MINISTRY OF EDUCATION CURRICULUM PLANNING AND DEVELOPMENT DIVISION CONTINUOUS ASSESSMENT COMPONENT SEA - MATHEMATICS
MINISTRY OF EDUCATION CURRICULUM PLANNING AND DEVELOPMENT DIVISION CONTINUOUS ASSESSMENT COMPONENT SEA - MATHEMATICS
TABLE OF CONTENTS
Page Number Rationale Rationale for CAC of the the SEA Mathema Mathematics tics ............................................................................ 1 Curriculum Curriculum Objectives Objectives of CAC in SEA SE A Mathematics Mathematics .................................................................. 2 General Objectives Objectives .............................................................................................................2 Specific Objectives Objectives ............................................................................................................. 2 Features Features of CAC Mathematics Mathematics ................................................................................................... 3 Content and Pedagogy ..................................................................................................... Pedagogy ..................................................................................................... 3 CAC Mathematics Curriculum Objectives ........................................................................ Objectives ........................................................................ 3 Pre-Knowledge ................................................................................................................. Pre-Knowledge ................................................................................................................. 4 Assessment Objectives ...................................................................................................... Objectives ...................................................................................................... 4 Requirements for Performance Tasks in CAC Mathematics Mathematics .............................................. 4 Criteria for Assessment .................................................................................................... 5 Scoring Scoring Rubrics ......................................................................................................................... 6
Rationale for CAC of the SEA Mathematics
Mathematics is a key to the development d evelopment of concepts and skills in all other curriculum areas, and therefore, poor Mathematics performance can hinder students from achieving their full potential not only in Mathematics but in all subject areas. Data Analysis of student examination performance identifies the following following areas of o f concern:
Student underperformance in the Number, Measurement and Geometry Strands.
Underachievement of male students in the Nu mber, Measurement and Geometry Strands.
The factors contributing to the underperformance of students in Mathematics at the Primary School level include three key factors:
Curriculum implementation is set in an exam-driven context where a regimented drill and practice style is used to deliver the curriculum curriculum with a focus on passing examinations.
Children are not provided with opportuni oppo rtunities ties to enjoy en joy Mathematics through explorations and hands-on experiences with resources.
More often than not, the children in our Mathematics classrooms experience what
Curriculum Objectives of CAC in SEA Mathematics
General Objective
To provide opportunities op portunities for students to demonstrate their knowledge, sk ills and understanding of Mathematics in a variety of contexts.
Specific Objectives
To introduce a variety of instructional strategies to cater to t he range of learning styles of pupils.
To engage students in authentic authent ic assessment strategies strategies such as Per formance Tasks.
To use a variety of manipulative materials to enhance the understanding of mathematical concepts and principles and to enjoy Mathematics through fun-filled activities involving team work, investigations and outdoor activities.
Features of CAC Mathematics
Content and Pedagogy
The recommended pedagogical approach to implementing the CAC in SEA Mathematics is to incorporate more aspects of hands-on tasks or explorations (Performance Tasks) using Mathematics resources. These tasks should be set in problem-solving contexts to achieve optimum benefits to students.
The Programme of Work for the CAC in SEA Mathematics Project will focus on three specific strands:
Number
Measurement
Pre-knowledge
The above objectives rest on student mastery of the following: two (2) digit number bond t heory, formulae for perimeter, area, circumference, volume and relevant vocabulary.
Assessment Objectives
1. Calculate perimeter of shapes outlined on Geoboards and Geoboard dot paper 2. Calculate area of shapes outlined on Geoboards and Geoboard dot paper, including triangles rectangles and simple compound shapes 3. Represent on Geoboards a real life situation requiring knowledge and understanding of perimeter and area 4. Draw nets of solids 5. Construct solids from their nets
Criteria for Assessment
The following skills and mathematical processes will be assessed in each per formance task. Use of Manipulative
Work with appropriate manipulative to solve a problem
Problem Solving
Make a plan, based on the information supplied
Select a strategy (steps to solve the problem)
Apply the strategy (multiple solutions may exist)
Verify that solutions satisfy criteria
Representation
Transfer abstract thinking to concrete representations to table/visual or symbolic representations
Scoring Rubrics
A rubric is a scoring guide that seeks to evaluate a student's performance based on the sum of a full range of criteria rather than a single numerical score. A rubric is a wo rking guide for students and teachers, usually handed out before the assignment begins in order to get students to think about the criteria on which their work will be judged. When students receive rubrics beforehand, they understand how they will be evaluated and can prepare accordingly. Common Features of Rubrics
Rubrics can be created in a variety of forms and levels of complexity, however, they all contain three common features which: focus on measuring a stated objective (performance, behaviour, or quality). use a range to rate performance. contain specific performance criteria arranged in levels indicating the degree to which the criteria have been met.
The Geoboard
The focus of the following CAC Mathematics Assessments is based, initially, on the use of the Geoboard to introduce a hands-on approach to Mathematics. The Geoboard allows the exploration of basic concepts in Measurement, Number and Geometry such as perimeter, area or the characteristics of geometrical figures and to apply knowledge, sk ills and competencies gained to solve real-world problems.
Using the Geoboard in Teaching and Learning
The Geoboard is a mathematical manipulative used to explore basic concepts in Plane Geometry. Geoboards were invented and popularized in the 1950s by Egyptian mathematician Caleb Gattegno (1911-1988). It consists of a physical board with a certain number of nails half-driven in, around which are wrapped rubber bands. Each square of the Geoboard has dimensions 1 unit x 1 unit. Basic Features of the Geoboard
GEOBOARD DOT PAPER
Topics which can be explored using the Geoboard include: perimeter reflection counting plane shapes similarity angles translation area patterns rotation fractions polygons
scaling position congruence classification
INTRODUCING THE GEOBOARD IN THE CLASSROOM
Finding Area and Perimeter of a Rectangle made on Geoboard
1. Form a RECTANGLE of your choice. 2. Count the TOTAL NUMBER OF UNITS AROUND THE SHAPE. This is the PERIMETER. Record the Perimeter in units. 3. Count the TOTAL NUMBER OF SQUARES INSIDE THE SHAPE. T his is the AREA. Record the Area in square units. Geoboard Activities Instructional Objectives:
Students will explore activities on the geoboard to compare area and perimeter Instructional Materials: Geoboards, rubber bands
Reasoning: Area of Rectangle is divided into four equal parts. Two parts make up area of triangle. Conclusion: Area of triangle is half area of rectangle
Activity IV: To reinforce the concept of the height of a Triangle.
Form a few triangles with base on either one of the two parallel lines, including scalene triangles
Ask students to indicate heights using rubber bands o f different colours
Reinforce concept that height is perpendicular distance from the vertex to the base
Repeat exercise with different orientations of bases
Activity V
Place student in pairs
Ask each student to create a 4-sided shape
Activity IX: Comparison of area
Students use rubber bands to divide the geoboard into different areas
Students express each area as a fraction (decimal, percent) of the whole area
Activity X: Reflection
Students design a shape on one half of the geoboard
Students construct a reflection of the shape formed in a mirror line
Activity XI: Area and Perimeter of a Rectangle
Form a RECTANGLE having a Perimeter = 24 units
Form other rectangles having a Per imeter = 24 units Options Possible [Reasoning ½ Perimeter = 12. To make 2 sides with a sum of 12
General Teacher Instructions
1.
Teachers are required to have the resources, task sheets, manipulative and scoring rubrics ready prior to the administration of the task.
2.
Each student should be provided with a task sheet, scoring rubrics and manipulative for the task.
3.
Assistance with the reading of instructions for struggling learners should be provided.
4.
Support personnel for the visually impaired students should be arranged in a timely manner.
5.
Teachers must allow sufficient time for students to complete the task.
6.
Practice assessments are opportunities to provide feedback and additional time to improve
CONTINUOUS ASSESSMENT COMPONENT FOR SEA MATHEMATICS
TEACHER’S SHEET
Specific Content Objectives: Students will 1. Demonstrate an understanding of the concepts of area and perimeter of rectangles 2. Identify and use number combinations of two digit numerals 3. Determine the perimeter of rectangles by counting units around the shape and by calculation. 4. Determine the area of rectangles by counting squares and by calculation. Specific Performance Objectives:
ACTIVITY 1: Creating Rectangles using the Geoboard
Gary wants to make a wooden fence along the perimeter of his model farm to enclose the toy animals. The fence is to be rectangular in shape with a perimeter of 18 units. Use your Geoboard and rubber bands to show Gary all the different rectangular shapes he can make. Your shapes should satisfy the following criteria: Perimeter = 18 units Your rectangles may overlap.
ACTIVITY 2: Representing length, width and area of rectangles using a table
Gary wishes to select the rectangle which gives the largest area for his model farm with perimeter of 18 units. Complete the table below to show the length, the width and the area of each rectangle you made in Activity 1. Length in units
Width in units
Area in square units
ACTIVITY 3: Materials needed for the Wooden Fence
Gary wants to use 3 rows of horizontal bars along the entire perimeter of the farm. The horizontal bars are made of flat wooden strips. What is the total length of wooden strips, in units, Gary would need to complete the horizontal bars along his model fence?
SOLUTIONS: WOODEN FENCE ACTIVITY 1: Perimeter of Geoboard Rectangles Student applies criteria for making rectangles 8 units by 1 unit 7 units by 2 units 6 units by 3 units 5 units by 4 units
Explanation: Student’s explanation to i nclude
- selecting sides to give Perimeter of 18 units. - using smaller or larger sides to make new rectangle and checking that perimeter stays 18 units.
Teacher Scoring Rubric – Practice Assessment #1 Wooden Fence Use of Manipulative [2] Attempted task in given time [1] Last name
First name
Demonstrated persistent ontask behaviour [1]
Problem Solving [4] Drew rectangle with largest area and Perimeter of 18 units on Geoboard [1]
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Drew one other rectangle with Perimeter 18 units [1]
Calculated largest area in square units [1]
Representatio n [2] Calculated correctly student’s total length of wooden strips in units [1]
Completed table showing student’s correct length and width of rectangles constructed on Geoboard [1]
Showed correct areas of rectangles in table [1]
Communication [2] Selecting sides to give Perimeter of 18 units [1]
Using smaller or larger sides to make new rectangle and checking that perimeter stays 18 units [1]
CONTINUOUS ASSESSMENT COMPONENT FOR SEA MATHEMATICS
TEACHER’S SHEET
Specific Content Objectives
Students will 1.
Differentiate between the properties of plane geometrical shapes
2. Calculate the areas of plane geometrical shapes using formulae 3. Use strategies to estimate the areas of plane shapes Specific Performance Objectives
Students will 1.
Work with manipulative appropriate for the task
ACTIVITY 1: Dividing the vegetable garden into sections
Grandmother has a vegetable garden in the shape of a square, measuring 10 units by 10 units. She wants to divide the vegetable garden into 4 sections to grow different vegetables. The rules for making the 4 sections are as follows: The sections must have no spaces between them. The hot pepper section measures 10 units by 2 units and will be located along the length of the backyard. The cabbage section is rectangular in shape and measures 8 units by 4 units.
Explain how you made the 4 sections of Grandmother’s vegetable garden. Name the shape of the remaining area.
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ACTIVITY 2: Drawing the sections of the vegetable garden
Use the Geoboard dot paper to draw the 4 sections of the vegetable garden.
Label each section with the name of the vegetable grown in it.
Estimate the area of each section of the vegetable garden by counting squares.
Area of Hot Pepper Section =
SOLUTIONS - VEGETABLE GARDEN ACTIVITY 1: Dividing the vegetable garden into sections
Explanation to divide shape into vegetable garden - Place hot pepper section measuring 10 units by 10 units along one end of
vegetable garden - Select orientations of cabbage and bodi sections so that bodi section is half the area of the cabbage section - Check that a remaining shape is present OR - Total area of vegetable garden is 100 square units - Hot pepper section uses 20 square units of area - Remaining sections will add up to 80 square units - Bodi section is 16 square units - Remaining shape is trapezium
Drawing the shapes of four (4) sections on Geoboard dot paper Possible layout of vegetable garden on Geoboard dot paper HOT PEPPER
BODI
Teacher Scoring Rubric – Practice Assessment #2 Vegetable Garden
Use of Manipulative [2]
Last name
First name
Attempted task in given time [1]
Demonstrated persistent ontask behaviour [1]
Problem Solving [4]
Drew all Named the 4 sections remaining correctly shape on correctly Geoboard [1] [1]
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Estimated correctly area of student bodi section [1]
Representation [2]
Estimated correctly area of student lettuce section [1]
Represented correctly 4 Geoboard sections using Geoboard dot paper [1]
Labelled at least two sections correctly [1]
Communication [2]
Placed hot pepper section 10 units by 10 units along one end of vegetable garden [1]
Made bodi section half the area of the cabbage section and checked that a remaining shape has 4 sides. [1]
APPENDIX
Sample Unit of Work for Mathematics Project
Curriculum Level & Strand
Topic
Measurement
Linear Measure
Objectives
1. Calculate the perimeter of plane geometrical shapes having only vertical and horizontal sides using estimations and formulae 2. Use informal/non-standard units of length to measure and record dimensions 1. Calculate the area of shapes using formulae
Area
2. Use informal/non-standard units of area to measure and record areas of plane shapes 1. Draw solid shape given dimensions of faces
Geometry
Volume/ Capacity
Assessment
Draw plane geometrical shapes using rubber bands and the Geoboard
Obtain measurements of length by counting units horizontally or vertically
Problem-solving Performance Task
Draw plane geometrical shapes using rubber bands and the Geoboard Obtain measurements of area by counting squares inside the plane shape
Problem-solving Performance Task
Draw solid shapes using Geoboard Problem-solving Performance Task
2. Use the Volume formula to calculate volume based on lengths of edges of cubes and cuboids 1. Describe the properties of prisms and pyramids
Solids
Geoboard Activities
Construct prisms from their faces using Folding Geometric solids and paper cut-outs Construct frames of prisms using straws,
Problem-solving Performance Task
Glossary of Terms Terms
Meanings
Assessment
In schools, assessment is concerned with observing learners and collecting information about those observations. Assessment of learners is a way of finding out what they know, understand and can do. Teachers gather information informally by observation or by assigning students specific activities related to the curriculum and by analyzing the students’ performance on those activities.
Assessment Activity
Activity or exercise used for finding out what learners know and can do. Sometimes called an Assessment Task.
Checklists
A list of objectives, skills, competencies and understandings of learners. Teachers indicate learner performance on the checklist to show achievement or an unsuccessful attempt.
Classroom based Assessment
Assessment that takes place in the classroom, usually carried o ut by the teacher.
Grading
Assigning numbers or letters to student assessment activities.
Group Assessment
Assessing learners for the work they complete in a gro up.
Individual Assessment
Examines what an individual learner knows and ca n do. This can be compared with a group assessment when learners working in a group are assessed together. Even if learners work in a group they can sometimes be assessed individually.
Manipulative
Manipulative is concrete material commonly used in teaching Mathematics. It includes blocks, tiles, geometric shapes of different colours and sizes, etc.
Marking
Checking learner assessment for quality. This requires reading and observing. A mark or grade is assigned.
NonStandard Units
Non-standard units are objects that are used to make rough measurements. Example: hand span, thickness of a book, but these vary in size which makes it more difficult to use for an accurate measurement
Performance
An activity in which a teacher observes and makes a judgment about the student’s
TEACHER REFLECTION SHEET
Standard Four
Today’s reflection
Student engagement My Planning
STUDENT REFLECTION SHEET
Standard Four
As I reflect on today’s activity
I particularly remember
I gained new knowledge of
CHECKLIST Developing Performance Tasks Tick
Areas of Focus
Title Strands assessed Specific Objectives (Measurable) Content Objectives (appropriate cognitive level) Performance Objectives Value Outcomes
Resources/Manipulative Task Description – Presentation of Challenge Instructions
Additional Sample Teaching and Learning Tasks for Classroom Use TRANSFORMATIONS Transformation means change .
Under a Geometrical Transformation, the position and dimension of a shape are sometimes changed. The image of a shape is the figure that results after the Transformation.
Types of transformation
1. Slide 2. Flip 3. Turn
APPROACHES TO THE TEACHING OF TRANSFORMATIONS 1. Computer aided drawings
2. Geoboard Grid Paper Game
#1 Topic - Transformations in Geometry Task: Flip using the Geoboard Plane Shapes
#2 Topic-Transformations in Geometry: Task: Turn using the Geoboard
1. Make a right-angled triangle on the left side of your Geoboard as shown below
1.
2. Transform your object by making one quarter of a turn in a clockwise direction. Make image on Geoboard. 3. Transform your object by making one - half of a turn in a clockwise direction. Make image on Geoboard.
# 3 Topic – Spatial Reasoning in Geometry Task - Tangram Puzzle Instructions:
THIS IS A LARGE TRIANGLE:
[Teacher customizes size to fit size of Tangram pieces used at school]
Solutions
#4 Topic - Algebraic Thinking: Number Task: Making Towers of Twenty Resources: Math link cubes/ Bristol board
1. Create one strip of Math link cubes or Bristol Board to denote the number 20.
2. Using Math link cubes /Bristol board create the strips below as follows 2 ten strips 2 six strips 2 three strips 2 nine strips 2 five strips 2 two strips 2 eight strips 2 four strips 2 unit strips
8
8
7
7
6
6
5
5
Scoring Rubric - Making Towers of Twenty (12 Marks) Variable assessed: Number of correct towers made Performance Levels 5 correct combinations ................... [10 marks] 4 correct combinations ..................... [8 marks] 3 correct combinations ..................... [6 marks] 2 correct combinations ..................... [4 marks] 1 correct combination ........................ [2 marks] No correct combination ...................... [0 mark]
Explanation of strategy used to solve problem - Use of number bonds to get numbers which add up to 20 - Selecting sets of strips to make of 20
MATH CLUB LOGO
The Junior Math Club of a Primary School invited Standard Five students to create a logo for a Math Club using tiles of four different shapes.
Triangle
Rhombus
Trapezium
Hexagon
Activity 2: Costing the Logo
The members of the Junior Math Club decided to purchase tiles of the same shape and colour to make the logo. The logo will be posted on the front wall of the Mathematics Club Meeting Room.
A price chart for the tiles is shown below
Bill for Math Club Logo
