Fourth GRADE CURRICULUM MAP - School Webmasters€¦ · FOURTH GRADE CURRICULUM MAP . Result...

BLACKFORD COUNTY SCHOOLS

FOURTH 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.

Kindergarten First Grade Second Grade Third Grade Fourth Grade Fifth Grade Sixth Grade 2-dimensional 3-dimensional Addition Array Attributes Compose Decompose Edges Equal sign Equation Greater than Least Less Less than Mental images Missing number More Most Number Number line Number word Numeral Object Patterned arrangement Place value Rectangular array Solve Sort Subtraction Symbol Tally marks Vertices Whole number Write

Analog clock Attributes Composite shape Counting on Data Decompose Defining attribute Digit Digital clock Equal sign Equation Equivalent Face Find mentally Fourths/quarters Halves Non-defining Non-standard unit Number pattern Numeral Operations Ordinal number Partition Place Value Properties of Strategy Sum Symbol Unknown number Value Whole number

Analog clock Arrays Associative prop of addition Bar graph Commutative prop of addition Compose Cube Data set Decompose Digit Equation Equivalent Estimate Even Expanded form Extend Face Fluently Fourths Halves Identical wholes Investigate Length Measure Models Number line Odd Ordered set Ordinal numbers Partition Picture graph Place value Plot Predict Prism Reasonable Represent Right rectangular Rule Side Standard form Sum Symbol Thirds Unit Value Vertex Volume Whole number Word form

Analog clock Area Area model Array Attribute Endpoint Equal-sized groups Equivalent Equivalent fraction Expanded form Fluently Frequency table Interval Inverse Line plot Mass Models Multiplicative identity of 1 Multiplicative property Of 0 Number line Partitioned Perimeter Place value Polygon Property of 0 in division Property of 1 in division Quantity Quotient Scaled bar graph Scaled picture graph Standard from Tools Unit fraction Volume Whole number Word form

Algorithmic approach Area Circle graph Decompose Decompose a fraction Denominator Equivalent Equivalent fraction Expanded form Fluently Fraction Improper fraction Inverse operation Line plot Mass Mixed numbers Model Numerator Parallel line Parallelogram Perimeter Perpendicular line Place value Quadrilateral Quotient Ray Rhombus Standard form Symmetry Trapezoid Triangle Volume Whole number Word form

Acute triangle Algorithmic approach Coordinate plane Coordinates Diameter Equation Equilateral triangle Equivalence Estimate Experiment Expression Fluently Isosceles triangle Mean Median Mode Number line Number sense Observations Obtuse triangle Ordered pairs Origin Percent Place value Polygon Product Quadrant Quotient Radius Right triangle Scalene triangle Solid figure Survey Unit fraction Volume

Absolute value Algorithmic approach Box plots Center Complex shape Composing Composite numbers Constraint Decomposing Dependent variable Distribution Double number line Fluently Greatest common factor Histograms Independent variable Integer number system Interquartile range Least common multiple Line plot Magnitude Mean Median Net Prime numbers Proportional relationship Quotient Range Rate Ratio Rational number Spread Surface area Tables of equivalent ratio Tape diagrams Unit rate Variability Volume

Test 1: Weeks 1-4 Week 1 4.C.4: Multiply fluently within 100.

4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.2: Compare two whole numbers up to 1,000,000 using >, =, and < symbols.

Week 2 4.C.4: Multiply fluently within 100. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value.

Week 3 4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

Week 4 4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).


4.AT.3: Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations.

Week 6 4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning.

Week 7 4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property.

Week 8 4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 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.] 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.


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.

Week 10 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.

Week 11 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.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.]


4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures.

4.M.5: Understand that an angle is measured with reference to a circle, with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. Understand an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure.

Week 13 4.C.4: Multiply fluently within 100. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures.

Week 14 4.C.4: Multiply fluently within 100. 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry.


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 4.C.4: Multiply fluently within 100. 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. 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 17 4.C.4: Multiply fluently within 100. 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.


4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.]

Week 19 4.C.4: Multiply fluently within 100. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.]

Week 20 4.C.4: Multiply fluently within 100. 4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). 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.

Week 21 4.C.4: Multiply fluently within 100. 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.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).


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 23 4.C.4: Multiply fluently within 100. 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 24 4.C.4: Multiply fluently within 100. 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).


4.NS.7: Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).

Week 26 4.C.4: Multiply fluently within 100. 4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter. 4.DA.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots.

4.AT.6: Understand that an equation, such as y = 3x + 5, is a rule to describe a relationship between two variables and can be used to find a second number when a first number is given. Generate a number pattern that follows a given rule.

Week 27 4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.DA.3: Interpret data displayed in a circle graph.

Week 28

4.C.4: Multiply fluently within 100.


Week 30 4.C.4: Multiply fluently within 100.







Weeks 1-4:

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

4.C.4: Multiply fluently within 100. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.2: Compare two whole numbers up to 1,000,000 using >, =, and < symbols. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value.

4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10.

3.NS.1: Read and write whole numbers up to 10,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 10,000.

3.NS.2: Compare two whole numbers up to 10,000 using >, =, and < symbols.

3.NS.9: Use place value understanding to round 2- and 3-digit whole numbers to the nearest 10 or 100. 3.C.1: Add and subtract whole numbers fluently within 1000.

3.AT.1: Solve real-world problems involving addition and subtraction of whole numbers within 1000 (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

Week 1:

Benchmarks to be taught:

Standards: 4.C.4: Multiply fluently within 100. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.2: Compare two whole numbers up to 1,000,000 using >, =, and < symbols. Students will:

Read whole numbers up to 1,000,000

Write whole numbers up to 1,000,000

Use words to represent equivalent forms of whole numbers

Use models to represent equivalent forms of whole numbers

Use standard form to represent equivalent forms of whole numbers

Use expanded form to represent equivalent forms of whole numbers

Compare whole numbers using correct symbols

Millions Thousands Ones

One Millions

Hundred Thousands

Ten Thousands

One Thousand

Hundreds Tens Ones

Resources:

Compare Equivalent Equivalent forms Expanded form Fluently Greater than Less than Model Multiply Represent Standard form Symbol Whole number Word form

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiwrtKfjbnLAhWGxIMKHVPcADUQjRwIBw&url=https://www.tes.com/lessons/aga3fO9xVkHvHQ/math-unit-2-whole-numbers&bvm=bv.116573086,d.amc&psig=AFQjCNGlPHVlX0OWzWxOqhCagtRFWw-ogQ&ust=1457801840306001

Week 2:


Standards: 4.C.4: Multiply fluently within 100. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. Students will:

Read whole numbers up to 1,000,000

Write whole numbers up to 1,000,000

Use words to represent equivalent forms of whole numbers

Use models to represent equivalent forms of whole numbers

Use standard form to represent equivalent forms of whole numbers

Use expanded form to represent equivalent forms of whole numbers

Use place value to round

Round any number from any given place value

Millions Thousands Ones

One Millions

Hundred Thousands

Ten Thousands

One Thousand

Hundreds Tens Ones

Resources:

Equivalent Expanded form Fluently Model Multiply Represent Standard form Symbol Whole number Word form

Week 3:


Standards: 4.C.4: Multiply fluently within 100.

4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Students will:

Add multi-digit whole numbers fluently

Subtract multi-digit whole numbers fluently

Solve real-world problems with addition of whole numbers

Solve real-world problems with subtraction of whole numbers

Use standard algorithm for addition

Use standard algorithm for subtraction

Find an unknown number in an equation

Solve for an unknown number using a symb

Resources: Palindromic Ponderings

Subtraction Palindromes

Two-Digit Turn Around Step by Step

Mix-Ups and Mysteries

Addends Addition Algorithmic approach Difference Equation Fluently Inverse operation Operation Standard form Subtraction Sum Symbol Unknown number

https://www.google.com.pg/imgres?imgurl=https://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/e19da189-3d0c-431e-ad16-58fe8511113f.gif&imgrefurl=https://www.wyzant.com/resources/lessons/math/elementary_math/money/adding_and_subtracting_money&docid=JYAZsLZEjnsFDM&tbnid=5-pQarA2evt8TM:&w=153&h=132&safe=strict&bih=622&biw=1366&ved=0ahUKEwjLip2jr6zMAhXksIMKHWqOAdIQMwg5KBgwGA&iact=mrc&uact=8

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwic15ye5tXZAhURPN8KHYv1DhgQjRx6BAgAEAY&url=https://www.basic-math-explained.com/addition.html&psig=AOvVaw0XZm-zyRDa2s1ZG5JAyhTl&ust=1520360461391835

Week 4:



4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Students will:

Add multi-digit whole numbers using the standard algorithm

Subtract multi-digit whole numbers using the standard algorithm

Solve real-world problems with addition of whole numbers

Solve real-world problems with subtraction of whole numbers

Use equations to represent a problem

Use a symbol to represent an unknown number

Resources:

Addition Algorithm Algorithmic approach Decimal Difference Digit Equation Fluently Inverse operation Operation Place value Standard form Subtraction Sum Symbol Unknown number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwims7zc6dXZAhXwTN8KHY21AJIQjRx6BAgAEAY&url=http://www.mathemania.com/lesson/subtraction/&psig=AOvVaw1aixr7_nbVgRYIy1ttUCqt&ust=1520361394136042

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjs-NDh9-TaAhVNtFMKHRTFAVEQjRx6BAgBEAU&url=http://gigidiaries.com/4-digit-addition-with-regrouping-worksheets/double-digit-addition-and-subtraction-with-regrouping-two-step-2/&psig=AOvVaw0_s1D4bHP2B0u6bJWdad2X&ust=1525278592146853

Weeks 5-8:



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



Spiral Review of Current Curriculum 4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.3: Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.C.4: Multiply fluently within 100. 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. 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.] 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.C.1: Add and subtract whole numbers fluently within 1000. 3.AT.4: Interpret a multiplication equation as equal groups (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each). Represent verbal statements of equal groups as multiplication equations. 3.C.5: Multiply and divide within 100 using strategies, such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8), or properties of operations. 3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.C.2: Represent the concept of multiplication of whole numbers with the following models: equal-sized groups, arrays, area models, and equal "jumps" on a number line. Understand the properties of 0 and 1 in multiplication. 3.AT.3: Solve two-step real-world problems using the four operations of addition, subtraction, multiplication and division (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

Week 5:



4.AT.3: Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Students will:

Add multi-digit whole numbers

Subtract multi-digit whole numbers

Interpret multiplication equations as groups

Interpret multiplication equations as times as many

Represent verbal statements of multiplicative comparison

Use various strategies to represent multiplication

Resources:

Addition Comparison

Difference Equation Group Interpret Multiplication Product Subtract Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjlwtep69XZAhUoT98KHVdgBPUQjRx6BAgAEAY&url=http://www.truelifeimateacher.com/2015/03/skip-counting-repeated-addition-arrays.html&psig=AOvVaw2gX0cQfmLRTay9ktGdAIjn&ust=1520361826924383

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiGxemz69XZAhUHT98KHfBSBTwQjRx6BAgAEAY&url=https://www.tes.com/lessons/DQ6riMhstKrYxQ/3oa-1&psig=AOvVaw2gX0cQfmLRTay9ktGdAIjn&ust=1520361826924383

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjZ6_zI69XZAhULSN8KHaeIDgMQjRx6BAgAEAY&url=https://www.tes.com/lessons/I7ajlvKPefMpyQ/multiplication&psig=AOvVaw2gX0cQfmLRTay9ktGdAIjn&ust=1520361826924383

Week 6:


Standards: 4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. Students will:

Multiply whole number up to four digits by one-digit

Multiply two two-digit numbers

Use strategies based on place value

Use properties of operations

Describe strategy used

Explain reasoning of strategy

Resources:

Addends Addition Algorithmic approach Digit Factor Fluently Operation Place value Product Properties Reasoning

Strategy Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjGwru47NXZAhUSU98KHWL5B9wQjRx6BAgAEAY&url=http://www.mathemania.com/lesson/multiplication/&psig=AOvVaw0x5r2gB3HTLRt40b7U9BZy&ust=1520362130992437

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjH3Nnl7NXZAhUDON8KHRMbAJcQjRx6BAgAEAY&url=https://study.com/academy/lesson/4-digit-by-2-digit-multiplication.html&psig=AOvVaw2cstkz0BJYPCh4CqrRAGFQ&ust=1520362161240327

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwin7fuB7dXZAhUjm-AKHa4aA44QjRx6BAgAEAY&url=https://study.com/academy/lesson/4-digit-by-1-digit-multiplication.html&psig=AOvVaw3gSYq7ZX3n_8ZqX97ZVAYE&ust=1520362282402307

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiig9nH7NXZAhVFhOAKHezdDF4QjRx6BAgAEAY&url=https://www.homeschoolmath.net/teaching/md/multiply_2_digit.php&psig=AOvVaw2cstkz0BJYPCh4CqrRAGFQ&ust=1520362161240327

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjEupOk9-TaAhXEylMKHQr6BqMQjRx6BAgBEAU&url=http://www.mathcoachscorner.com/2013/09/alternate-strategies-for-multi-digit-multiplication/&psig=AOvVaw0feIE516UI0xWdbRL38auz&ust=1525278472049238

Week 7:


Standards: 4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning.

4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. Students will:

Multiply a whole number up to four digits by one-digit

Multiply two two-digit numbers by two digit numbers

Describe strategy used for multiplication

Explain reasoning of multiplication


Use properties to show numbers can be multiplied in any order

Use commutative property

Use associative property

Understand the distributive property

Resources: Frame Filling

Multiplication Stretch

Picturing Rectangles

Writing Rectangles

Quick Sticks and Lattice

Multiplication

Associative property Commutative property Digit Distributive property Factors Fluently Multiply Operations Place value Product Reasoning Strategies Whole number

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwi2xrvilLnLAhUGkIMKHSS3DA8QjRwIBw&url=https://www.pinterest.com/purplepenguin42/multiplication/&bvm=bv.116573086,d.amc&psig=AFQjCNEdK6GYy0gibwIJaVhGm_dRV0kRSw&ust=1457803866730305

Week 8:



4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 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.] 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Students will:

Solve real-world problems with whole numbers

Use multiplicative comparison using drawings

Use multiplicative comparison using equations with a symbol for unknown number

Distinguish multiplicative comparison from additive

Find all factor pairs for a whole number

Recognize that a whole number is a multiple of it factors

Unknown product Group size unknown Number of groups unknown

A goldfish costs $3. A hamster costs 6 times as much. How much does the hamster cost?

3 X h = 6

A hamster costs $18. That is 3 times as much as a goldfish. How much does the goldfish cost?

18 g = 3, 3 X g = 18

A hamster costs $18. A goldfish costs $6. How many times as much does the hamster cost compared to the goldfish?

18 6 = ? , 6 X ? = 18

Resources: Estimating Everything

Additive Decomposition Digit Dividend Divisor Drawings Equation Explain Factor Factor pairs Fluently Inverse Multiple Multiplicative Product Quotient

Reasoning Rectangular array Remainder Represent Strategy Symbol Unknown number Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwilzLKCornLAhXFtYMKHdKpA8YQjRwIBw&url=http://etc.usf.edu/clipart/41700/41704/fc_dev_41704.htm&bvm=bv.116573086,d.amc&psig=AFQjCNF0Ro1kzZvyV-g3gzxIE4mDtSCezQ&ust=1457807429798431

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwilzLKCornLAhXFtYMKHdKpA8YQjRwIBw&url=http://etc.usf.edu/clipart/41700/41704/fc_dev_41704.htm&bvm=bv.116573086,d.amc&psig=AFQjCNF0Ro1kzZvyV-g3gzxIE4mDtSCezQ&ust=1457807429798431

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwilsdH8qrnLAhWDw4MKHc_sBOYQjRwIBw&url=https://www.pinterest.com/mhdowning/math/&bvm=bv.116573086,d.amc&psig=AFQjCNHuN5maGP9rvpLYt4zqB9I6fK6IAw&ust=1457809813792167

Weeks 9-11:



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



Spiral Review of Current Curriculum 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.]

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.C.4: Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each). 3.C.3: Represent the concept of division of whole numbers with the following models: partitioning, sharing, and an inverse of multiplication. Understand the properties of 0 and 1 in division. 3.AT.2: Solve real-world problems involving whole number multiplication and division within 100 in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 3.AT.3: Solve two-step real-world problems using the four operations of addition, subtraction, multiplication and division (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

Week 9:



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. Students will:

Demonstrate division of a multi-digit dividend (up to four digits) by a one digit divisor

Find whole number quotients

Check answer by using the inverse

Resources: Pack-10 Trading

Centers

Candy Factory One Number Indivisible

Digit Dividend Divisor Equal groups

Equation Explain Factor Fluently Inverse Multiple Place value Product Quotient Reasoning Remainder Share Strategy Whole number

Week 10:



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. Students will:


Find whole number remainders

Divide with four digit dividends

Divide with one digit divisors



Understand the relationship between multiplication and division

Apply relationships between addition and multiplication

Apply relationships between subtraction and division

Solve real-world multiplication problems

Solve real-world division problems

**remainders will be a focus for week 11**

Resources:

Digit Dividend Division Divisor Equal groups Inverse Justify Multiplication Place value Properties Quotient Reasoning Relationships Share Solve Strategy Symbol Unknown number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjAkMXXgNjZAhUFuFMKHWzbA24QjRx6BAgAEAY&url=http://www.ducksters.com/kidsmath/division_basics.php&psig=AOvVaw3cd3CPhBVCQhYi2IoawLRj&ust=1520436283171252

Week 11:



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.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.] **4.C.3 allows for remainders** Students will:


Find whole number remainders up to four digit dividend



Understand relationship between multiplication and division

Use appropriate strategy

Solve real world problems with whole numbers

Find unknown numbers in an equation

Understand the meaning of a remainder

**remainders will be a focus for week 11**

Resources:

Digit Dividend Division Divisor Equal groups Equation Fluently Inverse Justify Multiplication Place value Properties Quotient Reasoning Share Solve Strategy Symbol Unknown number Whole number

Weeks 12-14:



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



Spiral Review of Current Curriculum 4.C.4: Multiply fluently within 100. 4.M.5: Understand that an angle is measured with reference to a circle, with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. Understand an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry.

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.G.3: Identify, describe and draw points, lines and line segments using appropriate tools (e.g., ruler, straightedge, and technology), and use these terms when describing two-dimensional shapes. 3.G.2: Understand that shapes (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize and draw rhombuses, rectangles, and squares as examples of quadrilaterals. Recognize and draw examples of quadrilaterals that do not belong to any of these subcategories.

Week 12:



4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. 4.M.5: Understand that an angle is measured with reference to a circle, with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. Understand an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure. Students will:

Identify rays, angles, and perpendicular and parallel lines

Describe rays, angles, and perpendicular and parallel lines

Draw rays, angles, and perpendicular and parallel lines using appropriate tools

Recognize angles are formed when two rays share a common endpoint

Classify triangles based on types of lines and angles

Classify quadrilaterals based on types of lines and angles

Understand that an angle is measured with reference to a circle

Understand the center is a common endpoint of rays

Understand an angle is measured in degrees

Measure angles in whole-number degrees

Use a protractor to create an angle given a specific measurement

Resources: Flight Paths Hall of Mirrors

Lines to Design Mirrors That Multiply

Protractor Ground School

Acute angle Angle Center Circle Classify Degree Endpoint Fluently Intersect Line Line segment Obtuse angle Parallel line Perpendicular line Protractor Quadrilateral Ray Right angle Ruler Straightedge Tools Triangles Two dimensional Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjtw5j6krnLAhUksYMKHb-yDDoQjRwIBw&url=http://4thgradegeometry.weebly.com/monday.html&bvm=bv.116573086,d.amc&psig=AFQjCNEfZEIaiVT0wLKBXJ-ZVS0o5Dk1gQ&ust=1457803380229041

Week 13:



4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. Students will:

Identify parallelograms, rhombuses, and trapezoids

Describe parallelograms, rhombuses, and trapezoids

Draw parallelograms, rhombuses, and trapezoids

Identify rays, angles, lines

Describe rays, angles, lines

Draw rays, angles, lines

Identify types of lines: parallel and perpendicular

Identify two-dimensional figures

Resources:

Angles Draw Fluently Horizontal Identify Line Parallel Parallel line Parallelogram Perpendicular Perpendicular line Ray Rhombus Ruler Straightedge Symmetry Technology Tools Trapezoid Two-dimensional Vertical

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwizw_eUkbnLAhWLwYMKHYmyDWMQjRwIBw&url=http://bridges1.mathlearningcenter.org/resources/blog/201211/video-know-your-quadrilaterals&bvm=bv.116573086,d.amc&psig=AFQjCNFqfC-kQFeT9JFHYAKw9Zs4F_GknA&ust=1457802901537695

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiDj_bm8NXZAhUQNd8KHROqAp0QjRx6BAgAEAY&url=http://www.geom.uiuc.edu/~demo5337/Group3/angle.html&psig=AOvVaw1iiIFIrDO0PtlmIehjGdZg&ust=1520363299420985

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiMuIP38NXZAhXjQ98KHc6QAikQjRx6BAgAEAY&url=http://www.mathactivities.net/lessons/parallel-and-perpendicular-lines.htm&psig=AOvVaw1tdg_REAlBhi57DigNKYlG&ust=1520363332910648

Week 14:



4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry. Students will:

Recognize lines of symmetry in two-dimensional figures

Draw lines of symmetry in two-dimensional figures

Identify figures with lines of symmetry

Classify triangles

Classify quadrilaterals

Understand types of lines

Understand types of angles

Resources: Line Symmetry, Naturally

Mirror Twins

Describe Draw Fluently Horizontal Identify Line Lines Parallel Parallel line Parallelogram Perpendicular Perpendicular line Quadrilateral Rhombus Ruler Straightedge Symmetry Technology Tools Trapezoid Triangle Vertical

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj15K_mkbnLAhWmtIMKHQcQCToQjRwIBw&url=http://hotmath.com/hotmath_help/topics/line-symmetry.html&bvm=bv.116573086,d.amc&psig=AFQjCNHH4SuW1ptO9kzQKu9v1OKbsGVUow&ust=1457803060099877

Weeks 15-17:



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




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. 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. 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.

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.M.6: Multiply side lengths to find areas of rectangles with whole-number side lengths to solve real-world problems and other mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 3.M.1: Estimate and measure the mass of objects in grams (g) and kilograms (kg) and the volume of objects in quarts (qt), gallons (gal), and liters (l). Add, subtract, multiply, or divide to solve one-step real-world problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale, to represent the problem).

Week 15:



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. Students will:

Identify situations that require the use of the perimeter formula in real-world situations (example: amount of fencing needed to make a rectangular pig pen)

Find the perimeter formula in real world situations

Identify situations that require the use of the area formula in real-world situations (example: using carpet, covering a wall to paint)

Apply the area formula in real world situations

Write area measurements in square units

Solve problems involving the area of a rectangle with length or width missing

Find the area of a rectangle

Find the area of a complex shape

Recognize area as additive

Resources: Essential Math: Perimeter and

Area of

Rectangles book

Hall of Mirrors

Additive Apply Area Complex shape Compose Decompose Fluently Formula Length Non-overlapping Perimeter Rectangles Width

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwi34J-7qLnLAhXDwYMKHQ98AVUQjRwIBw&url=http://imanins.blogspot.com/2014/09/top-ten-toolkit-strategies-name-of.html&bvm=bv.116573086,d.amc&psig=AFQjCNFrGjmpEyD65ase7XfxxhoGUNgsVQ&ust=1457809120782950

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjpltvxqLnLAhVisoMKHVn5CFoQjRwIBw&url=https://www.youtube.com/watch?v%3DjF88UDJEDWs&bvm=bv.116573086,d.amc&psig=AFQjCNGDpEPxLvtbG4XTyQ7EvvpcTyMSNA&ust=1457809263568270

Week 16:



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. 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 (week 18) and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Students will:

Identify situations that require the use of perimeter

Apply perimeter in real world situations

Identify situations that require the use of area

Apply area in real world situations

Use all operations to solve real-world problems for distances

Use all operations to solve rea-world problems for intervals of time

Use all operations to solve real-world problems for volume

Use all operations to solve real-world problems for mass of objects

Use all operations to solve real-world problems with money

Find area of a rectangle

Find area of complex shapes

Resources: Essential Math: Perimeter

and Area of

Rectangles book

Hall of Mirrors

Additive Area Complex shaped Compose Decompose Distance Elapsed Fluently Formula Interval Mass Objects Operations Perimeter Rectangle Time Volume

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwi85JGd8tXZAhXtmuAKHdCyCWYQjRx6BAgAEAY&url=https://study.com/academy/lesson/what-is-elapsed-time-definition-examples.html&psig=AOvVaw3ZLtqtoGWYL3uIgihrUIG3&ust=1520363684327473

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiDwp3X8tXZAhUxSN8KHdLOAOoQjRx6BAgAEAY&url=https://missstoutsclassroom.weebly.com/math--science.html&psig=AOvVaw3BGRktH3g3cN1ssdmrO7Ad&ust=1520363772536296

Week 17:



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 (week 18) and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Students will:

Measure length to a specified amount

Know relative sizes of measurement units within one system of units

Express various unit sizes

Record measurement equivalents in a two column table

Solve real-world problems involving distances

Solve real-world problems involving intervals of time

Solve real-world problems involving masses of objects

Solve real-world problems involving money

Use addition and subtraction problems involving simple fractions expressing measurements

lb oz ft in

1 16 1 12

2 32 2 24

3 48 3 36

Resources: Measure for Measure Step by Step

Mix-Ups and Mysteries

Centimeter (cm) Distance Eighth- inch Equivalent Express Fluently Fraction Gram (g) Hour (hr) Interval of time Kilogram (kg) Kilometer (km) Length Liter (l) Mass Measure Meter (m) Milliliter (ml) Millimeter Minute (min) Operation Ounce (oz) Pound (lb) Quarter- inch Second (sec) Unit Volume

http://www.google.com.pg/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiq85Xf9cLLAhWjlYMKHWqMAAAQjRwIBw&url=http://www.math-salamanders.com/liquid-measurement-chart.html&bvm=bv.116636494,d.amc&psig=AFQjCNHSX4_gKPUYtLd71z7M39LbAbIz7A&ust=1458139046680051

Weeks 18-21:



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



Spiral Review of Current Curriculum 4.C.4: Multiply fluently within 100. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] 4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). 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.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).

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.NS.4: Represent a fraction, 1/b, on a number line by defining the interval from 0 to 1 as the whole, and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 3.NS.7: Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). 3.NS.6: Understand two fractions as equivalent (equal) if they are the same size, based on the same whole or the same point on a number line. 3.NS.8: Compare two fractions with the same numerator or the same denominator by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).

Week 18:



4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] Students will:

Explain equivalent fractions using models or number lines

Recognize how to display 1 in the form of a fraction (3/3, 4/4)

Explain using visual representation how and why fractions can be equivalent even though the numbers are different

Explain that fractions can only be compared when they refer to the same whole (1/2 of a small pizza is very different from ½ of a large pizza)

Compare two fractions visually (using an array, area, or linear model)

Determine whether a fraction is closest to zero, to one whole, or to a benchmark fraction such as ¼, ½, ¾)

Compare two fractions with different numerators and different denominators by: 1. Reasoning about their size or location on a number line 2. Multiplying by one in the form of a fraction to create common numerators 3. Multiplying by one in the form of a fraction to create common denominators

Resources: Fraction Fringe: On the

Cutting Edge

Same Name Frame

Shady Fractions Ordering Up Fractions

Half Track

Between Zero and One

Benchmark Compare Conclusion Denominator Equivalent Equivalent fraction Fluently Fraction Fraction model Greater than Improper fraction Justify Less than Mixed numbers Model Numerator Part to whole Visual model Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjux7aNg9jZAhVD6VMKHXNcBG8QjRx6BAgAEAY&url=http://edublog.amdsb.ca/glennlynes/2017/05/12/fractions/&psig=AOvVaw1ahO_R7e0btlJSdEGHWQTM&ust=1520436879003766

Week 19:



4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] Students will:

Express whole numbers as fractions

Recognize fractions that are equivalent to whole numbers

Name mixed numbers using objects or pictures

Write mixed numbers using objects or pictures

Name mixed numbers as improper fractions using objects or pictures

Write mixed numbers as improper fractions using objects or pictures

Explain why a fraction is equivalent to a fraction by visual fraction models

Understand part out of the whole

Resources:

Benchmark fraction

Denominator Equal Equivalent Fluently Fraction Improper fraction Mixed number Model Numerator Part out of whole Visual Whole number

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjPobDZ89XZAhUITt8KHYxxBeEQjRx6BAgAEAY&url=http://egw.hpsd.ca/parents_and_students/teachers/6_b_mrs__granata/math/mixed_numbers_and_improper_fractions/&psig=AOvVaw2bI7iImU_BC6053Y_S6C_W&ust=1520364077864374

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjPobDZ89XZAhUITt8KHYxxBeEQjRx6BAgAEAY&url=https://www.slideshare.net/martagrovello/converting-mixed-numbers-and-improper-fractions&psig=AOvVaw2bI7iImU_BC6053Y_S6C_W&ust=1520364077864374

Week 20:



4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). 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. Students will:

Use visual models (number lines, rectangles, etc) that adding fraction within the same whole is joining parts of that whole

Demonstrate visual models (number lines, rectangles, etc) that subtracting fractions within the same whole is separating parts of that whole

Compare two fraction with different numerators

Compare two fractions with different denominators

Create common denominators

Create common numerators

Compare two fractions

Justify conclusions by visual model

Decompose a fraction in more than one way using visual models, including decomposing a fraction into a combination of several unit fractions

Resources: Cindy’s Carpet Emporium

Benchmark Common Comparison Compose Conclusion Decompose a fraction Denominator Equal to Fluently Fraction Greater than Improper number Justify Less than Mixed numbers Model Numerator Symbol

Week 21:



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.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). Students will:

Add and subtract fraction with common denominators

Add and subtract mixed numbers with common denominators

Decompose and compose mixed numbers

Compare fractions with different numerators and different denominators

Express fractions as equivalent fractions

Express fractions and decimals as equivalents

Resources:

Combining Compare Decompose Denominator Equal to Equation Fraction Greater than Improper fraction Less than Mixed fractions Model Numerator Part to whole Separating Sum Visual model

http://www.google.com.pg/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj5183t8sLLAhVEl4MKHduqCA8QjRwIBw&url=http://www.basic-math-explained.com/adding-fractions.html&bvm=bv.116636494,d.amc&psig=AFQjCNEjVE4NCcqjawifLKUNDp0i32t-Dw&ust=1458138359403557

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjDgoGh59XZAhVuhuAKHe3sBNAQjRx6BAgAEAY&url=http://www.mathcaptain.com/number-sense/adding-fractions.html&psig=AOvVaw3OkOyE9Wtx-kBv8Eyg8LyU&ust=1520360719775030

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




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). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10.

Week 22:



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). Students will:

Add mixed numbers with common denominators

Subtract mixed numbers with common denominators

Replace mixed number with an equivalent fraction


Solve real-world problems involving addition of fractions

Solve real-world problems involving subtraction of fractions

Use visual fraction models

Use equations to represent problems

Resources:

Addition Denominator Equation Equivalent Mixed number Model Numerator Properties Relationship Represent Subtraction Visual

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiXnvPM59XZAhUQmeAKHeYoDMYQjRx6BAgAEAY&url=https://www.visualfractions.com/AddEasy/addlines.html&psig=AOvVaw3OkOyE9Wtx-kBv8Eyg8LyU&ust=1520360719775030

Week 23:



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). Students will:

Add mixed numbers with common denominators

Subtract mixed numbers with common denominators

Replace mixed number with an equivalent fraction


Use relationships between addition and subtraction

Solve real-world problems involving addition of fractions

Solve real-world problems involving subtraction of fractions

Use visual fraction models

Use equation to represent problems

Resources:

Addition Denominator Equivalent Fraction Mixed number Model Numerator Operations Properties Relationship Subtraction

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjeho3zhdjZAhVG4VMKHRnxDBkQjRx6BAgAEAY&url=http://rachel.golearn.us/modules/en-GCF2015/content/collections/fractions/10698/full.html&psig=AOvVaw3Cra678th_b3LCgR4qo35M&ust=1520437682212717

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiT8taihtjZAhUOn1MKHYI3DGsQjRx6BAgAEAY&url=https://mathspace.co/ebook/chapter/55659&psig=AOvVaw2_3K-SNKcPkHWoMpDjwRzf&ust=1520437770949216

Week 24:



4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). Students will:

Write tenths in decimal and fraction form

Write hundredths in decimal and fraction form

Use words, models, standard form and expanded form to represent decimals

Know the fraction and decimal equivalents for halves and fourths

Compare two decimals to hundredths by reasoning about their size based on the same whole

Record the results of comparisons with the correct symbols

Justify conclusions of comparisons (such as a visual model)

0.28 = 28/100

.32 < .05

Resources: Dueling Decimals

Show Me the Money

Compare Conclusions Decimal Equivalent Expanded form Fluently Fourths Fraction Greater than Halves Hundredths Justify Less than Model Place value Represent Standard form Tenths Whole number

Weeks 25-28:



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



Spiral Review of Current Curriculum 4.C.4: Multiply fluently within 100. 4.NS.7: Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). 4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter. 4.DA.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. 4.AT.6: Understand that an equation, such as y = 3x + 5, is a rule to describe a relationship between two variables and can be used to find a second number when a first number is given. Generate a number pattern that follows a given rule 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.DA.3: Interpret data displayed in a circle graph.

3.C.6: Demonstrate fluency with multiplication facts and corresponding division facts of 0 to 10. 3.NS.8: Compare two fractions with the same numerator or the same denominator by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). 3.M.2: Choose and use appropriate units and tools to estimate and measure length, weight, and temperature. Estimate and measure length to a quarter-inch, weight in pounds, and temperature in degrees Celsius and Fahrenheit. 3.DA.2: Generate measurement data by measuring lengths with rulers to the nearest quarter of an inch. Display the data by making a line plot, where the horizontal scale is marked off in appropriate units, such as whole numbers, halves, or quarters. 3.DA.1: Create scaled picture graphs, scaled bar graphs, and frequency tables to represent a data set—including data collected through observations, surveys, and experiments—with several categories. Solve one- and two-step “how many more” and “how many less” problems regarding the data and make predictions based on the data. 3.AT.6: Create, extend, and give an appropriate rule for number patterns using multiplication within 100.

Week 25:



4.NS.7: Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). Students will:

Write tenths in decimal and fraction form

Write hundredths in decimal and fraction form

Use words, models, standard form and expanded form to represent decimals

Know the fraction and decimal equivalents for halves and fourths

Compare two decimals to hundredths by reasoning about their size based on the same whole

Record the results of comparisons with the correct symbols

Justify conclusions of comparisons (such as a visual model)

Resources: Dueling Decimals

Show Me the Money

Compare Conclusions Decimal Equivalent Expanded form Fluently Fourths Fraction Greater than Halves Hundredths Justify Less than Model Place value Represent Standard form Tenths

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjstYzHhtjZAhVQ2lMKHerfC5AQjRx6BAgAEAY&url=https://www.theschoolrun.com/what-are-decimals&psig=AOvVaw3kVUKdmLBuyAdJnEX5wBIt&ust=1520437845026610

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjPtajehtjZAhUNzFMKHTUZA4IQjRx6BAgAEAY&url=https://www.math-salamanders.com/fractions-decimals-percents.html&psig=AOvVaw0Rxp0N1P6nptE8LAUOpWkc&ust=1520437895974361

Week 26:



4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter. 4.DA.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. 4.AT.6: Understand that an equation, such as y = 3x + 5, is a rule to describe a relationship between two variables and can be used to find a second number when a first number is given. Generate a number pattern that follows a given rule. Students will:

Distinguish multiplicative comparison (Sue has 3 times as many cousins as Mike) from additive comparison (Sue has 3 more cousins than Mike)

Solve word problems involving multiplicative comparison

Solve a word problem involving multiplicative comparison involving a symbol to represent the unknown number

Make a line plot to display a data set

Make a line plot in unit fractions

Solve problems involving addition and subtraction of fractions by using data displayed

Resources:

Comparison Data Eighth-inch Equation Fluently Length Line plot Measure Measurements Millimeter Multiplicative Pattern Quarter-inch Relationship Represent Ruler

Unit Variable

https://www.google.com.pg/imgres?imgurl=http://4.bp.blogspot.com/--KP-2AZFGGM/UqcrrGbaB0I/AAAAAAAAAHA/uCR8iXUDPdA/s1600/Bar%2BModel%2BAnchor%2BChart.JPG&imgrefurl=https://www.tes.com/lessons/JN9OPU0EyT1hqA/oa-1-multiplication-comparisons&docid=-IBfrLQuj8SdxM&tbnid=-vm9ywBO83u1BM:&w=890&h=671&safe=strict&bih=622&biw=1366&ved=0ahUKEwjZk_Psr6zMAhWEvoMKHU3gAGEQMwhcKDgwOA&iact=mrc&uact=8

https://www.google.com.pg/imgres?imgurl=http://www.sew4home.com/sites/default/files/1812-Inch-by-eights_0.png&imgrefurl=http://www.sew4home.com/tips-resources/sewing-tips-tricks/deciphering-marks-measuring-tape&docid=CzI0dsCP09ItGM&tbnid=zEU7I_siLKYh4M:&w=1000&h=660&safe=strict&bih=622&biw=1366&ved=0ahUKEwib98nNsKzMAhXqloMKHd9YCxwQMwgsKBMwEw&iact=mrc&uact=8

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiZ5NPEidjZAhUJvlMKHTdiDGYQjRx6BAgAEAY&url=https://www.homeschoolmath.net/teaching/f/multiplying_fractions_1.php&psig=AOvVaw0Rxp0N1P6nptE8LAUOpWkc&ust=1520437895974361

Week 27:



4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.DA.3: Interpret data displayed in a circle graph. Students will:

Devise questions that can be addressed with data

Use a variety of methods to interpret data from graphs

Interpret data displayed in a circle graph

Interpret data from frequency table

Interpret data from line plots

Interpret data from bar graphs

Resources:

Bar graph Circle graph Collect Data Data set Experiment Fluently Formulate Frequency table Graph Interpret Line plot Measurement Observation Pattern Represent Survey Table Unit

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwiilaqi99XZAhXEg-AKHWw8CZwQjRx6BAgAEAY&url=https://sites.google.com/site/bhe6thgrade/quests/statistics-challenge/6-types-of-graphs&psig=AOvVaw03OBrB3Gq8L8AyTegEovHk&ust=1520365031840257

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwikydqx99XZAhUEUt8KHU0HAm4QjRx6BAgAEAY&url=https://math.tutorvista.com/statistics/frequency-distribution.html&psig=AOvVaw2V8sKxW0rih-KFTIbddo_o&ust=1520365068460028

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjI8N6799XZAhUOhuAKHQiQAhkQjRx6BAgAEAY&url=http://www.mathsteacher.com.au/year8/ch17_stat/03_freq/freq.htm&psig=AOvVaw2V8sKxW0rih-KFTIbddo_o&ust=1520365068460028

Week 28:


Standards: 4.C.4: Multiply fluently within 100. Review multiplication and division. Students will:

Resources:

Weeks 29-32:



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



Spiral Review of Current Curriculum

Week 29:


Standards: 4.C.4: Multiply fluently within 100. Students will:

Resources:

Week 30:



Resources:

Week 31:



Resources:

Week 32:



Students will:

Resources:

Weeks 33-35:



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



Spiral Review of Current Curriculum

Week 33:



Resources:

Week 34:



Resources:

Week 35:



Resources:

Week 36:

Benchmarks to be taught: Activities Vocabulary


Resources:


Standards: Students will:

Resources:

Date post:	18-Jun-2020
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