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# Mathematics 5

2016/17

Curriculum Mathematics Grade 5
PDF Grade-Set: k-9

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### Big Ideas

### Grandes idées

Numbers describe quantities that can be represented by equivalent fractions.

Numbers

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- How can you prove that two fractions are equivalent?
- In how many ways can you represent the fraction ___?
- How do we use fractions and decimals in our daily life?
- What stories live in numbers?
- How do numbers help us communicate and think about place?
- How do numbers help us communicate and think about ourselves?

Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.

fluency

- Computational Fluency: Computational fluency develops from a strong sense of number.
*Sample questions to support inquiry with students:*- How many different ways can you solve…? (e.g., 16 x 7)
- What flexible strategies can we apply to use operations with multi-digit numbers?
- How does fluency with basic multiplication facts (e.g., 2x, 3x, 5x) help us compute more complex multiplication facts?

Identified regularities in number patterns can be expressed in tables.

patterns

- Patterning: We use patterns to represent identified regularities and to make generalizations.
*Sample questions to support inquiry with students:*- How do tables and charts help us understand number patterns?
- How do tables help us see the relationship between a variable within number patterns?
- How do rules for increasing and decreasing patterns help us solve equations?

Closed shapes have area and perimeter that can be described, measured, and compared.

area and perimeter

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- What is the relationship between area and perimeter?
- What standard units do we use to measure area and perimeter?
- When might an understanding of area and perimeter be useful?

Data represented in graphs can be used to show many-to-one correspondence.

Data

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
*Sample questions to support inquiry with students:*- How do graphs help us understand data?
- In what different ways can we represent many-to-one correspondence in a graph?
- Why would you choose many-to-one correspondence rather than one-to-one correspondence in a graph?

## Learning Standards

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### Curricular Competencies

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*Students are expected to be able to do the following:*### Reasoning and analyzing

Use reasoning to explore and make connections

Estimate reasonably

Estimate reasonably

- estimating by comparing to something familiar (e.g., more than 5, taller than me)

Develop mental math strategies and abilities to make sense of quantities

mental math strategies

- working toward developing fluent and flexible thinking of number

Use technology to explore mathematics

technology

- calculators, virtual manipulatives, concept-based apps

Model mathematics in contextualized experiences

Model

- acting it out, using concrete materials, drawing pictures

### Understanding and solving

Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Visualize to explore mathematical concepts

Develop and use multiple strategies to engage in problem solving

multiple strategies

- visual, oral, play, experimental, written, symbolic

Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

connected

- in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration
- First Peoples people value, recognize and utilize balance and symmetry within art and structural design; have students pose and solve problems or ask questions connected to place, stories, and cultural practices.

### Communicating and representing

Communicate mathematical thinking in many ways

Communicate

- concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas; may use technology such as screencasting apps, digital photos

Use mathematical vocabulary and language to contribute to mathematical discussions

Explain and justify mathematical ideas and decisions

Explain and justify

- using mathematical arguments
- “Prove it!”

Represent mathematical ideas in concrete, pictorial, and symbolic forms

concrete, pictorial, and symbolic forms

- Use local materials gathered outside for concrete and pictorial representations.

### Connecting and reflecting

Reflect on mathematical thinking

Reflect

- sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions

Connect mathematical concepts to each other and to other areas and personal interests

other areas and personal interests

- to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, the environment, popular media and news events, social justice, and cross-curricular integration)

Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

Incorporate

- Invite local First Peoples Elders and knowledge keepers to share their knowledge.

make connections

- Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining (csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)
- aboriginaleducation.ca
*Teaching Mathematics in a First Nations Context,*FNESC fnesc.ca/k-7/

### Content

*Students are expected to know the following:*number concepts to 1 000 000

number concepts

- counting:
- multiples
- flexible counting strategies
- whole number benchmarks

- Numbers to 1 000 000 can be arranged and recognized:
- comparing and ordering numbers
- estimating large quantities

- place value:
- 100 000s, 10 000s, 1000s, 100s, 10s, and 1s
- understanding the relationship between digit places and their value, to 1 000 000

- First Peoples use unique counting systems (e.g., Tsimshian use of three counting systems, for animals, people and things; Tlingit counting for the naming of numbers e.g., 10 = two hands, 20 = one person)

decimals to thousandths

equivalent fractions

whole-number, fraction, and decimal benchmarks

benchmarks

- Two equivalent fractions are two ways to represent the same amount (having the same whole).
- comparing and ordering of fractions and decimals
- addition and subtraction of decimals to thousandths
- estimating decimal sums and differences
- estimating fractions with benchmarks (e.g., zero, half, whole)
- equal partitioning

addition and subtraction of whole numbers to 1 000 000

whole numbers

- using flexible computation strategies involving taking apart (e.g., decomposing using friendly numbers and compensating) and combining numbers in a variety of ways, regrouping
- estimating sums and differences to 10 000
- using addition and subtraction in real-life contexts and problem-based situations
- whole-class number talks

multiplication and division to three digits, including division with remainders

multiplication and division

- understanding the relationships between multiplication and division, multiplication and addition, and division and subtraction
- using flexible computation strategies (e.g., decomposing, distributive principle, commutative principle, repeated addition, repeated subtraction)
- using multiplication and division in real-life contexts and problem-based situations
- whole-class number talks

addition and subtraction of decimals to thousandths

decimals

- estimating decimal sums and differences
- using visual models such as base 10 blocks, place-value mats, grid paper, and number lines
- using addition and subtraction in real-life contexts and problem-based situations
- whole-class number talks

addition and subtraction facts to 20 (extending computational fluency)

addition and subtraction facts to 20

- Provide opportunities for authentic practice, building on previous grade-level addition and subtraction facts.
- applying strategies and knowledge of addition and subtraction facts in real-life contexts and problem-based situations, as well as when making math-to-math connections (e.g., for 800 + 700, you can annex the zeros and use the knowledge of 8 + 7 to find the total)

multiplication and division facts to 100 (emerging computational fluency)

facts to 100

- Provide opportunities for concrete and pictorial representations of multiplication.
- Use games to provide opportunities for authentic practice of multiplication computations.
- looking for patterns in numbers, such as in a hundred chart, to further develop understanding of multiplication computation
- Connect multiplication to skip-counting.
- Connect multiplication to division and repeated addition.
- Memorization of facts is not intended this level.
- Students will become more fluent with these facts.
- using mental math strategies such as doubling and halving, annexing, and distributive property
- Students should be able to recall many multiplication facts by the end of Grade 5 (e.g., 2s, 3s, 4s, 5s, 10s).
- developing computational fluency with facts to 100

rules for increasing and decreasing patterns with words, numbers, symbols, and variables

one-step equations with variables

one-step equations

- solving one-step equations with a variable
- expressing a given problem as an equation, using symbols (e.g., 4 + X = 15)

area measurement of squares and rectangles

relationships between area and perimeter

area and perimeter

- measuring area of squares and rectangles, using tiles, geoboards, grid paper
- investigating perimeter and area and how they are related to but not dependent on each other
- use traditional dwellings
- Invite a local Elder or knowledge keeper to talk about traditional measuring and estimating techniques for hunting, fishing, and building.

duration, using measurement of time

time

- understanding elapsed time and duration
- applying concepts of time in real-life contexts and problem-based situations
- daily and seasonal cycles, moon cycles, tides, journeys, events

classification of prisms and pyramids

classification

- investigating 3D objects and 2D shapes, based on multiple attributes
- describing and sorting quadrilaterals
- describing and constructing rectangular and triangular prisms
- identifying prisms in the environment

single transformations

transformations

- single transformations (slide/translation, flip/reflection, turn/rotation)
- using concrete materials with a focus on the motion of transformations
- weaving, cedar baskets, designs

one-to-one correspondence and many-to-one correspondence, using double bar graphs

many-to-one correspondence

- many-to-one correspondence: one symbol represents a group or value (e.g., on a bar graph, one square may represent five cookies)

probability experiments, single events or outcomes

probability experiments

- predicting outcomes of independent events (e.g., when you spin using a spinner and it lands on a single colour)
- predicting single outcomes (e.g., when you spin using a spinner and it lands on a single colour)
- using spinners, rolling dice, pulling objects out of a bag
- representing single outcome probabilities using fractions

financial literacy — monetary calculations, including making change with amounts to 1000 dollars and developing simple financial plans

financial literacy

- making monetary calculations, including making change and decimal notation to $1000 in real-life contexts and problem-based situations
- applying a variety of strategies, such as counting up, counting back, and decomposing, to calculate totals and make change
- making simple financial plans to meet a financial goal
- developing a budget that takes into account income and expenses

**Note:**Some of the learning standards in the PHE curriculum address topics that some students and their parents or guardians may feel more comfortable addressing at home. Refer to ministry policy regarding opting for alternative delivery.