OUTCOME: N4.1 Demonstrate an understanding of whole numbers to 10 000 (pictorially, physically, orally, in writing, and symbolically) by: • representing • describing • comparing two numbers • ordering three or more numbers. [C, R,V] Instructional Strategies -students write numbers between 1 and 10 000 on a card, and then put them in order. -Human number line -Solar system (students find the distance of the planets and the moon from the earth) Key Indicators - i) Explain the meaning of each digit in a 4-digit number representing a particular quantity. Concepts (Nouns, Knows) meaning of each digit in a four digit number Skills (Verbs, Dos) (4)Explain Big Ideas (Enduring Understandings) Essential Questions The position of a number determines its value. How many different numbers can you make with four digits? - k) Create and order three different 4-digit numerals. Concepts (Nouns, Knows) four digit numeral Skills (Verbs, Dos) (6)Create Order Big Ideas (Enduring Understandings) Essential Questions The position of a number determines its value. - m) Identify incorrectly placed numbers in an ordered sequence or shown on a number line Concepts (Nouns, Knows) incorrectly placed number Skills (Verbs, Dos) (4)Identify Big Ideas (Enduring Understandings) Essential Questions The position of a number determines its value. - n) Decompose and represent a 4-digit number at least three different ways. Concepts (Nouns, Knows) four digit numbers MATH Grade 4 (Updated FEB-6-2012) Skills (Verbs, Dos) (5)Decompose Represent three ways Big Ideas (Enduring Understandings) Essential Questions The position of a number determines its value. - o) Explain why two or more number compositions represent the same quantity. Concepts (Nouns, Knows) number compositions Skills (Verbs, Dos) (4)Explain Big Ideas (Enduring Understandings) Essential Questions The position of a number determines its value. MATH Grade 4 (Updated FEB-6-2012) OUTCOME: N4.2 Demonstrate an understanding of addition of whole numbers with answers to 10 000 and their corresponding subtractions (limited to 3 and 4-digit numerals) by: • using personal strategies for adding and subtracting • estimating sums and differences • solving problems involving addition and subtraction. [C, CN, ME, PS, R] Key Indicators - c) Estimate sums and differences using different strategies (e.g., front-end estimation and compensation). Concepts (Nouns, Knows) Sums Differences Skills (Verbs, Dos) (3)Estimate Big Ideas (Enduring Understandings) Numbers can be increased and decreased through the use of addition and subtraction. Essential Questions How can you tell if you are in the right ballpark? - e) Solve problems that involve addition and subtraction of more that two numbers. Concepts (Nouns, Knows) addition and subtraction problems Skills (Verbs, Dos) (4/5)Solve Big Ideas (Enduring Understandings) Whole numbers can be increased and decreased through the use of addition and subtraction. Essential Questions MATH Grade 4 (Updated FEB-6-2012) OUTCOME: N4.3 Demonstrate an understanding of multiplication of whole numbers (limited to numbers less than or equal to 10) by: • applying mental mathematics strategies • explaining the results of multiplying by 0 and 1 [C, CN, R] Key Indicators a) Explain the strategy used to determine a product Concepts (Nouns, Knows) strategy Skills (Verbs, Dos) (4)Explain determine product Big Ideas (Enduring Understandings) Whole numbers can be increased through the use of multiplication. Essential Questions How does skip counting help us to calculate more efficiently? b) Explain the strategy used in a given solution to a product Concepts (Nouns, Knows) Strategy Skills (Verbs, Dos) (4/5)Explain product of a given solution o halving o doubling o adding one more group o subtracting one more group o relating division:multiplication o skip counting Big Ideas (Enduring Understandings) Whole numbers can be increased through the use of multiplication. MATH Grade 4 (Updated FEB-6-2012) Essential Questions OUTCOME: N4.4 Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) by: • using personal strategies for multiplication, with and without concrete materials • using arrays to represent multiplication • connecting concrete representations to symbolic representations • estimating products • solving problems. [C,ME, PS, R, V] Key Indicators a) Model a multiplication problem (concretely or symbolically) using the distributive property Concepts (Nouns, Knows) distributive property Skills (Verbs, Dos) (3)model Big Ideas (Enduring Understandings) Whole numbers can be increased through the use of multiplication. Essential Questions How can you use place value to solve 2 or 3 digit multiplication. b) Use concrete materials, such as base ten blocks or their pictorial representations, to represent multiplication and record the process symbolically. Concepts (Nouns, Knows) concrete materials process Skills (Verbs, Dos) (3)use represent record symbolically Big Ideas (Enduring Understandings) Whole numbers can be increased through the use of multiplication. Essential Questions d) Estimate a product using a personal strategy. Concepts (Nouns, Knows) product Skills (Verbs, Dos) (3)estimate Big Ideas (Enduring Understandings) Whole numbers can be increased through the use of multiplication. Essential Questions f) Solve a multiplication problem and explain the strategies or processes used. Concepts (Nouns, Knows) problem MATH Grade 4 (Updated FEB-6-2012) Skills (Verbs, Dos) (5)solve strategies process explain Big Ideas (Enduring Understandings) Whole numbers can be increased through the use of multiplication. Essential Questions MATH Grade 4 (Updated FEB-6-2012) OUTCOME: N4.5 Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by: • using personal strategies for dividing with and without concrete materials • estimating quotients • explaining the results of dividing by 1 • solving problems involving division of whole numbers • relating division to multiplication. [C, CN, ME, PS, R, V] Key Indicators - d) Create and solve a word problem involving a 1- or 2-digit dividend (the number being divided into). Concepts (Nouns, Knows) word problem Skills (Verbs, Dos) (6)create solve Big Ideas (Enduring Understandings) Whole numbers can be decreased through the use of division. Essential Questions When can division be used to solve a problem? e) Estimate a quotient using a personal strategy Concepts (Nouns, Knows) quotient Skills (Verbs, Dos) (3)estimate Big Ideas (Enduring Understandings) Whole numbers can be decreased through the use of division. Essential Questions - g) Explain, using examples, the relationship between division and multiplication. Concepts (Nouns, Knows) relationship Skills (Verbs, Dos) (4/5/6)explain division:multiplication Big Ideas (Enduring Understandings) Multiplication and division are opposite operations. MATH Grade 4 (Updated FEB-6-2012) Essential Questions MATH Grade 4 (Updated FEB-6-2012) OUTCOME: N4.6 Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to: • name and record fractions for the parts of a whole or a set • compare and order fractions • model and explain that for different wholes, two identical fractions may not represent the same quantity • provide examples of where fractions are used. [C, CN, PS, R, V] Instructional Strategies -Half measures (give students a half cup measure to make recipes in whole cup measures) -Function Box (a halving machine where the kids put in whole numbers and the kid inside the box has to halve the number) -Everyday halves (half of a sandwich, have of an orange, etc.) Key Indicators - b) Represent a fraction using concrete materials. Concepts (Nouns, Knows) fractions Skills (Verbs, Dos) (3)represent symbolically Big Ideas (Enduring Understandings) Numbers can be represented by parts of a whole or parts of a set. Essential Questions In real life, when do you use fractions? - c) Name and record the fraction for the included and not included parts of a set. Concepts (Nouns, Knows) parts of a set Skills (Verbs, Dos) (3)Name Record included not included Big Ideas (Enduring Understandings) Numbers can be represented by parts of a whole or parts of a set. Essential Questions - d) Name and record the shaded and non-shaded (included and not included) parts of a whole Concepts (Nouns, Knows) parts of a whole Skills (Verbs, Dos) (3)name record included not included Big Ideas (Enduring Understandings) Numbers can be represented by parts of a MATH Grade 4 (Updated FEB-6-2012) Essential Questions whole or parts of a set. - g) Explain how denominators can be used to compare two unit fractions with numerator 1 Concepts (Nouns, Knows) denomiators unit fractions Skills (Verbs, Dos) (4)explain compare numerator of 1 Big Ideas (Enduring Understandings) Numbers can be represented by parts of a whole or parts of a set. Essential Questions - k) Name fractions between two benchmarks on a number line Concepts (Nouns, Knows) fractions between benchmarks Skills (Verbs, Dos) (5)name Big Ideas (Enduring Understandings) Numbers can be represented by parts of a whole or parts of a set. Essential Questions - n) Provide an example of a fraction that represents part of a set, a fraction that represents part of a whole, or a fraction that represents part of a length from everyday contexts. Concepts (Nouns, Knows) Fractions Skills (Verbs, Dos) (6)provide part of a set part of whole part of a length Big Ideas (Enduring Understandings) Numbers can be represented by parts of a whole or parts of a set. MATH Grade 4 (Updated FEB-6-2012) Essential Questions MATH Grade 4 (Updated FEB-6-2012) OUTCOME: N4.7 Demonstrate an understanding of decimal numbers in tenths and hundredths (pictorially, orally, in writing, and symbolically) by: • describing • representing • relating to fractions. [C, CN, V] Instructional Strategies -Decimal Place Value -Clothesline Number Line -Dollars and Cents (give them money and they have to explain value in dollars and cents and tell where the decimals go) Key Indicators e) Record a money value using decimals. Concepts (Nouns, Knows) money value Skills (Verbs, Dos) (3)record Big Ideas (Enduring Understandings) Decimals are derived from fractions. Essential Questions How are fractions and decimals related? j) Express orally and in symbolic form a fraction with a denominator of 10 or 100 as a decimal. Concepts (Nouns, Knows) fraction as a decimal Skills (Verbs, Dos) (3)express denominator of 10 denominator of 100 Big Ideas (Enduring Understandings) Decimals are derived from fractions. Essential Questions k) Express a pictorial or concrete representation as a fraction or decimal. Concepts (Nouns, Knows) fraction pictorially concretely decimal pictorially MATH Grade 4 (Updated FEB-6-2012) Skills (Verbs, Dos) (3)express concretely Big Ideas (Enduring Understandings) Decimals are derived from fractions. Essential Questions l) Express orally and in symbolic form the decimal equivalent for a fraction. Concepts (Nouns, Knows) decimal and fraction equivalents Skills (Verbs, Dos) (3)express Big Ideas (Enduring Understandings) Decimals are derived from fractions. Essential Questions MATH Grade 4 (Updated FEB-6-2012) OUTCOME: N4.8 Demonstrate an understanding of addition and subtraction of decimals limited to hundredths (concretely, pictorially, and symbolically) by: • using compatible numbers • estimating sums and differences • using mental math strategies • solving problems. [C, ME, PS, R, V] Key Indicators b) Solve problems, including money problems, which involve addition and subtraction of decimals, limited to hundredths. Concepts (Nouns, Knows) money problems Skills (Verbs, Dos) (4)solve Big Ideas (Enduring Understandings) Decimals can be increased and decreased through the use of addition and subtraction. Essential Questions How can you tell if you are in the right ballpark? e) Count back change for a purchase. Concepts (Nouns, Knows) change Skills (Verbs, Dos) (3)count Big Ideas (Enduring Understandings) Decimals can be increased and decreased through the use of addition and subtraction. Essential Questions g) Represent a sum or difference of two decimals concretely or pictorially, and record the solution to the sum or difference symbolically. Concepts (Nouns, Knows) concretely pictorially Skills (Verbs, Dos) (6)represent record Big Ideas (Enduring Understandings) Essential Questions MATH Grade 4 (Updated FEB-6-2012) Decimals can be increased and decreased through the use of addition and subtraction. Concepts (Nouns, Knows) Skills (Verbs, Dos) Big Ideas (Enduring Understandings) Essential Questions MATH Grade 4 (Updated FEB-6-2012) OUTCOME: P4.1 Demonstrate an understanding of patterns and relations by: • identifying and describing patterns and relations in a chart, table or diagram • reproducing patterns and relations in a chart, table, or diagram using manipulatives • creating charts, tables, or diagrams to represent patterns and relations • solving problems involving patterns and relations [C, CN, PS, R] Key Indicators - a)Identify and describe a variety of patterns in a multiplication chart -b)Determine the missing element(s) in a table or chart and explained the strategies used -d)Describe the pattern found in a table or chart -e)Create a concrete representation of a pattern displayed in a table or chart -o)Solve a problem by using a chart or diagram to identify mathematical relationships Instructional strategies - review using simple pictorial and sound patterns - use “youtube” - send students on a “pattern treasure hunt” (equip each group with a video camera if available) - listening to patterns in music - finding patterns in clothing - review skip counting in relation to patterns a)Identify and describe a variety of patterns in a multiplication chart Concepts (Nouns, Knows) Patterns and Relations - patterns -multiplication chart Skills (Verbs, Dos) Patterns and Relations (Level 1) Identify (patterns in mult chart) (Level 2) Describe (patterns in mult chart) Big Ideas (Enduring Understandings) Essential Questions What do the values in a table tell you? The world is full of patterns b)Determine the missing element(s) in a table or chart and explain the strategies used Concepts (Nouns, Knows) Patterns and Relations - missing element(s) - table -chart - strategies MATH Grade 4 (Updated FEB-6-2012) Skills (Verbs, Dos) Patterns and Relations (Level 4) Determine (missing elements) (Level 2) Explain (strategies) Big Ideas (Enduring Understandings) Essential Questions The world is full of patterns What type of reasoning is being used to extend a pattern? (inductive) What type of reasoning is being used to find new entries in a table? (inductive) How do patterns help us make predictions? d)Describe the pattern found in a table or chart Concepts (Nouns, Knows) Skills (Verbs, Dos) Patterns and Relations - Pattern -Table -Chart (Level 2) Describe (pattern) Big Ideas (Enduring Understandings) Essential Questions Patterns and Relations What do the values in a table tell you? The world is full of patterns e)Create a concrete representation of a pattern displayed in a table or chart Concepts (Nouns, Knows) Patterns and Relations - concrete representation - patterns - table - chart Skills (Verbs, Dos) Big Ideas (Enduring Understandings) Essential Questions MATH Grade 4 (Updated FEB-6-2012) Patterns and Relations (Level 6) Create (concrete pattern) The world is full of patterns How many different ways can you represent the same pattern? o)Solve a problem by using a chart or diagram to identify mathematical relationships Concepts (Nouns, Knows) Patterns and Relations - problem - chart - diagram - mathematical relationships Skills (Verbs, Dos) Big Ideas (Enduring Understandings) Essential Questions Solving problems means trying many things How do patterns help us solve problems? Patterns and Relations (Level 3) Solve (problem) ( Level 1) Identify (mathematical relationships) When and why would you use a Venn or Carrol diagram? MATH Grade 4 (Updated FEB-6-2012) OUTCOME: P4.2 Demonstrate an understanding of equations involving symbols to represent an unknown value by: • writing an equation to represent a problem • solving one step equations. [C, ME, PS, R] Key Indicators -b) Write an equation in symbolic form for a given pictorial or concrete representation. -h) Represent and solve an addition or subtraction problem involving a “part-part-whole” or comparison context using a symbol to represent the unknown. -i) Represent and solve a multiplication or division problem involving equal grouping or partitioning (equal sharing) using a symbol to represent the unknown. Instructional strategies - introduce with a rebus story to show that symbols are representative - smart board activities, “mathletics” - going through exemplars of the process -b)Write an equation in symbolic form for a given pictorial or concrete representation. Concepts (Nouns, Knows) equation (symbolic form) -pictorial or concrete representation Big Ideas (Enduring Understandings) Symbols, numbers and pictures are all related. Skills (Verbs, Dos) (3)write Essential Questions How can you make an equation from pictures or numbers? -h) Represent and solve an addition or subtraction problem involving a “part-partwhole” or comparison context using a symbol to represent the unknown. Concepts (Nouns, Knows) addition or subtraction problem “part-part-whole” symbol (unknown) Big Ideas (Enduring Understandings) Skills (Verbs, Dos) (3)represent (3)solve Essential Questions Symbols can represent an unknown. MATH Grade 4 (Updated FEB-6-2012) How can you show an unknown in a addition or subtraction problem? -i) Represent and solve a multiplication or division problem involving equal grouping or partitioning (equal sharing) using a symbol to represent the unknown. Concepts (Nouns, Knows) multiplication or division problem equal grouping symbol (unknown) Big Ideas (Enduring Understandings) Skills (Verbs, Dos) (3)represent (3)solve Essential Questions Symbols can represent an unknown. MATH Grade 4 (Updated FEB-6-2012) How can you show the unknown in a multiplication or division problem? OUTCOME: SS4.1 Demonstrate an understanding of time by: • reading and recording time using digital and analog clocks (including 24 hour clocks) • reading and recording calendar dates in a variety of formats. [C, CN, V] Key Indicators c. Express the time orally and numerically shown on a 24-hour analog clock. f. Express time orally as “minutes to” or “minutes after” the hour. h. Write dates in a variety of formats (e.g., yyyy/mm/dd; dd/mm/yyyy; March 21, 2006; dd/mm/yy). Concepts (Nouns, Know) - time 24 hour analog clock Skills (Verbs, Dos) - (1) express orally and numerically - time minutes to the hour/after the hour - (1) express orally - dates (variety of formats) - (3) write Big Ideas (Enduring Understandings) Time is represented using clocks and calendars. Essential Questions Possible Instructional Applications: - Have students create a vacation itinerary complete with dates and times in 24 hr. format for all activities. For differentiation students could outline their day using 24 hr. format. MATH Grade 4 (Updated FEB-6-2012) Why is it important to know how to tell time? OUTCOME: SS4.2 Demonstrate an understanding of area of regular and irregular 2-D shapes by: • recognizing that area is measured in square units • selecting and justifying referents for the units cm2 or m2 • estimating area by using referents for cm2 or m2 • determining and recording area (cm2 or m2) • constructing different rectangles for a given area (cm2 or m2) in order to demonstrate that many different rectangles may have the same area. [C, CN, ME, PS, R, V] Key Indicators a. Describe area as the measure of surface recorded in square units. c. Provide a referent for a square centimetre and explain the choice. d. Provide a referent for a square metre and explain the choice. h. Determine the area of an irregular 2-D shape and explain the strategy used. j. Illustrate, and verify, how more than one rectangle is possible for a given area by drawing at least two different rectangles with that area (e.g., identifying the dimensions of each rectangle drawn, or superimpose the rectangles on each other). Concepts (Nouns, Knows) Skills (Verbs, Dos) - area, square units - (2) describe - referent, square centimetre - (3) provide, (2) explain - referent, square metre - (3) provide, (2) explain - area, irregular 2D shape, strategy - (3) determine, (2) explain - two different rectangles same dimensions - - (3) illustrate, (4) verify, (3) drawing,(1) identifying, (4) superimpose Big Ideas (Enduring Understandings) Essential Questions Area is the surface measurement of a two dimensional shape. When would you need to find the area of a given space? What units do we use to represent area? Why can two different rectangles have the same area? Possible Instruction Application: - Students will design a leisure center for their community. Students would be given a designated area and specific guidelies. For differentiation students could just design the MATH Grade 4 (Updated FEB-6-2012) swimming pool area. OUTCOME: SS4.3 Demonstrate an understanding of rectangular and triangular prisms by: • identifying common attributes • comparing • constructing models. [C, CN, R, V] Key Indicators a. Identify and name common attributes of rectangular prisms from sets of rectangular prisms. b. Identify and name common attributes of triangular prisms from sets of triangular prisms. c. Sort a set of rectangular and triangular prisms using the shape of the base. e. Construct and describe a model of rectangular and triangular prisms. Concepts (Nouns, Knows) - common attributes, rectangular prisms, sets Skills (Verbs, Dos) - (1) identify, (1)name - common attributes, triangular prisms, sets - (1) identify, (1) name - regtangular, triangular prisms, shape, base - (4) sort using shape of the base - model, rectangular and triangular prisms - (6) construct, (2) describe Big Ideas (Enduring Understandings) Essential Questions 3D shapes can be identified by common characteristics. Where are 3D shapes found in the environment? Possible Instructional Applications: - Students will do a playground/school scavenger hunt for triangular and rectangular prisms. Students will sort prisms according to their attributes into venn diagrams. For differentiation some students would have to find fewer items. MATH Grade 4 (Updated FEB-6-2012) O MATH Grade 4 (Updated FEB-6-2012) MATH Grade 4 (Updated FEB-6-2012) OUTCOME: SS4.4 Demonstrate an understanding of line symmetry by: • identifying symmetrical 2-D shapes • creating symmetrical 2-D shapes • drawing one or more lines of symmetry in a 2-D shape. [C, CN, V] Key Indicators a. Identify the characteristics of given symmetrical and non-symmetrical 2-D shapes. d. Explain how symmetry and fractions are related. e. Identify lines of symmetry in a set of 2-D shapes and explain why each shape is symmetrical. g. Create a symmetrical shape with and without manipulatives. Concepts (Nouns, Knows) - characteristics, symmetrical, non symmetrical 2D shapes Skills (Verbs, Dos) - symmetry, fractions - (2) explain how related - symmetry, 2D shapes - (1) identify,(2) explain why - symmetrical shape with/out manipulatives - (6) create Big Ideas (Enduring Understandings) Essential Questions Not all 2D shapes are symmetrical. How do we know if a shape is symmetrical? Possible Instruction Applications: - Students build half a symmetrical shape using pattern blocks. They then switch with a partner and complete their symmerical shape. MATH Grade 4 (Updated FEB-6-2012) - (1) identify OUTCOME: SP4.1 Demonstrate an understanding of many-to-one correspondence by: • comparing correspondences on graphs • justifying the use of many-to-one correspondences • interpreting data shown using a many-to-one correspondence • creating bar graphs and pictographs using many-to-one correspondence. [C, R, T, V] Key Indicators b) Compare graphs in which the same data has been displayed using a one-to-one and a many-to-one correspondence, and explain how they are different. f) Create and label (with categories, title, and legend) a pictograph to display a set of data using a many-to-one correspondence, and justify the correspondence used. g) Create and label (with axes and title) a bar graph to display data using a many to one correspondence, and justify the correspondence used. h) Answer a question using a graph in which data are displayed using a many-to-one correspondence. Instructional strategies - graphing objects children would like - teaching students how to gather and organize data - how symbols are used as representations (ie. map legends in s.s.) - teach students how to graph using a computer program - use and analogy to teach them parts of a graph - showing exemplars of graphs through various media (internet, newspapers, magazines) (b) Compare graphs in which the same data has been displayed using a one-to-one and a many-to-one correspondence, and explain how they are different. Concepts (Nouns, Knows) graphs data (same) correspondence (one-to-one and many-to-one) Big Ideas (Enduring Understandings) Data can be represented in different ways. Skills (Verbs, Dos) (4) compare (4) explain Essential Questions How can the same data be shown in different kinds of graphs? How are various types of graphs similar/different? f) Create and label (with categories, title, and legend) a pictograph to display a set of data using a many-to-one correspondence, and justify the correspondence used. MATH Grade 4 (Updated FEB-6-2012) Concepts (Nouns, Knows) pictograph (with categories, title, legend) correspondence (many-to-one) Big Ideas (Enduring Understandings) Skills (Verbs, Dos) (6) create (3) label (5) justify Essential Questions Data can be represented in different ways. How can a pictograph be used to show data? How can one picture show more than one object? g) Create and label (with axes and title) a bar graph to display data using a many to one correspondence, and justify the correspondence used. Concepts (Nouns, Knows) bar graph (with axes and title) many-to-one correspondence Big Ideas (Enduring Understandings) (6) create (3) label (5) justify Essential Questions How can a bar graph be used to show data? Data can be represented in different ways. How can skip-counting and estimation help when making and reading a bar graph? h) Answer a question using a graph in which data are displayed using a many-to-one correspondence. Concepts (Nouns, Knows) question many-to-one correspondence MATH Grade 4 (Updated FEB-6-2012) Skills (Verbs, Dos) (4) answer (3) using Big Ideas (Enduring Understandings) Data can be represented in different ways. Essential Questions MATH Grade 4 (Updated FEB-6-2012) What information is needed to read a graph? How do I read a graph?