Sequence of Units for Grade 7 Mathematics
Indicators and learning outcomes have been grouped into units to assist teachers in planning. These units of work need to be taught and learnt in a specific order for the following reasons:
· Some topics require prerequisites (e.g. patterns with fractions and decimals - in Patterns and Algebra - require students to have learnt about fractions and decimals first in Number).
· External assessment - EMSA and Final Examinations - put some constraints on what units need to be taught in specific trimesters.
TRIMESTER 1:Strand / Unit Code / Unit Title / Recommended period allocation
- / - / Preparatory Unit / 6
Space and Geometry / 7SG1 / Angles, 2D and 3D / 18
Number / 7N1 / Working with Numbers / 24
Patterns and Algebra / 7PA1 / Patterns, Relationships and Graphing / 18
Measurement and Data / 7MD2 / Time / 18
TOTAL / 84
TRIMESTER 2:
Strand / Unit Code / Unit Title / Recommended period allocation
Number / 7N2 / Fractions / 15
Measurement and Data / 7MD1 / Measurement / 18
Number / 7N3 / Decimals and Percentages / 18
Measurement and Data / 7MD3 / Data / 18
TOTAL / 69
TRIMESTER 3:
Strand / Unit Code / Unit Title / Recommended period allocation
Patterns and Algebra / 7PA2 / Expressions and Equations / 18
Number / 7N4 / Probability / 18
Space and Geometry / 7SG2 / Transformations / 18
TOTAL / 54
Grade 7 Learning Outcomes
Grade 7 Standard
Students develop an understanding of mathematical notation to explain mathematical relationships. They interpret tables, diagrams and text in mathematical situations and link concepts and processes within and between mathematical contexts. Students apply mental strategies and logical reasoning to solve problems, judge reasonablenessandjustify solutions.
Students apply numeracy strategies and algorithms to solve problems with whole numbers, integers, decimals and percentages and simple wage and salary problems. They calculate with fractions including mixed numbers and improper fractions. They solve probability problems in experimental and theoretical contexts and compare results.
Students use words and symbols to generalize patterns and represent patterns on the number plane. They simplify and substitute values into algebraic expressions and solve linear equations using a variety of strategies.
Students solve problems involving perimeter, area and volume relationships including problems requiring unit conversions. They complete calculations involving times and explain and use time zones. They examine data within the statistical inquiry cycle using multiple-line, divided bar, pie graphs and stem-and-leaf plots, and means, modes and range to interpret information.
Students use and explain angle relationships and build and draw 3D solids using isometric and plane views. They complete and describe rotations and enlargements and create designs involving transformations and tessellations.
NUMBER / Working With Numbers / 7N1Indicator
By the end of the grade, students will be able to:
§ Use numeracy strategies and algorithms to calculate and solve problems with whole numbers and integers
Pedagogical Approach
Throughout this unit, students will spend the majority of their time learning by:
§ Having opportunities to understand, visually represent, explain, compare, select and use a range of strategies for working with different types of numbers and number properties
§ Using numbers and number properties in real life contexts
§ Using number sense and estimation when solving problems to help judge the reasonableness of a solution
§ Using a variety of hands-on tools and strategies, including but not limited to number lines (horizontal and vertical), hundreds boards, arrays, play money, counters, drawings, base 10 materials, number fans, and multi-link cubes
Learning Outcomes
Students learn to:
Mastered
(Learning Outcome) / Developing / Emerging
7N1.1 / Add and subtract integers / Add and subtract integers using manipulatives and/or diagrams / Add integers using manipulatives and/or diagrams
Explanatory Notes
§ In Grade 6 students ordered and compared integers but this is the first time they have added and subtracted them. Multiplication and division of integers is covered in Grade 8.
§ An integer is a number with no fractional part. Integers include the counting numbers {1, 2, 3, .
..}, zero {0}, and the negatives of the counting numbers {-1, -2, -3, ...}. The students do not need to know this definition, but rather how to work with integers.
§ This is the only LO in this unit where students use integers. For the other LOs, students will be working with whole numbers.
§ Adding and subtracting integers needs to be taught in a very concrete and practical way rather than just giving a set of rules. Students need to experience multiple practical activities involving physically moving forward and backwards / up and down, as well as working with manipulatives and visual representations such as two colors of counters to represent positive and negative and number lines.
§ If temperature is to be used as a context for integers, teachers need to be aware that some students may not have experienced negative temperatures. Use situations within the UAE e.g. Ski Dubai or ice skating at the mall or ask students in the class who may have travelled to colder countries to describe their experiences. It may be more effective to use buildings (basement car park levels = negative numbers, ground floor = 0, upper floors = positive numbers), stairs (with a card stuck to each step giving it a value from -5 to 5), or bank balances, especially when introducing the concepts.
§ When working with integers, many students find that vertical number lines make more sense than horizontal number lines. They may find it easier to connect movement up and down on a vertical number line with positive and negative change (as opposed to movement left and right on a horizontal number line).
Mastered
(Learning Outcome) / Developing / Emerging
7N1.2 / Use and explain algorithms for multiplying a number of any size by a 2 digit number / Use algorithms for multiplying a number of any size by a 2 digit number / Use algorithms for multiplying a number of any size by a 1 digit number
Explanatory Notes
§ In previous grades, students were introduced to the multiplication algorithm. In Grade 6, students learned to multiply a 2 or 3 digit number by a 2 digit number. In Grade 7, students learn to multiply a number of any size by a 2 digit number.
§ The algorithm process can be taught, but students also need to understand how it works. This process was explained in LO 6N1.8.
§ For Mastered, students need to be able to explain the algorithm. They may choose to do this by describing the various areas in the array diagram and how they relate to the steps in the algorithm. Students need to be able to describe the numbers relating to their place value e.g. 1 387 × 23 does not mean multiply the 1 by 2, but rather multiply 1 000 by 20
Mastered
(Learning Outcome) / Developing / Emerging
7N1.3 / Use and explain algorithms for dividing a number of any size by a 1 digit number, and interpret remainders appropriately for the context / Use algorithms for dividing a number of any size by a 1 digit number, and find remainders / Use algorithms for dividing a number of any size by a 1 digit number
Explanatory Notes
§ In Grade 6, students were introduced to the algorithm for division for the first time. They divided a 2 digit number by a 1 digit number. In Grade 7, students are dividing numbers of any size by a 1 digit number.
§ Only short division is needed (not long division).
§ The algorithm process can be taught, but students also need to understand how it works. This process was explained in LO 6N1.10.
§ The words quotient, divisor and dividend are not needed.
For Mastered, students need to interpret remainders appropriately for the context of the problem. Sometimes they need to round to the closest whole number, sometimes they need to round up, and sometimes they need to round down. For example: Aisha is packaging chocolates into boxes to give to the students at her school. Each box can hold 8 chocolates. She has 1 254 chocolates. How many complete boxes can she fill? SOLUTION: 1 254 ÷ 8 = 156, with remainder 6. She can pack 156 complete boxes of chocolates (must round down, because she cannot give out incomplete boxes).
Mastered
(Learning Outcome) / Developing / Emerging
7N1.4 / Select and use an appropriate numeracy strategy or algorithm to solve multiplication and division problems and justify the choice of strategy / Select and use an appropriate numeracy strategy to solve multiplication and division problems / Use an appropriate numeracy strategy to solve multiplication and division problems
Explanatory Notes
§ In previous grades, students were introduced to a variety of numeracy strategies. These will need to be revisited thoroughly. These strategies include: partitioning, using known facts, reversing, compensation, and double one, halve the other.
§ As students become proficient with various strategies, the focus in Grade 7 is learning to identify when to use particular strategies. Students must become familiar with all the numeracy strategies so that they are able to select a strategy that is suitable for a given problem. The strategy must be effective (allows them to obtain the correct answer), efficient (will obtain the correct answer quickly) and suitable (suited to the particular problem i.e. the numbers and operation involved).
§ Students need to develop an understanding of when certain strategies are particularly useful, e.g. doubling and halving is useful where there is a ‘5’ number (5, 15, 50, 500 ...); compensation is useful when there is a number close to a tens number (19, 31 ...); partitioning can be used for most problems.
To develop and learn numeracy strategies, students need to progress through concrete and representational stages before being able to use the strategies more abstractly. However, the goal is to be able to use numeracy strategies mentally i.e. without written working or visual representation.
Mastered
(Learning Outcome) / Developing / Emerging
7N1.5 / Solve simple wage and salary problems / Explain the difference between a wage and a salary / Identify the relationships between days, weeks, months and years
Explanatory Notes
§ This is the first time this concept has been introduced. Begin by reviewing work done in 6MD2 on the calendar and units of time, including establishing how many days are in a week, weeks in a year, months in a year, days in a year
§ Amounts in both questions and answers need to be whole numbers, e.g.
Ahmed earns 6500 AED per month. Find his annual salary. / ü / Amounts in question and answer are both whole numbers
Ahmed earns 80 000 AED per year. Find his weekly salary. / û / Decimal amount in answer
Ahmed earns 28.50 AED per hour. How much will he earn if he works 40 hours? / û / Decimal amount in question
§ At Grade 7, problems should only involve one conversion e.g. finding monthly amount from a yearly salary figure.
§ Include the word ‘annual’ but not ‘per annum’ or the abbreviation ‘p/a’.
§ At Grade 7, students only study wages and salaries – not overtime / piecework / commission / bonuses etc.
Teachers should be aware that in the UAE, salaries in real life contexts are commonly described using a monthly figure (e.g. 16 000 AED per month). This is in contrast to Western countries, where salaries are commonly described using an annual figure (e.g. $31 000 per year).
Mastered
(Learning Outcome) / Developing / Emerging
7N1.6 / Classify numbers as prime, composite or neither and justify the decision / Classify numbers as prime, composite or neither / State some prime and composite numbers
Explanatory Notes
§ This is the first time this concept has been introduced. In Grade 6 students were introduced to factors and multiples, but this will need to be revisited before introducing prime and composite numbers.
§ Teaching for this LO can be integrated with teaching of 7N1.7 (squares and square roots) – see notes and diagrams below for 7N1.7.
§ After establishing the concepts of prime and composite numbers in a concrete way, students should find all the prime and composite numbers up to 100 using a systematic approach such as the Sieve of Eratosthenes (do not use this title with the students).
§ Students need to know that 1 is neither prime nor composite. The definition of a prime number is that it has exactly 2 factors; the definition of a composite number is that it has more than 2 factors; the number 1 has only 1 factor so is neither prime nor composite.
§ Sample question for Emerging: ‘Name 3 prime numbers and 3 composite numbers’
Sample question for Developing: ‘Classify these numbers as prime, composite or neither: 37, 12, 81, 4, 11, 1’
Mastered
(Learning Outcome) / Developing / Emerging
7N1.7 / Find and explain squares and related square roots of numbers / Find squares and related square roots of numbers / Find squares of numbers
Explanatory Notes
§ This is the first time this concept has been introduced.
§ Use whole numbers only, from 12=1 up to 102 = 100.
§ Teaching for this LO can be integrated with teaching of 7N1.6 (prime and composite numbers). Students should use manipulatives and diagrams to explore making arrays which represent different numbers (e.g. using multilink cubes, grid paper). This can be done within real-life contexts such as making chocolate bars. Students can identify numbers that can only be arranged in one way, as a single row (prime numbers); numbers that can be arranged in multiple ways (composite numbers); and numbers that can be arranged in a square (square numbers).
3 / 4 / 5 / 6
/ / / / /
Prime
(only one arrangement) / Composite (more than one arrangement)
AND a square number (square arrangement) / Prime
(only one arrangement) / Composite (more than one arrangement)
§ Ensure students understand the relationship between square numbers and square roots (the word ‘inverse’ is not required; simply a conceptual understanding of the relationship). Also help students see why the name ‘square numbers’ is appropriate (consider square arrays as above).
A student at the Mastered level would be able to explain in words what square numbers and square roots are (describing the concept of squares and square roots, not only listing examples), and explain why a particular number is or is not a square number. This could involve drawing a diagram or using manipulatives.
Mastered
(Learning Outcome) / Developing / Emerging
7N1.8 / Solve and explain simple problems involving order of operations / Solve simple problems involving order of operations / Identify the order of operations
Explanatory Notes
§ This is the first time this concept has been introduced.
§ Students need to investigate the impact that changing the order has when performing a series of operations to establish the need for an agreed order of operations
e.g. Solve 2+4×3-1
Solution using the order of operations: 2+12-1=13
Solution working from left to right: 6×3-1=17
§ Many different acronyms and mnemonics for the order of operations and different terms for the operations themselves are used in different education systems. It is important that our students have consistency so all teachers should use BEDMAS – Brackets, Exponents, Division and Multiplication, Addition and Subtraction.
§ In Grade 7, exponents should be limited to squares as this is all students have learned up to this point.
§ Students must know that division and multiplication have the SAME priority and are done from left to right, and that addition and subtraction have the SAME priority and are done from left to right. This is required even at the emerging level.