10
GOOD PRACTICE EXAMPLES

Targeted competencies: Computing with natural numbers in different contexts Validating computing results Solving problems based on the studied concepts

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Page 1: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

GOOD PRACTICE EXAMPLES

Page 2: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

Targeted competencies: Computing with natural numbers in different contexts Validating computing results Solving problems based on the studied concepts

Objectives:• to solve multiplication exercises using different methods;• to solve different life situations using appropriate operations;• to use their multiplication knowledge in a variety of contexts;

Targeted activities:• multiplication of natural digits smaller than 1000• practicing calculation in different contexts• getting used to other calculation methods;• identifying numbers and using them in calculations• interdisciplinary correlation of contents• identifying and correcting possible errors• checking calculations in different ways• identifying everyday life situations in which we use such calculations: planning and organizing a party.

THE CHILDREN’S PARTY

Page 3: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

Resources:• student’s guide, multimedia guide,

computer

Types of activities:• frontal , individual and pair activities

Suggestions for class activities:What have we got to do?

• getting into the unit according to the social standard of the class; the teacher will gradate the term “party” so as to meet reality;• more atypical methods to solve the exercises are introduced in the unit; do not insist on learning them, just introduce them as curiosities which might be useful; they might play a motivating role in getting involved in mathematical activities;• allow enough time to check the correctness of the calculations, encourage cooperation and mutual help;• insist on questions which might facilitate understanding: Are there enough…? Why? How many should there be to….. ? Is it possible that ….? Why? ; allow enough time for reasoning;• support your students in making up a budget; encourage them to repeat for other situations ( in class or family);• understanding each step should be one of the main concerns; use frontal activity whenever you feel that certain tasks are above the students’ level of understanding;• encourage the finding of more solutions and personal approach ;• allow time for interdisciplinary correlation; encourage students to use their own experience or to look for new information;• throw a party in the classroom getting the students involved in planning and organization.

Page 4: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

How to monitor?

• give feedback to the students’ answers;• offer further explanations if necessary;• keep a systematic eye on the students’ contribution in the activity;• do not insist on the solving speed but on the correct solving;• encourage cooperation and mutual help;• use a monitoring sheet to record the correctness of the answers for each student;• encourage self- assessment and evaluation in pairs;• make sure all the mistakes have been corrected.

Reflection moment:

• What happened during the activity?• Which part of the activity was the most interesting for the

students?• Which were the difficulties?

• What have I learned during the activity?

Page 5: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

Different methods to do multiplications .

Using the fingers

(only for multiplication by 9):1. Number each finger in your mind.

Don’t forget the number you have given each finger.

2. Bend the finger which represents the number you want to multiply by 9.

Eg.: for 2 x 9 bend finger number 2.

On the left side there is one finger, on the right there are 8 fingers. 2 x 9 = 18

Using a rectangle26 x 2 = ?

We use a rectangle divided in two parts because we have a two-digit number.

Each part is divided by an oblique line. We write the two-digit number above and the one digit number on the lateral.

In turns we multiply the two digits with 2 and we write the results in the rectangle .

We add the numbers in diagonal.The result: 52

Multiplication with linesLet’s say we want to multiply this:

35 X 3.1. Represent the first number with lines.

Group 3 lines for tens and 5 lines for units.

2. Cut both groups of lines with 3 lines (from number 3)

3. Count the points where the lines meet in each group.For units there is 5.There are 10 tens.(from 9 + 1)The result is105(35 X 3 = 105). Check it!

Page 6: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

SETTING UP THE BUDGET FOR THE PARTY

1.I have made a list with things necessary for the party : paper hats, whistles, plates, glasses, drinking straws, napkins. Here is the price list:

2lei/pc 3lei/pc 6lei (set of 20pcs)

4lei(set of10pcs)

5lei(setof10pcs)

3lei(set20pcs)

Set up the budget for these products knowing that:- we consider 40 children-each child will get a paper hat and a whistle-for each child we need two plates, two glasses, two drinking straws, two napkins

Page 7: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

FRIENDS OF NATURE

Targeted competencies

• Validating the results• Recording the data observed in the environment and representing them• Solving problems with the studied concepts

Objectives:• to identify in a text relevant information to solve a problem;• to drop out irrelevant information from a text to facilitate understanding ;• to identify contradictory information ;• to reword information for better understanding.

Suggested activities• improving analysis abilities of a text in order to search , select and use relevant information• appreciating information in terms of : useful/useless, complete/incomplete, corellated/contradictory, redundant, etc.• rewording certain information in oder to clear up and better understand • identifying the appropriate behaviour to protect environment.

Resources:• student’s guide, multimedia guide, computer, information/images about animals

Types of activities• individual activities• frontal activities(explanations,che-cking)

Page 8: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

Suggestions for class activities:What have we got to do?

• this unit has many texts and is based on reading and analysing them in order to figure out the useful information;• the texts are approached from a searching for and selecting information perspective ; encourage students to read the texts several times and to come back to the texts whenever necessary;• guide your students into a “mathematic” reading , helping them to make the difference between the answers they can explicitly find in the text and the ones which need correlating information from the text ; • lead them into choosing the information which need to be correlated;• guide students in their activity of filling in with certain data; emphasize the importance of using real data, particularly when it comes to animals’, plants’ objects’ phenomena’s characteristics, which might require a former documentation;

How shall we monitor the activity?• give feedback to the students’ answers;• come with additional explanations if needed ;• observe systematically the students’ involvement in the activity;• do not insist on the solving speed but on the correct solving;• encourage cooperation and mutual help ;• use a monitoring sheet to record the correctness of the answers for each student;• encourage self- assessment and evaluation in pairs/ groups ;• make sure all the mistakes have been corrected.

Reflection moment• What happened during the activities?• Why did this happen?• Which part of the activity was the most interesting for the students?• Where have I encountered difficulties?• Which activities shall I do again in other occasions?

Page 9: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

My tree !

The III rd grades A, B and C students took part in the project "Adopt a tree".Each student has chosen a tree in the surroundings or in a park and has observed its evolution all through the school year , recording the findings in a worksheet. Students have taken photos of the tree in different seasons and aspects : when in bud , blooming, leafy, partly or completely bare. They organized an exhibition with 312 photos, each child displaying 4 photos of his tree. All the students involved in the project brought photos for the exhibition. They have also made up poems and stories about their trees and put them in a book of the class. Each student made a page in the book. The book of the students in III C had 28 pages , while the books of those in III A and B had an equal number of pages. The students brought out the books at the school year end ceremony .

Write the answers to the following questions :What project did the students take part in?What grade were the participants in the project? How many photos did each child bring for the exhibition? How many pages in the book did each child make? Where did the children bring out the books?Could you answer these questions? What helped you?

Observe, think, solve!1. How many children brought photos? Can you find the answer to this question in

the text?Is there any information in the text which could help you find the answer ?Read the statement:They organized an exhibition with 312 photos, each child displaying 4 photos of his tree.What do we know?- the number of photos- How many photos each child has brought

What do we want to find out?- how many children brought photosHow can we find this?We divide the total numbers of photos with 4 (because each child has brought 4 photos): Think and answer:Is the number of the children who brought photos for the exhibition equal with the number of the children involved in the project?Explain your answer. Use information from the text.

Page 10: Targeted competencies:  Computing with natural numbers in different contexts  Validating computing results  Solving problems based on the studied concepts

Animals can live in your house, too! You can breed birds, a dog or a cat, a hamster or fish...But, to do this properly, you have to learn about their needs.

THE FISH BOWL

Imagine you badly want an aquarium! Be it a small one, it is not easy to take care of.You need: a glass bowl 20 lei Water filtering/ oxygenation device 10 lei Warming system with thermometer 7 lei Lighting system 6 lei fish net 2 lei decorations: stones, plants 2 lei guppi fish 1 leu/piece, Xifo fish 2 lei/piece.

In a small aquarium you can’t keep more than 3 fish ,that is why you buy only three .How much are the objects for the aquarium, the bowl and the 3 fish?You will add up the prices for the objects: 47 lei. You know that you can buy 3 fish, but they can be different so they will have different prices. Here is how we should think:If I buy 3 guppy, how much will it be?47 + 3 x 1 = 47 + 3 = ? leiIf I buy2 guppy and 1 xifo, how much will that be? If I buy 1guppy and 2 xifo, how much is it in all? If I buy3 xifo, how much is it? Which is the cheapest variant? But the most expensive one?