. Sylvia divides the circles into eight equal sec:ons. One morning Sylvia no:ces 18 dewdrops on the web. There was an even number of dewdrops in each of the three circles, and there was an even number of dewdrops within each each of eight sec:ons of the circles. What are the two possible arrangements of the dewdrops? Extend it Can you make up your own problems with more dewdrops and new condi:ons? Write a Number Sentence Strategy Alden, Tony and David were building sandcastles in the sandpit during big lunch. They built ______ sandcastles. Megan and Aaron came along and built more sandcastles. They had _________ sandcastles in all. How many did Megan and Aaron build? Extend it Can you rewrite this problem with an element of :me added?
Develop an organised approach as they get into recording their work on a problem
Discuss their mathema:cal work and begin to explain their thinking
Draw simple conclusions of their own and give an explana:on of their reasoning
Explain and jus:fy their methods and solu:ons
Iden:fy and obtain necessary informa:on to carry through a task and solve mathema:cal problems
Iden:fy more complex paUerns, making generalisa:ons in words and begin to express generalisa:ons using symbolic nota:on
Iden:fy paUerns as they work with the assistance of probing ques:ons and prompts
Make generalisa:on with the assistance of probing ques:ons and prompts
Make connec:ons to previous work
Make their own sugges:ons of ways to tackle a range of problems
Organise their work from the outset, looking for ways to record systema:cally
Organise wriUen work eg. record results in order
Pose and answer ques:ons related to a problem
Predict what comes next in a simple number, shape or spa:al paUern or sequence and give reasons for their opinions 4
5
Australian Curriculum By the end of Year 5, students solve simple problems involving the four opera:ons using a range of strategies. They check the reasonableness of answers using es:ma:on and rounding. Students iden:fy and describe factors and mul:ples. They explain plans for simple budgets. Students connect three-‐dimensional objects with their two-‐dimensional representa:ons. They describe transforma:ons of two-‐dimensional shapes and iden:fy line and rota:onal symmetry. Students compare and interpret different data sets.
Students order decimals and unit frac:ons and locate them on number lines.
They add and subtract frac:ons with the same denominator.
Students con:nue paUerns by adding and subtrac:ng frac:ons and decimals.
They find unknown quan::es in number sentences.
They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles.
They convert between 12 and 24 hour :me.
Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabili:es between 0 and 1. Students pose ques7ons to gather data, and construct data displays appropriate for the data.
Make a List Three children walk down a fimeen step fire escape. Lisa walks down one step at a :me. She begins by punng her lem foot on the first step. Alex is in a hurry and walks down two steps at a :me, star:ng with his right foot. He starts on the second step. Joel is in more of a hurry and takes three steps at a :me, beginning on the third step with his lem foot. Which step will be the first one they all step on? Extend it Will all the children stand on the same step with their lem foot? Assessment
With
Supp
ort
With
out
Supp
ort
Able to iden:fy informa:on that is important to solving the problem, and determine what is missing
Able to use appropriate mathema:cal vocabulary to explain thinking
Able to describe strategies and methods used to successfully solve problem
Able to solve problem pose a similar problem for another learner
The chart below is a star:ng point for assessment combining the highlighted red dots on pages 3, 4 and 5. Pages 3 and 4 have a progression chart, showing the suggested development of thinking and problem solving over :me www.nrich.maths.org. On page 5 the Year 5 Australian Curriculum Mathema:cs standard has been listed.
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