Curriculum Primary 1 Whole Numbers Concept of multiplication and division - Equal groups of objects and finding the total Primary 3 number of objects. Fractions Primary 2 Equivalent fractions Expressing fraction in its simplest form. Whole Numbers Mixed numbers, Improper fractions Multiplication tables of 2,3,4,5,10 Addition and Subtraction of fractions . Primary 3 Primary 4 Whole Numbers ( factual fluency) Multiplication tables of 6,7,8,9 Decimals 4 operations of decimals Primary 4 Whole Numbers Multiplication algorithm
Assessments P4 P5 & 6 Item Types No of questions Marks allocated No of questions Marks allocated 2 marks per 1 or 2 marks MCQ 20 15 question per question 2 marks per 1 or 2 marks SAQ 20 20 questions per question 4 marks per 3, 4 or 5 marks LAQ 5 13 questions per question Complexity and demand of the questions Time management
How are concepts connected and interdependent? The figure shows a table mat. The outside edge of the mat is formed by 8 semicircles and 4 quarter circles, each of radius 7 cm. (a) Find the perimeter of the mat. (b) Find the area of the mat. PSLE 2014 Question 14 ( Paper 2) Problem Solving ( Circles) Primary 1-3 Geometry ( 2D figures) Identifying squares , semi-circles and circles. Measurement ( Area and perimeter) Finding area and Perimeter of squares and rectangles
How are concepts connected and interdependent? The figure shows a table mat. The outside edge of the mat is formed by 8 semicircles and 4 quarter circles, each of radius 7 cm. (a) Find the perimeter of the mat. (b) Find the area of the mat. PSLE 2014 Question 14 ( Paper 2) Problem Solving ( Circles) Primary 4 Area and Perimeter of Squares and Rectangles. Find the area of a composite figure made up of rectangles and squares.
How are concepts connected and interdependent? The figure shows a table mat. The outside edge of the mat is formed by 8 semicircles and 4 quarter circles, each of radius 7 cm. (a) Find the perimeter of the mat. (b) Find the area of the mat. PSLE 2014 Question 14 ( Paper 2) Problem Solving ( Circles) Primary 6 Area and circumference of circle • Find the area and circumference of a circle. • Find the area and perimeter of semi-circle and quarter circle. Area and perimeter of composite figure. • Find the area and perimeter of a figure made up of some of the following shapes. - square, rectangle ( P4) , triangle (P5) , semicircle, quarter circle ( P6)
How are concepts connected and interdependent? Problem Solving ( Circles) Primary 4 Primary 6 Area and Perimeter of Squares and Rectangles. Area and circumference of circle • Find the area and circumference of a circle. • Find the area of a composite figure made up of Find the area and perimeter of semi-circle rectangles and squares. and quarter circle. Area and perimeter of composite figure. • Find the area and perimeter of a figure made up of some of the following shapes. - square, rectangle ( P4) , triangle (P5) , semicircle, quarter circle ( P6)
How are concepts connected and interdependent? A set of objects A teacher has a number of buttons in three colours: blue, red and green. Fraction of set of objects of the buttons are blue. How many blue buttons are there? Problem Solving ( Fractions ) A set of buttons Primary 4 Fractions Fraction of a set of objects × 30 = 9
How are concepts connected and interdependent? A set of objects A teacher has a number of buttons in three colours: blue, red and green. Fraction of set of objects of the buttons are blue. The number of blue buttons is twice the number of red buttons. PSLE 2014 What fraction of the buttons are green? Question 5 ( Paper 2) Problem Solving ( Fractions ) New concepts are tested. Primary 5 The number of objects is not given in this question. ( red buttons ) Four Operation of fractions • Divide a proper fraction by a whole number. • Solve word problems involving the 4 operations. ( green buttons ) 1 whole denotes the set of objects
How are concepts connected and interdependent? Problem Solving ( Fractions ) Primary 4 Primary 5 Fractions Four Operation of fractions • Divide a proper fraction by a whole number. • Fraction of a set of objects Solve word problems involving the 4 operations.
Factual ctual Concep ceptual ual under erstanding standing Under erstan standing ding Problem Pr oblem Solvi lving ng Thi hink nking ing skil ills ls and Atti titu tudes des Heuri risti stics cs
Points to note Number operation (14 – 2) ÷ 3 = 4 14 – 2 = 12 ÷ 3 = 4 14 – 2 = 12 2 – 14 = 12 12 ÷ 3 = 4 3 ÷ 12 = 4
Percentage ¼ × 100 = 25% ¼ × 100% = 25% ¼ × 100% = 25 60 - 25 = 35% 25% = 0.25 60% - 25%= 35% 60 - 25% = 35% ¼ × 100 = 25 60% - 25% = 35
Measures 2.50 p.m. + 4.40 = 7.30 p.m . 2.50 p.m. + 4h 40 min = 7.30p.m. 2h 50 min + 4 h 40 min = 7h 30 min = 7.30 p.m.
Unitary method 6 units $42 6 = $42 6 units = $42 1/6 = 42
Referencing
Referencing Metacognition Application of ideas Checking
What is Problem Solving? It is a process by which a pupil uses previously acquired knowledge, skills and understanding to obtain an answer in an unfamiliar situation.
Polya’s 4-step model The Polya’s 4-step model provides a framework for problem solving that can h e l p p u p i l s p ra c t i s e s y s t e m a t i c t h i n k i n g .
Polya’s 4-step model 1. Understanding the Problem 2. Devising a Plan 3. Carrying out the Plan 4. Reflecting
1. Understanding the Problem • Look for information given • Visualise the information • Organise the information • Connect the information
2. Devising a Plan (Heuristics) • Act it out • Use a model/diagram • Make a systematic list • Look for patterns • Work backwards • Use before-after concept • Guess and Check • Make supposition • Restate the problem in another way • Simplify the problem • Solve part of the problem
3. Carrying out the Plan • Use computational skills • Use geometrical skills • Use logical reasoning
Incorporating these thinking skills • Classifying • Comparing • Sequencing • Analysing parts and whole • Identifying patterns & relationship • Induction • Deduction • Spatial visualisation
4. Reflecting • Check solution • Improve on the method used • Seek alternative solutions • Extend the method to other problems
Why use model drawing? • Represent the mathematical relationships in a problem pictorially • Help pupils visualise what could otherwise be abstract concepts • Help clarify a problem and plan the steps for the solution
PART-WHOLE MODEL …from pictures to model whole part part
COMPARISON MODEL Using two or more bars to compare two or more items or variables.
Comparison model Mark bought a pen and a book. The book cost 3 times as much as the pen. If the book cost $20 more than the pen, how much did Mark pay for both items? Pen $20 1 unit ? Book 1 unit 1 unit 1 unit 2 units $20 1 unit $20 ÷ 2 = $10 4 units 4 x $10 = $40 Mark paid $40 for both items.
Before - After John had 850 more chickens than ducks. After selling ¾ of the chickens, he had 140 more ducks than chickens. How many chickens did he have at first? chickens ducks 140 850 3 units 140 + 850 = 990 4 units 330 x 4 = 1320 990 ÷ 3 1 unit = 330 He had 1320 chickens at first.
Alan, Betty and Cindy shared a packet of sweets. 1 Alan took of the sweets and was given 6 more. Betty 3 1 took of the remaining sweets and was given 4 more. 2 Cindy took the remaining 3 sweets. How many sweets were 2 units there in the packet? 6 Alan 4 3 Cindy Betty 1 part 2 parts
After - Before 2 units 6 Alan 4 3 Cindy Betty 1 part 2 parts 1 part 4 + 3 = 7 2 units 14 + 6 = 20 2 parts 7 x 2 = 14 1 unit 20 ÷ 2 = 10 3 units 10 x 3 = 30 There were 30 sweets .
Guess & Check Involves making a reasonable guess, checking the guess and revising the guess if necessary. A correct solution may not be arrived at immediately but it provides information that can be used to better understand the problem.
Guess & Check There were 160 motorcycles and cars at a carpark. The total number of wheels was 510. How many cars were there at the carpark? Total no. of vehicles = 160 Total no. of wheels = 510 Each car has 4 wheels. Each motorcycle has 2 wheels.
Guess & Check Condition 1 :Total no. of wheels = 510 Condition 2 :Total no. of vehicles = 160 First guess : 80 cars & 80 motorcycles No. of No. of wheels Total no. of Check wheels(cars) (motorcycles) wheels 80 x 4 = 320 80 x 2 = 160 320 + 160 = 480 X 90 x 4 = 360 70 x 2 = 140 360 + 140 = 500 X 95 x 4 = 380 65 x 2 = 130 380 +130 = 510 There were 95 cars.
Make supposition • Involve making use of simulated numbers to make the situation real
Make supposition There were 160 motorcycles and cars at a carpark. The total number of wheels was 510. How many cars were there at the carpark? Suppose all vehicles are motorcycles … Total no. of wheels 160 x 2 = 320 No. of excess wheels 510 – 320 = 190 Each car has ( 4 – 2 = 2) more wheels than each motorcycle. No. of cars 190 ÷ 2 = 95 There were 95 cars.
How to help your child to strengthen his/her problem solving skills • Get your child to communicate, reason and reflect. • Use questions to probe their understanding. • Relate to real-life situation.
Mathematics Sharing Any Question? Email us at: phua_ei_ling@moe.edu.sg (HOD Maths) or yeo_sharon @moe.edu.sg (LH Maths)
SCIENCE SHARING FOR PARENTS
OBJECTIVES OF SESSION • To gain an overall understanding of the primary science curriculum. • To gain an insight of how science concepts are tested. • To equip parents with a better understanding of the strategies involved in answering open-ended science questions.
What does my child learn in science? How does my child learn science? Why does my child learn science? How can I support my child in How is my child assessed in science? learning science?
Why does my child learn science ? Learn basic concepts to understand themselves and things around them Develop skills Cultivate attitudes Have learning experiences which build on interest and stimulate curiosity
What does my child learn in science ? Themes * Lower Block (P3-P4) ** Upper Block (P5-P6) Diversity of living and non-living things Diversity (General characteristics and classification) Diversity of materials Cycles in plants and animals (Life cycles) Cycles in plants and animals (Reproduction) Cycles Cycles in matter and water (Matter) Cycles in matter and water (Water) Plant System Plant System Systems (Plant parts and functions) (Respiratory and circulatory systems) Human System Human System (Digestive system) (Respiratory and circulatory systems) Cell System Electrical System Interaction of forces Interaction of forces Interaction (Magnets) (Frictional force, gravitational force, force in springs) Interaction within the environment Energy Forms and Uses Energy Energy Forms and Uses (Photosynthesis) (Light and Heat) Energy Conversion Note: • *Lower Block (Primary 3 and 4); ** Upper Block (Primary 5 and 6). • Topics which are underlined are not required for the Foundation Science .
SCIENCE THEMES / TOPICS LOWER BLOCK PRIMARY 3 PRIMARY 4 • • INTERACTIONS DIVERSITY - Magnets - Living things - Plants • CYCLES - Animals - Life cycles of Animals - Fungi & bacteria - Life cycles of Plants - Exploring materials - Matter • SYSTEMS • ENERGY - Body systems - Light & shadows - Plant systems - Heat & temperature
SCIENCE THEMES / TOPICS UPPER BLOCK PRIMARY 5 PRIMARY 6 • • SYSTEMS ENERGY - Cells - Forms of energy - Air & living things - Energy & the sun - Plant transport system • - Electrical systems INTERACTIONS - Forces • CYCLES - The environment - Heredity & reproduction - Environmental interactions - Reproduction in plants - Adapting to the environment - Water matters - People & the environment
What does my child learn in science ? Collecting and Reasoning; Making Engaging with an presenting meaning of event, phenomenon evidence information and or problem through: through: evidence through: Formulating Observing Comparing hypothesis Using apparatus Classifying Generating and equipment Inferring Skills possibilities Analysing Predicting Evaluating Communicating Creative problem-solving, Investigation and Decision-making Processes
What does my child learn in science ? • Curiosity • Creativity • Integrity • Objectivity • Open-mindedness • Perseverance • Responsibility
How does my child learn science ? • Introduction to concepts. • Exploring through hands-on activities. • Applying concepts in various contexts. • Making links between concepts.
How is my child assessed in science ? • Holistic Assessment : Both paper and pencil tests and performance assessments are used. • Focus is on conceptual understanding and application of concepts and skills. • Students can explain their understanding of concepts in their own words. • Concepts which are correct in the context of the questions will be carefully evaluated and awarded marks.
How can I support my child in learning science ? • Challenges of early science learners: • Language - Lack of vocabulary range and language precision. • Concepts - Unable to visualise abstract concepts. • Complexity - Unable to link and apply complex concepts.
How can I support my child in learning science ? • Science is not about : • Memorizing ‘correct’ keywords. • Knowing lots of information. • Drilling theoretical questions that are not workable in real life.
How can I support my child in learning science ? • Carry out science activities at home. • Relate the science learnt in school to things in everyday life. • Ask questions that require description or explanation. Encourage them to discuss and talk about science ideas. • Encourage your child to read beyond the textbooks (e.g. science comics).
TESTING OF SCIENCE CONCEPTS
QUESTION 1 George arranged a torch and three objects, A, B and C, in a straight line in front of a whiteboard. Shadow formed on screen C Whiteboard B A Torch The shadows formed by the objects are shown above. Based on the information above, tick the correct property of object A. Does not allow light to Allows all light to pass Allows some light to pass pass through through through
QUESTON 2 The set-up below uses a light sensor to count the number of identical object X on a moving belt. light sensor connected to a counter moving belt light source The belt moves at a constant speed. When an object X is between the light source and the sensor, it blocks light from reaching the sensor. The data recorded is shown in the graph below.
(a) Based on the graph, how many object X passed the sensor in 22 seconds? 5 objects (b) The light source and the sensor are placed 3 cm above the belt. State whether an object that is less than 3 cm in height can be counted. Give a reason for your answer. No, an object that is less than 3 cm in height cannot block the light and so light will still reach the light sensor.
QUESTION 3 The graph below shows the number of steel pins attracted to different parts (R, S, T and U) of a bar magnet. 14 12 Number of staples 10 Number of pins 8 6 4 2 0 R S T U Parts of a magnet Parts of a magnet Label the diagram of the bar magnet below with the correct parts for R and U. R U U Bar magnet
QUESTION 4 Aishah was given 2 similar rods, P and Q. One of the rods was a magnet and the other was a magnetic material. She wanted to find out which rod was the magnet. Aishah arranged the rods P and Q as shown in Figure 1. She found that there was a strong force of attraction between the rods. When she rearranged the rods as shown in Figure 2, the force of attraction was weak. Figure 1 Figure 2
Which rod, P or Q, was the magnet? Give a reason for your answer. Rod P was the magnet because its end had a stronger force of attraction on Q compared to the weaker force of attraction using its centre.
COMMON PROBLEMS IN ANSWERING OPEN-ENDED QUESTIONS
QUESTION 5 Study the diagrams of Animal A and Animal B below. Animal A Animal B Based on what you can observe, list 2 similarities between Animals A and B. (a) Both animals can fly. (b) Both animals lay eggs. The answer must be observed in the diagram. It cannot be stated from prior knowledge. (a) Both animals have wings. (b) Both animals have legs.
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