fifth grade curriculum map - school webmasters · making friendly numbers/ landmark numbers...

BLACKFORD COUNTY SCHOOLS

FIFTH GRADE CURRICULUM MAP

http://www.bcs.k12.in.us/Home

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How

many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to

the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass

before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on

the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples

were on the table before?

? – 2 = 3

Total Unknown Addend Unknown Both addends Unknown

Put Together/ Take Apart

Three red apples and two green apples are on the table. How many

apples are on the table?

3 + 2 = ?

Five apples are on the table. Three are red and the rest are green. How

many apples are green?

3 + ? = 5, 5 – 3 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2 Difference Unknown

Bigger Unknown

Smaller Unknown

Difference Unknown Bigger Unknown Smaller Unknown

Compare

(“How many more?” version): Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy? (“How many fewer?” version): Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie? 2 + ? = 5, 5 – 2 = ?

(Version with “more”): Julie has 3 more apples than Lucy. Lucy has two apples. How many

apples does Julie have? (Version with “fewer”):

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ?, 3 + 2 = ?

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”): Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ?, ? + 3 = 5

Addition Strategies Name Clarification Work Sample

Counting All

• Student counts every number • Students are not yet able to add on from either addend, they must mentally build every number

8 + 9 1,2,3,4,5,6,7,8,9,10,11,12,13

Counting On

• Transitional strategy • Student starts with 1 number and counts on from this point

8 + 9 8…9,10,11,12,13,14,15

Doubles/

Near Doubles

• Student recalls sums for many doubles 8 + 9 8 + (8 + 1) (8 + 8) + 1 16 + 1 = 17

Making Tens

• Student uses fluency with ten to add quickly 8 + 9 (7 + 1) + 9 7 + (1 + 9) 7 + 10 = 17

Making Friendly

Numbers/ Landmark Numbers

• Friendly number are number that are easy to use in mental computation • Student adjusts one or all addends by adding or subtracting to make friendly numbers • Student then adjusts the answer to compensate

23 + 48 23 + (48 + 2) 23 + 50 = 73 73 -2 =71

Compensation

• Student manipulates the numbers to make them easier to add • Student removes a specific amount from one addend and gives that exact amount to the other addend

8 + 6 8 -1 =7 6 + 1 = 7 7 + 7 =14

Breaking Each

Number into its Place Value

• Strategy used as soon as students understand place value • Student breaks each addend into its place value (expanded notations) and like place value amounts are

combined • Student works left to right to maintain the magnitude of the numbers

24 + 38 (30 + 4) + (30 + 8) 20 + 30 = 50 4 + 8 = 12 50 + 12 = 62

Adding up in

Chunks

• Follows place value strategy • Student keeps one addend whole and adds the second addend in easy to use chunks • More efficient than place value strategy because student is only breaking apart one addend

45 + 28 45 + ( 20 + 8) 45 + 20 = 65 65 + 8 = 73

Subtraction Strategies Name Clarification Sample

Adding up

• Student adds up from the number being subtracted to the whole • The larger the jumps, the more efficient the strategy • Student uses knowledge of basic facts, doubles, making ten, and counting on

14 – 7 7… 8,9,10,11,12,13,14 (+1 each jump)

7 + 3= 10 10 + 4= 14

Counting Back

• Strategy used by students who primarily view subtraction as taking away • Student starts with the whole and removes the subtracting in parts • Student needs the ability to decompose numbers in east to remove parts

65 – 32 65 – (10 + 10 + 10 + 2) 65, 55, 45, 35, 33 65 – (30 + 2) 65 – 30 = 35 35 – 2 = 33

Place Value

• Student breaks each number into its place value (expanded notation) • Student groups like place values and subtracts

999 – 345 (900 + 90 + 9) – (300 + 40 + 5) 900 – 300 = 600 90 – 40 = 50 9 – 5 = 4 600 + 50 + 4 = 654

Keeping a Constant

Difference

• Student understands that adding or subtracting the same amount from both numbers maintains the distance between the numbers

• Student manipulates the numbers to create friendlier numbers

123 – 59 123 + 1 = 124 59 + 1 = 60 124 – 60 = 64

Adjusting the

Create and Easier Number

• Strategy requires students to adjust only one of the numbers in a subtraction problem

• Student chooses a number to adjust, subtracts, then adjusts the final answer to compensate

• Students must understand part/whole relationships to reason through this strategy

123 – 59 59 + 1 = 60 123 – 60 = 63 I added 1 to make an easier number. 63 + 1 = 64 I have to add 1 to my final answer because I took away 1 too many.

Common Multiplication and Division Situations

Unknown Product 3 X 6 = ?

Group Size Unknown (How many in each group)

Number of Groups Unknown (How many groups?)

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example: You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example: You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example: You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays, Area

There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example: What is the area of a 3 cm by 6cm rectangle?

If 18 apples are arranged into 3 equal rows, how may apples will be in each row? Area example: A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example: A rectangle has area 18 square centimeters. If one side is 6cm long, how long is a side next to it?

Compare

A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost? Measurement example: A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue bat cost? Measurement example: A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example: A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

General a x b = ? a x ? = p and p ÷ a = ? ? x b = p and p ÷ b =?

Multiplication Strategies Name Clarification Student Work Sample

Repeated Addition/Skip

Counting

• Beginning strategy for students who are just learning multiplication • Connection to an array model provides an essential visual model

6 × 15 15+15+15+15+15+15 = 90 2 × 15 = 30 2 × 15 = 30 2 × 15 = 30 30 + 30 + 30 = 90

Friendly Numbers/Landmark

Numbers

• Students who are comfortable multiplying by multiples of 10 9 × 15 Add 1 group of 15 10 × 15 = 150 We must now take off 1 group of 15. 150 – 15 = 135

Partial Products

• strategy based on the distributive property and is the precursor for our standard U.S. algorithm

• student must understand that the factors in a multiplication problem can be broken into addends

• student can then u se friendlier numbers to solve more difficult problems

12 × 15 12 × (10 + 5) 12 × 10 = 120 12 × 5 = 60 120 + 60 =180

Breaking Factors into Smaller Factors

• Strategy relies on students’ understand of breaking factors into smaller factors

• Associate property

12 × 25 (3 × 4) × 25 3 × (4 × 25) (4 × 25) + (4 × 25) + (4 × 25) = 300

Doubling and

Halving

• Used by students who have an understanding of the concept of arrays with different dimensions but the same area

• Student can double and halve numbers with ease • Student doubles one factor and halves the other factor

8 × 25 8÷2 = 4 25 × 2 = 50 4 × 50 = 200

Division Strategies Name Clarification Student Work Sample

Repeated Subtraction/Sharing

• Early strategy students use when they are developing multiplicative reasoning

• Repeated subtraction is one of the least efficient division strategies

• Presents opportunities to make connections to multiplication

30 ÷ 5 30 – 5 = 25 25 – 5 = 20 20 = 5 = 15 15 – 5 = 10 10 – 5 = 5 5 – 5 = 0 I took out 6 groups of 5 30 ÷ 5 = 6

Multiplying Up

• Strategy is a natural progression from repeated subtraction • Student uses strength in multiplication to multiply up to reach the

dividend • Students relying on smaller factors and multiples will benefit from

discussions related to choosing more efficient factors

384 ÷ 16 10 × 16 = 160 384 – 160 = 224 10 × 16 = 160 224 – 160 = 64 2 × 16 = 32 64 – 32 = 32 2 × 16 = 32 32 – 32 = 0 10 + 10 + 2 + 2 = 24

Partial Quotients

• Maintains place value • Allows students to work their way toward the quotient by using

friendly numbers such as ten, five, and two • As the student chooses larger numbers, the strategy becomes

more efficient

384 ÷ 16 _____ 16) 384 -160 224 -160 64 -32 32 -32 0

Proportional

Reasoning

• Students who have a strong understand of factors, multiples, and fractional reasoning

• Students’ experiences with doubling and halving to solve multiplication problems can launch an investigation leading to the idea that you can divide the dividend and the divisor by the same number to create a friendlier problem

384 ÷ 16 384 ÷ 16 ÷2 ÷2 192 ÷ 8 ÷2 ÷2 96 ÷ 4 ÷2 ÷2 48 ÷ 2 = 24 384 ÷ 16 = 24

Problem Solving Strategies Focus

By Grade Level

Grade Level Strategies Kindergarten Use Objects First Review Previous Grades

Draw a Picture Use a Number Sentence

Second Review Previous Grades Find a Pattern Make a Table

Third Review Previous Grades Work Backwards Make It Simpler

Fourth Review Previous Grades Make an Organized List Guess and Check

Fifth Review Previous Grades Use Logical Reasoning

Sixth: Students should know all strategies that will be used all year.

Weeks 1-9 Pacing Guide: 1st Quarter

Week 1 5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach. 5.C.3: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Week 2 5.C.2: Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used.

Week 3 5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem.

Week 4 5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.

5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols.

Week 5 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable.

Week 6 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.

Week 7 5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem).

5.C.6: Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n × a)/(n × b), to the effect of multiplying a/b by 1.

Week 8 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem).

Week 9 Review of all fractions

Weeks 10-18 Pacing Guide: 2nd Quarter

Week 10 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. 5.NS.3: Recognize the relationship that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right, and inversely, a digit in one place represents 1/10 of what it represents in the place to its left.

Week 11 5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem). 5.NS.5: Use place value understanding to round decimal numbers up to thousandths to any given place value.

Week 12 5.NS.6: Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models). Review of all decimal operations

Week 13 5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter.

Week 14 5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties.

Week 15 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems.

Week 16 Review perimeter (grades 3 and 4) 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures.

Week 17 5.M.2: Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Week 18 5.M.4: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base. 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems. 5.M.6: Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems and other mathematical problems.

Weeks 19-27 Pacing Guide: 3rd Quarter

Week 19 5.DS.2: Understand and use measures of center (mean and median) and frequency (mode) to describe a data set. Week 20 5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and

experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data.

Week 21 5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 5.AT.7: Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Week 22 5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values.

Week 23 5.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property. 5.NS.4: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Week 24 Countdown

Week 25 Countdown

Week 26 ISTEP

Week 27 Review of all fractions

Weeks 28-36 Pacing Guide: 4th Quarter

Week 28 Review Geometry Standards

Week 29 Review Measurement Standards

Week 30 Review Algebra/Graphing standards

Week 31 ISTEP round 2

Week 32 Prepare for 6th grade

6.NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Week 33 6.NS.6: Identify and explain prime and composite numbers 6.NS.7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.

Week 34 6.C.2: Compute with positive fractions and positive decimals fluently using a standard algorithmic approach.

Week 35 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach.

Week 36 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach.

Weeks 1-3:

Problem Solving: Should be embedded within daily instruction:

Make sense of problems and persevere in

solving them.

PS.1

Reason

abstractly and quantitatively

PS.2

Construct viable arguments and

critique the reasoning of

others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6

Look for and make sure of

structure

PS. 7

Look for and

express regularity in repeated reasoning.

PS.8

DOK (Depth of Knowledge) Level 1:

identify, list, label, illustrate, measure, state, tell, use, match

Level 2: graph, classify, cause/effect,

estimate, compare, infer, construct, summarize, interpret,

estimate

Level 3: Revise, critique, construct, investigate, cite evidence,

conclusions, assess

Level 4: Design, connect, synthesize, critique,

analyze, create, prove, apply concepts

Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach.

5.C.2: Find whole-number quotients and remainders with up to four-digit dividends and two- digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. 5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem.

4.C.4: Multiply fluently within 100. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.AT.2: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve real-world and other mathematical problems. 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.]

Week 1:

Benchmarks to be taught:

Activities

Vocabulary

Standards: 5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach. 5.C.3: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Students will: (memory of all multiplication facts is a third grade standard)

• Multiply numbers fluently • Compare size of a product with another • Use correct comparison symbols

AIMS: Internet Resources:

Algorithmic approach Compare Equal to Factors Fluently Greater than Less than Multiply Product

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj21fz-udLLAhUll4MKHYRZCJcQjRwIBw&url=https://stopcommoncorewa.wordpress.com/2014/04/08/common-core-state-standards-for-mathematics-does-it-add-up-or-down-part-2/&bvm=bv.117218890,d.amc&psig=AFQjCNHiOJjWsrQEdtDE00fezz4UC4Y6RQ&ust=1458672856852780

Week 2:


Activities

Vocabulary

Standards: 5.C.2: Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. Students will:

• Determine quotients • Determine quotients with remainders • Divide by 1 digit • Divide by 2 digits • Use strategies based upon place value • Use strategies based upon properties of operations • Understand the relationship between multiplication and division • Describe the strategy that was used • Explain the reasoning

AIMS: Use Your Head Internet Resources:

Dividend Divisor Operations Place value Properties Quotient Reasoning Strategy

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjykNbrudLLAhVlnIMKHcyXC3oQjRwIBw&url=http://www.skanschools.org/districtpage.cfm?pageid%3D398&bvm=bv.117218890,d.amc&psig=AFQjCNEK5DAGFQRGmUYTT7PqkHbqqYbwxg&ust=1458672784472964

Week 3:


Activities

Vocabulary

Standards: 5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem. Students will:

• Solve real-world multiplication problems of whole numbers • Solve real-world division problems of whole numbers • Use equations to represent problem • Explain how remainder affects the solution


Dividend Division Divisor Equation Factor Multiplication Product Quotient Remainder

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjQoY6cutLLAhXItoMKHQOSDhUQjRwIBw&url=https://www.wyzant.com/resources/lessons/math/elementary_math/long_division/long_division_with_remainders&bvm=bv.117218890,d.amc&psig=AFQjCNH65TyDr_vD2sTr9OKd2LunhQ_gBg&ust=1458672916048934

Weeks 4-6:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable.

5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.

4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. 4.C.6: Add and subtract mixed numbers with common denominators (e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction). 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem).

Week 4:


Activities

Vocabulary

Standards: 5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.

5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols. (decimals will be during week 11) Students will:

• Explain different interpretations of fractions • Explain fractions as parts of a whole • Explain fractions as parts of a set • Explain division of whole numbers by whole numbers • Use a number line to compare fractions • Use a number line to order fraction • Use a number line to compare mixed numbers • Use a number line to compare decimals (week 11) • Use a number line to order mixed numbers • Use a number line to order decimals (week 11) • Use correct comparison symbols

AIMS: Deducing Decimals Dealing With Decimals Internet Resources:

Compare Denominator Division Equal to Fraction Greater than Interpretations Less than Mixed number Number line Numerator Order Part of set Part to whole Whole numbers

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwitlLyvutLLAhXinYMKHVUzAt0QjRwIBw&url=http://luminouslearning.weebly.com/blog1/teaching-tip-2-tackling-those-dreaded-fractions&bvm=bv.117218890,d.amc&psig=AFQjCNGQKbpcbaXzxX2_hiOodYyEcbNWrA&ust=1458672958445549

Week 5:


Activities

Vocabulary

Standards: 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers.

5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable.

Students will:

• Add fraction with unlike denominators • Add mixed numbers with unlike denominators • Subtract fractions with unlike denominators • Subtract mixed numbers with unlike denominators • Solve real-world problems involving addition of fractions • Solve real-world problems involving subtraction of fractions • Use a visual fraction model to represent the problem • Use equations to represent the problem • Use benchmark fraction to estimate answer • Assess whether the answer is reasonable when adding fractions • Assess whether the answer is reasonable when subtracting fractions

AIMS: Fraction Time Royal Rugs Fractions With Pattern Blocks Part 4: Fraction Action 54-72 Part 5: Fraction Action 73-81 Part 9: Fraction Action 94-103 Internet Resources:

Benchmark fraction Denominator Equation Estimate Fraction Mixed number Model Number sense Numerator Reasonable Unit fraction Visual fraction

https://www.google.com/imgres?imgurl=http://www.helpingwithmath.com/images/fra_ex9.gif&imgrefurl=http://www.helpingwithmath.com/by_subject/fractions/fra_adding.htm&docid=09euEMSowTZ5WM&tbnid=JFvMGBu0Wd6rKM:&w=413&h=256&safe=strict&ei=SUTwVq_xH8qpjgS9n7G4DQ

Week 6:


Activities

Vocabulary

Standards: 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number. Students will:

• Add fractions with unlike denominators • Add mixed numbers with unlike denominators • Subtract fractions with unlike denominators • Subtract mixed numbers with unlike denominators • Use visual fraction models to multiply a fraction by a fraction • Use visual fraction models to multiply a fraction by a whole number

AIMS: Fraction Time Royal Rugs Fractions With Pattern Blocks Part 4: Fraction Action 54-72 Part 5: Fraction Action 73-81 Part 9: Fraction Action 94-103 Internet Resources:

Denominator Fraction Mixed number Multiply Numerator Visual fraction model

https://www.google.com/imgres?imgurl=https://s-media-cache-ak0.pinimg.com/236x/53/e9/76/53e976fffe9e5279f62180dc6bb2e5fc.jpg&imgrefurl=https://www.pinterest.com/dingmanc/fractions-5th-grade/&docid=MyIkfzxISzNhJM&tbnid=QOw-rt31P1id7M:&w=236&h=238&safe=strict&ei=lETwVsWqHuHqjgTi8Y24Bw

Weeks 7-9:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction.

Week 7:


Activities

Vocabulary

Standards: 5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem). 5.C.6: Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n × a)/(n × b), to the effect of multiplying a/b by 1. Students will:

• Solve real-world problems involving multiplication of fractions • Solve real-world problems involving multiplication of mixed numbers • Use visual fraction models to represent a problem • Use equations to represent a problem • Explain why multiplying a positive number by a fractions great than 1 results in a

product great than the given number • Explain why multiplying a positive number by a fraction less than 1 results in a product

smaller than the given number • Understand fraction equivalence

AIMS: Fraction Time Royal Rugs Fair Squares and Cross Products Part 6: Fraction Action 82-90 Internet Resources:

Denominator Equation Equivalence Explain Fraction Mixed number Numerator Product Represent Visual fraction model

Week 8:


Activities

Vocabulary

Standards: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem). 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. Students will:

• Solve real-world problems in division of fractions • Solve real-world problems in division of whole numbers by unit fractions • Use visual fraction models to represent the problem • Use equations to represent the problem • Use visual fraction models to divide fractions

AIMS: Divide and Conquer Internet Resources:

Division Equation Non-zero whole number Unit fraction

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjJ2fjtu9LLAhXm74MKHSvADL8QjRwIBw&url=http://www.visualfractions.com/DivideEasy/dividelines.html&psig=AFQjCNHFUBFuIZKZ0fywoTeB24u9k361TA&ust=1458673358263240

Week 9:


Activities

Vocabulary

Standards: Review of all fractions Students will:

• Add fractions with unlike denominators • Add mixed numbers with unlike denominators • Subtract fractions with unlike denominators • Subtract mixed numbers with unlike denominators • Use a number line to order fractions • Use a number line to order mixed numbers • Multiply fractions • Divide fractions


Denominator Fraction Mixed number Numerator

Weeks 10-12:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. 5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem).

Week 10:


Activities

Vocabulary

Standards: 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. 5.NS.3: Recognize the relationship that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right, and inversely, a digit in one place represents 1/10 of what it represents in the place to its left. Students will:

• Add decimals to hundredths • Subtract decimals to hundredths • Multiply decimals to hundredths • Divide decimals to hundredths • Use various strategies for illustration of operation • Use strategies based on place values • Describe the strategy used to solve the problem • Use reasoning to justify answer • Understand relationship of place value of decimal

AIMS: Use Your Head Pack and Post Operation: Decimals Operation: Decimals Internet Resources:

Addition Decimals Division Hundredth Models Multiplication Operations Place value Property Reasoning Represents Strategy Subtraction

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj0oLKfvNLLAhUkvIMKHWMjDhgQjRwIBw&url=http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i4/bk8_4i2.htm&bvm=bv.117218890,d.amc&psig=AFQjCNEHNRMv1ykMZXcBVDiBJyTJImNPSA&ust=1458673461894617

Week 11:


Activities

Vocabulary

Standards: 5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols.

5.NS.5: Use place value understanding to round decimal numbers up to thousandths to any given place value. 5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem).

(focus on decimals) Students will:

• Use a number line to compare fractions • Use a number life to order fractions • Use a number line to compare mixed numbers • Use a number line to order mixed numbers • Use a number line to compare decimals to thousandths • Use a number line to order decimals to thousandths • Use correct comparison symbols when comparing • Solve real-world problems involving addition of decimals to hundredths • Solve real-world problems involving subtraction of decimals to hundredths • Solve real-world problems involving multiplication of decimals to hundredths • Solve real-world problems involving division of decimals to hundredths

AIMS: Deducing Decimals Dealing With Decimals Use Your Head Internet Resources:

Compare Decimal notation Decimals Equal to Equation Estimate Fractions Greater than Less than Mixed numbers Number line Order Place value Round Symbol Tenths Thousandths

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjPmuPNutLLAhWhmIMKHY4TDwIQjRwIBw&url=http://math.tutorvista.com/number-system/decimals-on-number-line.html&bvm=bv.117218890,d.amc&psig=AFQjCNGAdCvwEXIV8vsyogBibegQPCNcdA&ust=1458673022198870

Week 12:


Activities

Vocabulary

Standards: 5.NS.6: Understand, interpret, and model percent as part of a hundred (e.g. by using pictures, diagrams, and other visual models). Review of all decimal and percent operations Students will:

• Understand percent as part of a hundred • Interpret percent as part of a hundred • Model percent as part of a hundred • Use visual models to display percent


Percent

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjVmbvLvNLLAhWCtoMKHVnvBDgQjRwIBw&url=http://www.teacherswithapps.com/app_reviews-visual-fractions-decimals-and-percentages/&bvm=bv.117218890,d.amc&psig=AFQjCNFPRQVmPSv5Vpo4W8qyHegywomsow&ust=1458673555422133

Weeks 13-15:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems.

4.M.2: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit within a single system of measurement. Record measurement equivalents in a two-column table.

4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Week 13:


Activities

Vocabulary

Standards: 5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter. Students will:

• Identify types of triangles • Describe the types of triangles • Draw the types of triangles • Draw circles using appropriate tools • Understand radius • Understand diameter • Understand the relationship between radius and diameter


Acute angle Acute triangle Compass Diameter Obtuse angle Obtuse triangle Protractor Radius Right angle Right triangle Straightedge

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwijsdnvvNLLAhXrwYMKHedfCIsQjRwIBw&url=http://www.tvdsb.ca/webpages/murrellc/resources.cfm?subpage%3D133063&bvm=bv.117218890,d.amc&psig=AFQjCNHSZoLhNUASmSUFxvjdvfd9OsIj0Q&ust=1458673630070358

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiCkbaBvdLLAhVEvoMKHdibChUQjRwIBw&url=http://www.1728.org/triang.htm&bvm=bv.117218890,d.amc&psig=AFQjCNHSZoLhNUASmSUFxvjdvfd9OsIj0Q&ust=1458673630070358

Week 14:


Activities

Vocabulary

Standards: 5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties. Students will:

• Identify polygons • Classify polygons based on properties

AIMS: Classifying Quadrilaterals Internet Resources:

Acute angle Acute triangle Categorize Classify Equilateral triangle Hexagon Hierarchy Isosceles triangle Obtuse angle Obtuse triangle Pentagon Polygon Properties Quadrilateral Right angle Right triangle Scalene triangle Solid figure Triangle

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjPxZCavdLLAhXGxIMKHVdVDv4QjRwIBw&url=https://www.pinterest.com/pin/237213105349060848/&bvm=bv.117218890,d.amc&psig=AFQjCNFMRPIPMMqdQVpYXE49TE1-oSk58A&ust=1458673701695716

Week 15:


Activities

Vocabulary

Standards: 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems. Students will:

• Convert different-sized standard measurement units • Solve multi-step problems

AIMS: Straw Planes Internet Resources:

Conversions Convert Standard measurement

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiUxfa_vdLLAhWiw4MKHdJaBacQjRwIBw&url=http://www.inchcalculator.com/unit-conversion/from/inch/to/foot/&bvm=bv.117218890,d.amc&psig=AFQjCNGp6PbnUguouhe-o6humlLr2XpJPA&ust=1458673798332893

Weeks 16-18:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum

5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures. 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems.

4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems.

Week 16:


Activities

Vocabulary

Standards: 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures. Review Perimeter (grades 3 and 4) Students will:

• Develop formulas for area of triangles • Develop formulas for area of parallelograms • Develop formulas for area of trapezoids • Use formulas for area of triangles • Use formulas for area of parallelograms • Use formulas for area of trapezoids • Solve real-world problems with perimeter • Solve real-world problems with area • Use appropriate units for measures


Area Formulas Parallelogram Perimeter Trapezoid Triangle Unit

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjF8PvfvdLLAhVqt4MKHbNtC-wQjRwIBw&url=http://www.ck12.org/geometry/Triangle-Area/lesson/Triangle-Area-Grade-7/&bvm=bv.117218890,d.amc&psig=AFQjCNGNn6F4DQFmAuh39h8RFUzr2sfpvg&ust=1458673848272185

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj1osXpvdLLAhWkvIMKHUFiCdgQjRwIBw&url=http://dandumitrache.com/area-parallelogram/&bvm=bv.117218890,d.amc&psig=AFQjCNFOFFIRhkPwoWoXm8M0lJngZYZbCw&ust=1458673886410177

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiMh4j8vdLLAhUKsoMKHVUDAkQQjRwIBw&url=http://dandumitrache.com/area-trapezoid/&bvm=bv.117218890,d.amc&psig=AFQjCNH369PnYc7Vkw_43UNu1k_M8J68nA&ust=1458673917406997

Week 17:


Activities

Vocabulary

Standards: 5.M.2: Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Students will:

• Find area of a rectangle • Find area of a rectangle with fractional side • Show the area is same by multiplying • Represent fraction products as rectangular areas


Area Fractional side Length Modeling Product Rectangle Unit squares

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjVrMnz2rvMAhXssYMKHUqnD84QjRwIBw&url=https://www.youtube.com/watch?v%3D4JtcIEJclRA&bvm=bv.121070826,d.amc&psig=AFQjCNGX-UG9y675JGEoxxvsnV6c6lFfYg&ust=1462289435079145

Week 18:


Activities

Vocabulary

Standards: 5.M.4: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base. 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems. 5.M.6: Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems and other mathematical problems. Students will:

• Find the volume of a right rectangular prism • Show volume is same by multiplying side lengths • Apply formula to find volume • Find volume of sold figures of two prisms

AIMS: Luggage Limits Essential Math: Measurement of Rectangular Solids book Internet Resources:

Base Edge Face Height Length Non-overlapping Right rectangular prism Solid Unit cubes Vertex Vertices Volume Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiZipvbvtLLAhXqtYMKHfBnCYAQjRwIBw&url=http://www.skillsyouneed.com/num/volume.html&bvm=bv.117218890,d.amc&psig=AFQjCNEI8RbFiBNPQ3oUzdDmH6lb-F6ErA&ust=1458674113242212

https://www.google.com/imgres?imgurl=http://1.bp.blogspot.com/-Qxex7QG4zWI/Vf3crMrSHhI/AAAAAAAAB-U/PH44jDG8KXg/s1600/Screen%2BShot%2B2015-09-19%2Bat%2B6.07.00%2BPM.png&imgrefurl=http://awheelerfes.blogspot.com/2015/09/september-21st-25th-dont-have-time-to.html&docid=JAIo4K97z6htMM&tbnid=65Rp6gUCnkkYNM:&w=803&h=451&safe=strict&bih=622&biw=1366&ved=0ahUKEwiY546K27vMAhVos4MKHaszCPU4ZBAzCBgoFTAV&iact=mrc&uact=8

Weeks 19-21:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 19:


Activities

Vocabulary

Standards: 5.DS.2: Understand and use measures of center (mean and median) and frequency (mode) to describe a data set. Students will:

• Understand mean to describe a data set • Understand median to describe a data set • Understand mode to describe a data set


Data Data set Frequency Mean Median Mode

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwior8LwvtLLAhWCtoMKHVnvBDgQjRwIBw&url=http://www.funinroom4b.com/2012/04/mean-median-mode-and-range-foldable.html&bvm=bv.117218890,d.amc&psig=AFQjCNHob9KXEWTxz5zRWk_gqj_xky-6ZQ&ust=1458674167256210

Week 20:


Activities

Vocabulary

Standards: 5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data. Students will:

• Formulate questions that can be addressed with data • Make predictions about data • Use observations to interpret the data • Use surveys to interpret the data • Use experiments to collect data • Use experiments to represent data using tables • Understand the types of graphs • Recognize the differences in categorical data • Recognize the differences in numerical data


Bar graph Categorical data Data Experiment Formulate Frequency Frequency table Interpret Line graph Line plot Numerical data Observations Predictions Represent Survey Tables

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiSqqfj27vMAhXGmoMKHR2RCD4QjRwIBw&url=http://www.classroomcapers.co.uk/maths-graphs-school-poster.html&bvm=bv.121070826,d.amc&psig=AFQjCNEqZMezIHDBCbmglxPwXntJS67egA&ust=1462289699945140

Week 21:


Activities

Vocabulary

Standards: 5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate) 5.AT.7: Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Students will:

• Graph ordered pairs on a coordinate plane • Explain how coordinates relate distance from the origin • Understand the x-axis and y-axis • Understand the x-coordinate and y-coordinate • Represent real-world problems by graphing ordered pairs in first quadrant • Represent equations by graphing ordered pairs in the first quadrant • Interpret coordinate values of points

AIMS: Mark My Words Space Shuttle Coordinates Captain Kid’s Grid Hurkle Hide and Seek Plotting Planes Willie the Wheel Man Sticking Around Just Drop It! Internet Resources:

Coordinate Coordinate plane Equation Ordered pair Origin Quadrant Points Value x-axis x-coordinate y-axis y-coordinate

https://www.google.com/imgres?imgurl=http://www.mathsideas.com/resources/1347130506-1%20quadrant%20grid.bmp&imgrefurl=http://www.danasrhj.top/quadrant-coordinate-plane/&docid=G00nCT8YlO6WsM&tbnid=xB-eUg0ZB9FRhM:&w=635&h=491&safe=strict&bih=622&biw=1366&ved=0ahUKEwjbtOSx3LvMAhWBuIMKHVX6CJkQMwhHKCMwIw&iact=mrc&uact=8

Weeks 22-24:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 5.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property.

Week 22:


Activities

Vocabulary

Standards: 5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values. Students will:

• Define two variables to write linear expressions • Use two variables to write linear expressions • Solve real-world problems using linear expressions • Evaluate expressions for given values


Define Evaluate Expression Linear Expression Variable

Week 23:


Activities

Vocabulary

Standards: 5.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property. 5.NS.4: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Students will:

• Evaluate expressions with parentheses • Evaluate expressions with brackets • Use the commutative property of addition • Use the commutative property of multiplication • Use associative property of addition • Use associative property of multiplication • Use distributive property • Explain patterns in number of zeros by multiplying by power of 10 • Explain patterns of the decimal point when it is multiplied by power of 10 • Use whole number exponents for powers of 10


Associative property Bracket Commutative property Cubed Distributive property Exponent Expression Order of operation Parentheses Power Product Squared

https://www.google.com/imgres?imgurl=http://study.com/cimages/videopreview/videopreview-small/what-are-the-order-of-operations1_117116.jpg&imgrefurl=http://study.com/academy/course/pert-practice-study-guide.html&docid=J4CMm6qs-Y75OM&tbnid=sSqBIpA1Df6swM:&w=262&h=147&safe=strict&bih=622&biw=1366&ved=0ahUKEwjH4NeL3rvMAhVln4MKHRGKCWsQMwhBKB0wHQ&iact=mrc&uact=8

Week 24: Countdown


Activities

Vocabulary

Standards: Students will: The next two weeks determine which standards will need more practice.


Weeks 25-27:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 25:


Activities

Vocabulary

Standards: Students will: Continue to decide which standards that need to retaught in order to be prepared for ISTEP.


Week 26:ISTEP ROUND 2


Activities

Vocabulary

Standards: Students will:


Week 27:


Activities

Vocabulary

Standards: Review all fractions, decimals, percents

5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols.

5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers. 5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers. 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number. 5.C.6: Explain why multiplying a positive number by a fraction greater than 1 results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n × a)/(n × b), to the effect of multiplying a/b by 1. 5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction. 5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable. 5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem). 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem). 5.NS.4: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 5.NS.5: Use place value understanding to round decimal numbers up to thousandths to any given place value. 5.NS.6: Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models). 5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. 5.AT.5: Solve real-world problems involving addition, subtraction, mutliplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem).


Weeks 28-30:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 28:


Activities

Vocabulary

Standards: Review all Geometry standards 5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter. 5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties.


Week 29:


Activities

Vocabulary

Standards: Review all measurement standards 5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems 5.M.2: Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures. 5.M.4: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base. 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems. 5.M.6: Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems and other mathematical problems.


Week 30:


Activities

Vocabulary

Standards: Review Algebra and graphing standards 5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data. 5.DS.2: Understand and use measures of center (mean and median) and frequency (mode) to describe a data set. 5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 5.AT.7: Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values.


Weeks 31-33:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 6.NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Week 31:ISTEP round 2


Activities

Vocabulary



Week 32:


Activities

Vocabulary

Standards: 6.NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Students will:

• Compare rational numbers • Order rational numbers • Plot rational numbers on a number line • Write statements of order for rational numbers • Interpret statements of order for rational numbers • Explain statements of order for rational numbers


Compare Interpret Number line Order Plot Rational number

Week 33:


Activities

Vocabulary

Standards: 6.NS.6: Identify and explain prime and composite numbers.

6.NS.7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Students will:

• Identify prime numbers • Explain prime numbers • Identify composite numbers • Explain composite numbers • Find the greatest common factor of two whole numbers • Find the least common multiple of two whole numbers • Use the distributive property to express a sum


Composite numbers Distributive property Factor Greatest common factor Least common multiple Prime numbers

Weeks 34-36:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess



Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum 6.C.2: Compute with positive fractions and positive decimals fluently using a standard algorithmic approach. 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach.

Week 34:


Activities

Vocabulary

Standards: 6.C.2: Compute with positive fractions and positive decimals fluently using a standard algorithmic approach. Students will:

• Solve positive fractions fluently • Solve positive decimals fluently • Use standard algorithmic approach


Algorithmic approach Decimals Fluently Fractions

Week 35:


Activities

Vocabulary

Standards: 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach. Students will:

• Divide whole numbers fluently • Divide multi-digit whole numbers fluently • Divide using a standard algorithmic approach


Algorithmic approach Divide Dividend Divisor Fluently Quotient

Week 36:


Activities

Vocabulary

Standards: 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach. Students will:

• Divide whole numbers fluently • Divide multi-digit whole numbers fluently • Divide using a standard algorithmic approach


Algorithmic approach Divide Dividend Divisor Fluently Quotient


Activities

Vocabulary



fifth grade curriculum map - school webmasters · making friendly numbers/ landmark numbers...

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