Bay course of study math gr 4
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Content Domain/Subheading or StrandStandard Learning Target (I can statements) You can have multiple learning targets for one content standard. Put them all in the box. Use CTRL+ENTER to move to a second line within one box.Month Taught (units taught)Tier 3 Vocab (Content specific words)Central Resources for course - textbooks, workbooksSupplemental Resources
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Formative/Summative Assessment - Please note any common unit assessments. Please share what assessment methods might be used to gather evidence for this standard.
2
Operations and Algebraic Thinking
Use the four operations with whole numbers to
solve problems.
1. 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.I can interpret a multiplication equation as a comparison. (7 x 5 = 7 times as many as 5 and 5 x 7= 5 times as many as 7.
I can read and write multiplication equations as comparisons.
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Operations and Algebraic Thinking
Use the four operations with whole numbers to
solve problems.
2. Multiply or divide to solve word problems 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. I can solve multiplication and division word problem with multiplicatrive comparisons. by using drawings and equations.
I can solve word problems know when to use use additive comparison and mutiplicative comparison.
I can multiply or divide to find the unknown.
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Operations and Algebraic Thinking
Use the four operations with whole numbers to
solve problems.
3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. I can solve multistep problems using any or all of the four operations.
(using whole numbers and having whole number answers)
 I can solve division problems with remainders and determine what to do with the remainder.
I can represent multistep problems using equations that include a letter standing for the unkown.
I can use mental math and estimation (rounding) to detrmine weather my answer is reasonable.
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Operations and Algebraic Thinking
Gain familiarity with factors and multiples
4. 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. Determine whether a given whole number in the range 1–100 is prime or composite.

  I can find the factors pairs for any number up to 100.
  I can show that a whole numbers is a is a multiple of each of it factors.
  I can check to see if a given whole number is a multiple of numbers 1 through 9.
  I can Identify prime and composite numbers up to 100.
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Operations and Algebraic Thinking
Generate and analyze patterns.
5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the ruleitself. For example, given the rule “Add 3” and
the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
  I can follow a given pattern using numbers and shapes.
  I can identify the rule of a number or shape patterns and explain it..
  I can identify patterns within the given pattern.
7
Numbers and Operations Base 10
Generalize place value understanding for
multi-digit whole numbers.

1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applyingconcepts of place value and division.

I can explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
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Numbers and Operations Base 10
Generalize place value understanding for
multi-digit whole numbers.

2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.  I can read and write larger whole numbers (up to the millions place) in standard form, word form and in expanded form.
  I can compare two number with digits up to the millions place and identify weather they are less than, greater than or equal to another number by using symbols to show these comparisons.
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Numbers and Operations Base 10
Generalize place value understanding for
multi-digit whole numbers.

3. Use place value understanding to round multi-digit whole numbers to any place.  I can round numbers, up to the millions place, to any given to any place value.
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Numbers and Operations Base 10
Use place value understanding and properties
of operations to perform multi-digit arithmetic.
4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.  I can add and subtract multi digit whole numbers using standard algorithms.
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Numbers and Operations Base 10
Use place value understanding and properties
of operations to perform multi-digit arithmetic.
5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.  I can multiply 4 digits by a one digit number.
  I can multiply a 2 digit number by a 2 digit number.
  I can use 2 or more different strategies to multiply numbers.
  I can use words, drawings (area models and arrays) and equations to explain multiplication.
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Numbers and Operations Base 10
Use place value understanding and properties
of operations to perform multi-digit arithmetic.
6. 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

  I can divide a 4 digit number by a one digit number.
  I can model and explain the relationship between multiplication and division.
  I can create an array to explain a multiplication or division problem
  I can find the area of a space using multiplication.
  I can solve division problems with and without remainders.
  I can write and use equations to solve multiplication and division problems.
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Measurement and Data
Solve problems involving measurement and
conversion of measurements from a larger
unit to a smaller unit
1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec. Within a single system of measurement, express measurements ina larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft. is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36).  I can compare sizes of units within one system of measurement. 
  I can change a bigger measurement unit to a smaller measurement unit within the same system.
  I can show measurement equivalents in a two column charts.

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Measurement and Data
Solve problems involving measurement and
conversion of measurements from a larger
unit to a smaller unit
2. Use the four operations to solve word problems involving distances, intervals of time, liquidvolumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements givenin a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.  I can solve word problems about distance, liquid volume, solid mass, money, and time, including fractions and decimals.
  I can convert units of meausrement within a system to smaller units to solve the problems.
  I can use diagrams to show measured amounts.
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Measurement and Data
Solve problems involving measurement and
conversion of measurements from a larger
unit to a smaller unit
3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems.For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.  I can use the formula for area of a rectangle to solve problems.  a = l x w.
  I can use  the formula for perimeter of a rectangle to solve problems p =( 2 x l) + (2x w).
  I can solve perimeter and areaproblems in which there is an unknown factor (n).
  I can apply the formula for area and perimeter of a rectangle to solve real worldl problems.
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Measurement and Data
Represent and interpret data
4. 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 information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

  I can make a line plot to show a data set of measurements in fractions of a unit.
  I can use a line plot to solve problems with addition and subtraction of fractions.

 
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Measurement and Data
Geometric measurement: understand
concepts of angle and measure angles
5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
a. 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. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
  I can understand that an angle is formed when two rays meet at a common endpoint. 
  I can recognize a circle has 360 degrees.
  I can recognize that an angle is a fraction of a 360 degree circle
  I can explain the angle measurement in terms of degrees.
  I can compare angles within a circle.
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Measurement and Data
Geometric measurement: understand
concepts of angle and measure angles
6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
  I can read a protractor and determine which scale on the protractor to use based on the direction the angle is open.
  I can determine the kind of angle based on the specified measure to decide reasonableness of the sketch (ex. acute, obtuse, right and straight).
  I can measure angles in whole number degrees using a protractor.
  I can draw angles of specified measurements using a protractor.
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Measurement and Data
Geometric measurement: understand
concepts of angle and measure angles
7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping
parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

  I can recognize that an angle can be divided into smaller angles.
  I can solve addition and subtraction equations to find unknown angle measurements on a diagram.
  I can find an angle measure by adding the measurements of smaller angles that make up the larger scale.
  I can find an angle measure by subtracting the measurements of smaller angle from the larger scale.
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Geometry
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.

1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.  I can draw points, lines, line segments and rays.
  I can draw perpendicular and parallel.
  I can draw right, acute and obtuse angles.
  I can analyze 2 dimensional figures to identify points, lines, lines segments and rays.
  I can analyze 2 dimensional figures to identify right, actute, and obtuse angles.
  I can analyze 2 dimensional figures to identify parallel and perpendicular lines.
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Geometry
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.

2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicularlines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

  I can identify perpendicular lines in 2 dimensional figures
  I can identify parallel lines in 2 dimensional figures.
  I can recognize acute, obtuse, and right angles in 2 dimensional figures.
  I can identify right angles.
  I can classify 2 dimensional shapes based on parallel and perpendicular lines as well as size of angles.
  I can classify triangles as right triangles and not right triangles.
22
Geometry
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.

3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symetric figures and draw lines of symmetry.
  I can recognize lines of symmetry within a 2 dimensional figure.
  I can recognize a line of symmetry as a line across a figure that when folded along a line creates two matching parts.
  I can draw lines of symmetry for two dimensional figures.
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Numbers and Operations - Fractions
Extend understanding of fraction equivalence
and ordering.
1. 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.  I can explain why fractions are equivalent using fraction models.

  I can recognize and create equivalent fractions.


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Numbers and Operations - Fractions
Extend understanding of fraction equivalence
and ordering.
2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that 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.  I can compare fractions with different numerators and denominators using <, >, and =.

I can show the comparisons using a fraction model from the same whole. 

I can prove my comprisons using a fraction model.

I can compare fractions using benchmark fractions ( = to 1/2, more than 1/2, and less than 1/2.

  I can determine a common denominator for two fractions and then compare the two fractions.


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Numbers and Operations -Fractions
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers
3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like 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.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

  I can add fractions. (a)
  I can subtract fractions.  (a)
  I can break apart a fraction into a sum of fractions with the same denominator in more than one way.  (b)
  I can record each sum of fractions using an equation.  (b)
  I can prove my equation using a fraction model. (b)
  I can add and subtract mixed numbers with like denominators.  (c)


26
Numbers and Operations -Fractions
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers
4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fractionmodel to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6× (1/5), recognizing this product as 6/5. (In general, n × (a/b)= (n × a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef,and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

I can use a visual fraction model to show that fractions have multiples.
  I can us a fraction nodel to multiply a fraction by a whole number.
  I can use fraction models to solve word problems involving multiplication of a fraction by a whole number.
27
Numbers and Operations Base Ten - Fractions
Understand decimal notation for fractions, and
compare decimal fractions.

5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.  I can rename and recognize a fraction with a denominator of 10 as a fraction with a denominator of 100.
  I can recognize that two fractions with unlike denominators can be equivalent. 
  I can add two fractions with denominators of 10 and 100 by renaming tenths to hundredth.
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Numbers and Operations Base Ten - Fractions
Understand decimal notation for fractions, and
compare decimal fractions.

6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.  I can name the value of digits within a decimal number to hundredths.
  I can read and write decimals to the hundredths.
  I can rename fractions with 10 and 100 in the denominator as decimals.
  I can represent fractions with denominators of 10 and 100.
  I can represent fractions as decimals to the hundredths place.
  I can explain how decimals and fractions are related.
  I can represent decimals on a number line or meter stick up to the hundredths.
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