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The Math Page!
Mathematics includes a combination of simple and complex processes and skills that students need to acquire and apply. Through a combination of direct, explicit instruction in specific skills and more open-ended problem solving, it is our goal to create mathematicians who are able to:
- select appropriate tools and computational strategies, problem solve, reason, reflect, connect, represent, and communicate
The math program that we are using offers mathematics instruction in small chunks, with review of previous, required skills built right into instruction. Mathematical problems will have real-life applications that are meaningful and relevant, and students will be required to share their knowledge in a variety of ways. In our room, we focus on:
- promoting a positive learning environment and building confidence through praise and encouragement
- maintaining a balanced approach to mathematics by addressing both concept and procedure, explicit and inquiry-based learning
- achieving understanding and mastery by breaking mathematics down into sequential, scaffolded steps, while still allowing students to make discoveries
(Teacher's Guide, Jump Math, pg. 1)
Mathematics learning involves a variety of "Big Ideas"** - what is it, in the end, that we want students to come away with? During our math learning, we will be focusing on those big ideas as they relate to the various strands. Some of the big ideas are listed below along with our foci for the year. (**taken from "Big Ideas from Dr. Small" , Nelson Publishing; 2009)
Because our purpose in math class is to build strong foundational skills that will serve students as they move forward in their math learning, the second year of our math program will build on the skills and processes learned last year. Thus, students will continue to work at the same grade level as they did last year as they continue to explore additional concepts that were not covered in year one. Opportunities to expand that knowledge to their current grade level will occur when we are confident that the foundational skills have been solidified.
Please follow the threads below for the units being taught and for ways our math program can be supported at home.
GRADE 6
FOCUS |
SPECIFIC TOPICS |
BIG IDEAS ** |
HOME CONNECTIONS |
SEPTEMBER- OCTOBER
Number Sense |
fraction review
Read, represent, compare and order proper and improper fractions and mixed numbers |
Fractions: -Fractions can represent parts of regions, parts of sets, parts of measures, division or ratio. These meanings are equivalent. -A fraction is not meaningful without knowing what the whole is. -Renaming fractions is often key to comparing them or computing with them. Every fraction can be renamed in an infinite number of ways. -There are multiple models and/or procedures for comparing and computing with fractions, just as with whole numbers -Operations with fractions have the same emanings as operations with whole numbers, even though the algorithms differ.
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newspapers, magazines and television cooking, shopping and travel sports, art,
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NOVEMBER- DECEMBER
Number Sense |
Multiplication - develop automaticity in order to skip count and multiply by 2s, 3s, 5s, 10s, 100s and 1000s -solve problems using multiplication (arrays, groups or sets and repeated addition) -using patterns to aid in memory
Place Value - compose and decompose three-digit numbers into hundreds, tens, and ones in a variety of ways -represent and explain, using concrete materials, the relationship among the nunbers 1, 10, 100 and 1000 - identify and represent the value of a digit in a number according to its position in the number |
-There are relationships between the four operations ...you can represent multiplication as repeated addition and vice versa -There are many situations to which an algorithm is applied, and there are many procedures, or algorithms, for each operation. -Operation procedures should be taught meaningfully, taking into account the various meanings of the oeprations and the principles that apply to their use. -A personal 'invented' algorithm is often more meaningful and sometimes equally efficient as a conventional algorithm. |
-skip count when: walking, setting the table, folding laundry, taking a bath..... -ask how to use addition instead of multiplication and vice verca (ie., there are cookies in this box. How many cookies are there altogether if each person has six cookies? - hint: let them supply the missing numbers) -sing the
multiplication rap -encourage them to use the "if I know this... then I know that..." strategy (as in 'adding on' - if you know what 3x5 is, then 4x5 is one more....) -ask them to visualize the 100s chart - if you skip count by 2s, what numbers do you see? |
JANUARY - FEBRUARY
Number Sense
Geometry
Measurement |
Place value and whole numbers to 10 000
Geometry: polygons: edges, vertices, angles
Metric Measure - mm, cm dm |
Number Sense: -The place value system we use is built on patterns to make our work with numbers more efficient. -Students gain a sense of the size of numbers by comparing them to meaningful benchmark numbers
Geometry: -Some attributes of shapes are quantitative, others are qualitative (ie., shapes that have vertices, edges, etc.) -How a shape can be cut up and rearranged helps us pay attention to the properties of the shape -Many geometric properties and attributes of shapes are related to measurement
-The same object can be described using different measurements -Any measurement can be determined in more than one way -Familiarity with known benchmark measurements can help you estimate and calculate other measurements -The unit chosen for a measurement effects the numerical value of the mea |
-look for and discuss numbers in every day life and in a variety of contexts (money, tv channels, sports scores, measurements, etc.) -compare numbers - which is bigger? smaller? how do you know? -prompt: If you know that 'this length' is one meter, what does that tell you about 'that length'?
-look for 3-D shapes in isolation and in combinations in structures (boxes, buildings, etc.) -use a map or globe to aid in discussions about angles and degrees (ie., 90, 180 and 360)
-measure everything! -use terms and measures interchangeably -involve your child in measuring and constructing in real life - art, carpentry, sewing, etc.
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MARCH- APRIL
Number Sense
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Decimals to 100ths
Division and Multiplication
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-Decimals …allows for modelling, comparisons, and calculations that are consistent with whole numbers, because decimals extend the pattern of the base ten place value system -A decimal can be read and interpreted in different ways; sometimes one representation is more useful than another in interpreting or comparing decimals or for performing and explaining a computation
-There are relationships between the four operations ...you can represent multiplication as repeated addition and vice versa -There are many situations to which an algorithm is applied, and there are many procedures, or algorithms, for each operation. -Operation procedures should be taught meaningfully, taking into account the various meanings of the oeprations and the principles that apply
to their use. -A personal 'invented' algorithm is often more meaningful and sometimes equally efficient as a conventional algorithm. |
-make connections between decimals, fractions, money, and measurement -draw attention to decimals used in real life - |
MAY-JUNE
Geometry
Data Management
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Geometry: transformations
Probability: predicting outcomes |
-there are three motions, or transformations, that change the position or orientation but do not change size and shape -transformations have different effects on the position of the shape, so it is often but not always possible to look at the original shape and the image and determine how it was transformed -transformations are frequently observed in our everyday
world
-an experimental probability is based on past events and experiences -a theoretical probability is based on an analysis of what could or might happen -in a probability situation, you can never be sure what will happen next -sometimes a probability can be estimated by using an appropriate model and conducting an experiment
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-play Simon Says: move two stops right/left/up/down... turn 45/90/180 degrees...flip on this line of reflection -play mirror games -explore tesselations in tilework wallpaper, fabric, and the art of Escher
-make predictions on sports events (ie., is it more/less likely that Tiger Woods will get a hole in one?) -when playing games involving dice - record the number of times you roll certain numbers; ask "what do you notice about the pattern? what number do you predict will happen next"? -draw cards from a deck and record the number of times you draw a heart - if you do this 100 times, you know that there is a "x' number of chances in 100 to pull that type of card |
GRADE 7 and 8
FOCUS |
SPECIFIC TOPICS |
BIG IDEAS ** |
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SEPTEMBER- OCTOBER
Number Sense
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- fractions review
- read, represent, compare and order whole numbers to 1 000 000 and decimal numbers to thousandths
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Fractions: -Fractions can represent parts of regions, parts of sets, parts of measures, division or ratio. These meanings are equivalent. -A fraction is not meaningful without knowing what the whole is. -Renaming fractions is often key to comparing them or computing with them. Every fraction can be renamed in an infinite number of ways. -There are multiple models and/or procedures for comparing and computing with fractions, just as with whole numbers -Operations with fractions have the same emanings as operations with whole numbers, even though the algorithms differ.
Number Sense: -The place value system we use is built on patterns to make our work with numbers more efficient. -Students gain a sense of the size of numbers by comparing them to meaningful benchmark numbers -Decimals
…allows for modelling, comparisons, and calculations that are consistent with whole numbers, because decimals extend the pattern of the base ten place value system -A decimal can be read and interpreted in different ways; sometimes one representation is more useful than another in interpreting or comparing decimals or for performing and explaining a computation
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- newspapers, magazines and television
- cooking, shopping and travel
- sports, art,
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NOVEMBER- DECEMBER
Data Management and Probability
Meaasurement |
- collect, organize and display primary and secondary data and use that data to inform their choices and conclusions about the data
- determine the mean, median and mode of a set of data and tell how, when, or why you would use each
- Determine the relationships among units and measurable attributes, including capacity and volume
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Data Management: -Many data collection activities are based on the prior sorting of information into meaningful categories -To collect good first-hand data, you must decide what collection method is most suitable and how to best pose any questions required to collect the
data -To collect good second-hand data, you must be very clear on what you want to know and what source can be trusted to provide that data -Sometimes a large set of data can be usefully described using a summary statistic, usually a single meaningful number that describes the entire set or a combination of different statistics. The number might describe the values of individual pieces of data and/or how the data is distributed or spread
- The same object can be described using different measurements
- -Any measurement can be determined in more than one way
- -There is always value in estimating a measurement, sometimes because an estimate is all you need or all that is possible, and sometimes because an estimate is a useful check on the reasonableness of a measurement
- -Familiarity with known benchmark measurements can help you estimate and calculate other measurements
-The unit chosen for a measurement affects the numerical value of the measurement; if you use a bigger unit, fewer units are required
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make predictions on sports events (ie., is it more/less likely that Tiger Woods will get a hole in one?)
-when playing games involving dice - record the number of times you roll certain numbers; ask "what do you notice about the pattern? what number do you predict will happen next"?
-draw cards from a deck and record the number of times you draw a heart - if you do this 100 times, you know that there is a "x' number of chances in 100 to pull that type of card
-record the number of times you do something during your games - discuss mean (the average), median (the number in the middle when they're all placed in order) and mode (the number that occurs most frequently)
-examine containers for volume and capacity - discuss the labels! -using containers, ask how the area of a side is related to the volume of the container - how are they the same and different? -do volume / capacity experiments - how many small containers will fit in the large one? what if the containers are only half full - how much is in each one? Do the experiment to prove you're
right! |
JANUARY - FEBRUARY
Geometry |
- use a variety of tools (manipulatives, software, etc.) to construct, sort, compare and classify triangles and quadrilaterals according to symmetry, angles, sides, similarities and congruencies
- create, identify and classify various types of lines
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--Some attributes of shapes are quantitative, others are qualitative (ie., shapes that have vertices, edges, etc.) -How a shape can be cut up and rearranged helps us pay attention to the properties of the shape -Many geometric properties and attributes of shapes are related to measurement |
-look for 3-D shapes in isolation and in combinations in structures (boxes, buildings, etc.)
-use a map or globe to aid in discussions about angles and degrees (ie., 90, 180 and 360)
-play Simon Says: " I see a ____ that is 'congruent'/'similar to...."
-play guessing games: "I"m thinking of a shape that has this many sides, has one 45' angle, and...." What am I? |
MARCH- APRIL
Geometry
Number Sense |
- use a variety of tools (manipulatives, software, etc.) to create and analyse designs using rotations, reflections, and translations
- plot points using all four quadrants of the Cartesian coordinate plane
- use proportional reasoning along with a variety of strategies to identify, compare, represent, order, add and subtract integers
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-there are three motions, or transformations, that change the position or orientation but do not change size and shape -transformations have different effects on the position of the shape, so it is often but not always possible to look at the original shape and the image and determine how it was transformed -locations can be described using maps, using length and angle
measurements, and using coordinate grids -transformations are frequently observed in our everyday world
-The negative integers are the "opposites" of the whole numers. Each integer is a refletion of its opposite across a line that is perpendicular to the number line at 0. - In a number of ways, integers are more like whole numbers than like fractions or decimals -The zero property, that is, (-1) + (+1) = 0, plays an important role in many integer operations -The meanings for the operations that apply to whole numbers , fractions, and decimals, also apply to all integers. Each meaning can be represented by a model, although some models suit some meanings better than others |
-play Simon Says: move two stops right/left/up/down... turn 45/90/180 degrees...flip on this line of reflection -play mirror games -explore tesselations in tilework, wallpaper, fabric and the art of Escher
-discuss changes in temperature, investments, above/below sea level, sports scores (especially golf and fooball) -integrate integer questions with probability questions; for example: play the coin toss game - if a coin lands on heads, you gain a point; if it lands on tails, you lose a point. After 20 losses, what's your final score? |
MAY-JUNE
Patterning and Algebra
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- develop, represent, and make predictions about linear growing patterns using a variety of strategies, including algebraic expressions involving one or two operations
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-Patterns represent identified regularities. -There is always an element of repetition, whether the same items repeat, or whether a “transformation” repeats -The mathematical structure of a pattern can be represented in a variety of ways -Algebra is a way to represent and explain mathematical relationships and to describe and analyze
change
- -Using variables is a way to efficiently and generally describe relationships that can also be described using words
Common Algebraic Generalizations: -you can multiply numbers in any order without changing the product -the effect of doubling one number and adding it to double another nunber, is the same as if you add the numbers first, and then double the sum -to add two fractions with the same denominator, you can add the numerators to determine the new numerator, and use the same denominator -to symbolize the arbitrary multiple of 4, mathematicans use the expression 4n, since the 4n is the result of multiplying a whole number 'n' by 4
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-discuss examples of unit rates (renting a canoe costs $20 as a base rate, and then $5 per hour...how much would the canoe cost for 3 hours?) -then extend the question by supplying the total cost and one of the costs, but leave out the other.. (it costs $25 to rent the canoe; if it costs $5 per hour, how many hours did they rent the canoe?) -play the 'guess my
number' game: select any number; double it; subtract 3; divide by 4; what number did you start with? now try the trick in reverse; use your end number and work backwards; predict the number you will get and then check your predicition -talk to your child about 'balance' and how we can solve equations by maintaining a balance (2n + 3 = n + 5)
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