**California Common Core Standards**

What is the Common Core?

**California Common Core Standards**

**Gridley Unified Common Core Math Pacing Guides**

**Gridley Unified Common Core Math Pacing Guides**

6 units with two per trimesterFourth GradeUnit One-Place Value, Rounding, Fluency, with Addition and Subtraction of Whole Numbers. 4.NBT.1 I can explain the value of each digit in a multi-digit number as ten times the digit to the right 4.NBT.2 I can read/write multi-digit whole numbers using numerals, number names, and expanded form. I can compare two multi-digit numbers using >,=,< . 4.NBT.3 I can round multi-digit whole numbers to any given place. 4.NBT.4 I can fluently add/subtract multi-digit numbers. Unit TwoFactors and Multiples4.OA.4 I can find factor pairs for whole numbers 1-100. I can recognize a whole number as a multiple of each of its factors. I can decide whether a whole number (1-100) is a multiple of a given one-digit. I can determine if a whole number (1-100) is prime or composite. Unit Three-Multiplication and Division Using Place Value4.NBT.5 I can multiply four digit whole number by a one digit whole number using strategies and properties of operations. I can multiply two two-digit numbers using strategies and properties. 4.NBT.6 I can apply strategies to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors. I can represent/explain the calculation using an equation, rectangular Unit Four-Multiplication and Division Using Place Value4.OA.3 I can choose the correct operation to perform at each step of a multi-step word problem. I can interpret the meaning of remainders. I can represent problems using equations with a letter standing for the unknown quantity (variable). I can decide if my answer makes sense using mental math, estimation, and rounding. Unit Five-Fractions4.NF.1 I can explain why fractions are equivalent using fraction models. I can recognize and create equivalent fractions. 4.NF.2 I can compare two fractions with different numerators and denominators using <,>, and =. I can recognize that comparisons of two fractions are valid only when they refer to the same whole (congruent shape). I can show and prove my comparisons using a fraction model. 4.NF.3a-d I can use visuals models to add and subtract fractions within the same whole. I can use visual models to decompose a fraction in more than one way, including decomposing a fraction into a sum of its unit fractions. I can record each sum of fractions using an equation. I can prove my equation using a fraction model. I can add/subtract mixed numbers with denominators. I can solve word problems using addition/subtraction of fractions with the same denominator. Unit Six-Fractions and Decimals4.NF.4 a-c I can use a visual fraction model to show that fractions have multiples. I can use a fraction model 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. 4.NF.6 I can identify the tenths and hundredths place of a decimal. I can explain the relationship between a fraction and the decimal representation. I can represent fractions with denominators of 10 and 100 as a decimal. I can show the placement of a decimal on a number line. |
Fifth Grade7 units with 5 weeks for each unit Unit One- Place Value NBT.A .1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. NBT.A.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. NBT.A.4 Use place value understanding to round decimals to any place. Unit Two-Add, Subtract, Multiply, and Divide Whole Numbers and DecimalsNBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Unit Three- Algebra/ Add FractionsOA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Unit Four- Multiply and Divide FractionsNF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. NF.B.5 Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. NF.B.6 Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Unit 5-Using Fractions in real Life WaysNF.B.5 Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Unit 6-Measurement and GeometryMD.A.1 Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. G.B.3 Classify two-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. G.B.4 Classify two-dimensional figures in a hierarchy based on properties. G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Unit 7 Solid Figures and VolumeMD.C.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. MD.C.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. a. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. |