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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).
Test 2: Weeks 5-8 Week 5 4.C.4: Multiply fluently within 100.
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.
Test 3: Weeks 9-11 Week 9 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.
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.]
Test 4: Weeks 12-14 Week 12 4.C.4: Multiply fluently within 100.
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.
Test 5: Weeks 15-17 Week 15 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.
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.
Test 6: Weeks 18-21 Week 18 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 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).
Test 7: Weeks 22-24 Week 22 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 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).
Test 5: Weeks 25-18 Week 25 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).
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.
Test 9: Weeks 29-32 Week 29 4.C.4: Multiply fluently within 100.
Week 30 4.C.4: Multiply fluently within 100.
Week 31 4.C.4: Multiply fluently within 100.
Week 32 4.C.4: Multiply fluently within 100.
Test 10: Weeks 33-35 Week 33 4.C.4: Multiply fluently within 100.
Week 34 4.C.4: Multiply fluently within 100.
Week 35 4.C.4: Multiply fluently within 100.
Week 36 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
Week 2:
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.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:
Benchmarks to be taught:
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
Week 4:
Benchmarks to be taught:
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 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
Weeks 5-8:
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
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:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100.
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
Week 6:
Benchmarks to be taught:
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
Week 7:
Benchmarks to be taught:
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 strategies based on place value
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
Week 8:
Benchmarks to be taught:
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.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
Weeks 9-11:
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
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:
Benchmarks to be taught:
Standards: 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. 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:
Benchmarks to be taught:
Standards: 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. Students will:
Find whole number quotients
Find whole number remainders
Divide with four digit dividends
Divide with one digit divisors
Use strategies based on place value
Use properties of operations
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
Week 11:
Benchmarks to be taught:
Standards: 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.C.3 allows for remainders** Students will:
Find whole number quotients
Find whole number remainders up to four digit dividend
Use strategies based on place value
Use properties of operations
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:
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
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:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100.
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
Week 13:
Benchmarks to be taught:
Standards: 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. 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
Week 14:
Benchmarks to be taught:
Standards: 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. 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
Weeks 15-17:
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
Spiral Review of Current Curriculum 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. 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:
Benchmarks to be taught:
Standards: 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. 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
Week 16:
Benchmarks to be taught:
Standards: 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 (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
Week 17:
Benchmarks to be taught:
Standards: 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 (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
Weeks 18-21:
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
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:
Benchmarks to be taught:
Standards: 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.] 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
Week 19:
Benchmarks to be taught:
Standards: 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.] 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
Week 20:
Benchmarks to be taught:
Standards: 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. 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:
Benchmarks to be taught:
Standards: 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). 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
Weeks 22-24:
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
Spiral Review of Current Curriculum 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). 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:
Benchmarks to be taught:
Standards: 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). Students will:
Add mixed numbers with common denominators
Subtract mixed numbers with common denominators
Replace mixed number with an equivalent fraction
Use properties of operations
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
Week 23:
Benchmarks to be taught:
Standards: 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). Students will:
Add mixed numbers with common denominators
Subtract mixed numbers with common denominators
Replace mixed number with an equivalent fraction
Use properties of operations
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
Week 24:
Benchmarks to be taught:
Standards: 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). 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:
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
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:
Benchmarks to be taught:
Standards: 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). 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
Week 26:
Benchmarks to be taught:
Standards: 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. 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
Week 27:
Benchmarks to be taught:
Standards: 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. 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
Week 28:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Review multiplication and division. Students will:
Resources:
Weeks 29-32:
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
Spiral Review of Current Curriculum
Week 29:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Week 30:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Week 31:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Week 32:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100.
Students will:
Resources:
Weeks 33-35:
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
Spiral Review of Current Curriculum
Week 33:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Week 34:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Week 35:
Benchmarks to be taught:
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Week 36:
Benchmarks to be taught: Activities Vocabulary
Standards: 4.C.4: Multiply fluently within 100. Students will:
Resources:
Benchmarks to be taught:
Standards: Students will:
Resources: