The Mathematics Curriculum in Primary and Lower Secondary Grades

Qatar has developed curriculum standards for all subject areas in all grades, and has contracted to institutions and companies the preparation of curricula that cover these standards, which represent a key pillar in the educational reform of Qatar. The national curriculum standards identify educational objectives that students must attain at each grade level. The standards are used to ensure that students in Qatar are receiving high quality education similar to the education in developed countries. The standards also help public school graduates to enter prestigious universities and compete in the local and international labor markets. Qatar has participated in TIMSS to ensure the quality of its education outcomes.

Mathematics standards generally are designed to allow students to develop mathematical problem solving skills, routine and nonroutine, to develop proficiency in mental and written arithmetic, and to learn to use calculators and computers to support mathematical procedures. The curriculum standards for mathematics are organized according to the following strands:

Reasoning and Problem Solving
Numbers and Algebra
Geometry and Measurements
Data Handling, which is divided into Statistics and Probability

The standards for the reasoning and problem solving strand should be integrated at all times with the standards from each of the other three strands so that students learn to make connections in learning associated with success in mathematics. The proportion of each content strand devoted to reasoning and problem solving should increase steadily from grade to grade. Mathematical reasoning includes explaining mathematical facts, solving problems and puzzles, understanding mathematical procedures and formulas, and justifying and giving reasons for results. The logical thinking involved in reasoning leads to writing mathematical proofs, which lies at the heart of the subject.

Information and Communications Technology (ICT) is a powerful tool in mathematics. Used appropriately, it helps students to develop better knowledge and skills and makes a successful transition to the world beyond school. ICT does not replace the need for students to master mental and written calculation skills and other mathematical techniques. Basic calculators, when used to carry out tedious calculations, allow students to focus on the strategies needed to solve a problem. They also can be a useful support in learning arithmetic, helping students grasp ideas and concepts.

The mathematics standards for kindergarten to Grade 9 are grouped into four strands: Reasoning and Problem Solving; Numbers and Algebra; Geometry and Measurements; and Data Handling. The Reasoning and Problem Solving strand cuts across the other three strands and should be integrated with them in teaching and assessments. For Grade 4, approximately 50 percent of the teaching and assessment of each of the other three strands should be devoted to reasoning and problem solving. For Grades 1 to 6, the weighting of the three content strands relative to each other is as follows: Numbers and Algebra—60 percent; Geometry and Measurements—30 percent; Data Handling—10 percent. The mathematics standards at the fourth grade are outlined as follows:⁵

Reasoning and Problem Solving—Students represent and interpret routine and nonroutine mathematical problems using calculations, mathematical symbols, diagrams, graphs, charts, and tables. They explain orally in their own words, in writing, or by using diagrams the method used to solve a problem or why an answer is correct. They check that results are appropriate in the context of the problem. They justify their reasoning in simple cases.
Numbers and Algebra—Students represent whole numbers and decimals to two places in expanded form and use their understanding of place value to order numbers and to multiply and divide by multiples of 10 and 100. They round whole numbers to the nearest 10 or 100, and decimals to the nearest whole number, and estimate answers to calculations. They identify multiples of one-digit numbers and extend and find missing numbers in a simple linear sequence. They know multiplication and division facts to 10 × 10 and use factors to simplify mental multiplication and division calculations. They select, use, and explain written column methods to multiply and divide three-digit by one-digit whole numbers, multiply three-digit by two-digit whole numbers, add and subtract decimals to two places, and multiply a decimal with up to two places by a one-digit whole number. They add and subtract two simple fractions with the same denominator or where one denominator is a multiple of the other, expressing the answer as a mixed number. They solve routine and nonroutine problems (up to two steps with whole numbers or one step with decimals), including real life problems related to money or measures.
Geometry and Measurements—Students identify parallel and perpendicular lines, recognize lines of symmetry, and complete symmetrical figures. They identify angles as greater than or less than a right angle and order acute and obtuse angles according to size. They identify simple properties of squares, rectangles, and parallelograms. They construct squares and rectangles on grids and by using a set square and ruler, drawing lines to the nearest millimeter. They solve simple problems involving scale. They find the perimeter of irregular polygons and the perimeter and area of shapes that can be divided into squares and rectangles. They select and use suitable units for estimating and measuring and read scales with increasing accuracy. They convert centimeters to meters or millimeters, using decimal notation. They calculate time intervals of up to 1 hour in minutes, and larger time intervals that are multiples of 15 minutes.
Data Handling—Students complete, extract, and interpret information presented in lists, two-way tables, and simple Carroll diagrams. They solve problems using data presented in bar charts and tables.

The mathematics standards for kindergarten to Grade 9 are grouped into four strands: Reasoning and Problem Solving; Numbers and Algebra; Geometry and Measurements; and Data Handling. The Reasoning and Problem Solving strand cuts across the other three strands and should be integrated with them in teaching and assessments. For Grade 8, approximately 70 percent of the teaching and assessment of each of the other three strands should be devoted to reasoning and problem solving. For Grades 7 to 9, the proportion of algebra in the Numbers and Algebra strand increases as the proportion of number decreases. The weighting of the content strands relative to each other is as follows: Numbers—25 percent; Algebra—30 percent; Geometry and Measurements—27.5 percent; Data Handling—17.5 percent. The mathematics standards at the eighth grade are outlined below:⁶

Reasoning and Problem Solving—Students solve routine and nonroutine mathematical problems in a range of contexts. They represent and interpret problems and solutions in numeric, algebraic, geometric, or graphical form, using correct terms and notation. They select and use appropriate mathematical techniques and tools to solve problems, including ICT. They use diagrams and explanatory text to explain solutions and support them with evidence. They present concise, reasoned arguments orally and using symbols. They use step by step reasoning to deduce properties or relationships in given geometrical figures. They find counter-examples to show that conjectures are false and begin to consider special cases. They find alternative solutions to problems.
Numbers and Algebra—Students solve routine and nonroutine problems by calculating accurately with positive and negative whole numbers, decimals, and fractions, and with percentages, ratios, and proportions. They select mental, written, or calculator methods as appropriate and apply the commutative, associative, or distributive laws. They estimate and calculate positive integer powers of numbers and square and cube roots, using the power and root keys of a scientific calculator where appropriate. They simplify and evaluate algebraic expressions and formulas and find the sum or difference of simple algebraic fractions with integer denominators. They formulate and use linear expressions to model situations. They construct and solve linear equations, including those with simple fraction coefficients, and determine whether given values satisfy an equation. They extend and find missing terms in numeric, geometric, or algebraic sequences and generalize the relationship between one term and the next or describe the n^th term, using symbols. They interpret and sketch graphs of proportional or linear functions representing practical situations, including distance-time and conversion graphs. Given the graph of a function, they identify intercepts on axes and intervals where the function increases, decreases, or is constant.
Geometry and Measurements—Students identify all the symmetries of two-dimensional shapes. They calculate interior and exterior angles of polygons. They solve problems using angle and symmetry properties of polygons and angle properties of parallel and intersecting lines. They identify the reflection, rotation, or translation of two-dimensional shapes and draw simple transformations, including combinations of two transformations. They recognize similar shapes and enlarge shapes by a positive integer scale factor. They construct two-dimensional shapes from given information, including scale drawings. They visualize and describe three-dimensional shapes in different orientations. They convert measurements within systems of units. They solve problems involving speed or density, or the volume and surface area of cubes, cuboids, prisms, and cylinders, using a calculator where appropriate. They recognize that measurements are not precise.
Data Handling—Students solve problems by selecting and using an appropriate method of data collection, including from secondary sources. They collect and record continuous data using equal class intervals. They recognize that inappropriate grouping of data can be misleading. They construct bar charts, frequency diagrams, and pie charts. They compare two data sets, using the range, median, or mean, and the shape of the corresponding frequency distributions. They interpret data sets by drawing conclusions, making predictions, and estimating values between and beyond given points. They use data from experiments to estimate probability for favorable outcomes and understand that different outcomes may result from repeating an experiment. They use problem contexts to calculate theoretical probabilities for possible outcomes.