4.OA.A Use the four operations with whole numbers to solve problems.
4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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.OA.A.1.a Knowledge of and ability to apply understanding of multiplication as repeated addition (2.OA.C.4), as "equal groups of" (3.OA.A.1), and the Commutative Property (3.OA.B.5)
4.OA.A.1.c Ability to verbally explain which quantity is being multiplied and which number tells how many times as multiplication equations
4.OA.A.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.
4.OA.A.2.a Ability to solve various types of word problems involving multiplication comparison by using drawings (CCSS, Page 89, Table 2) through initial use of concrete materials and pictures, leading to the use of equations as a tool in solutions.
4.OA.A.2.b Ability to represent the solution to multiplicative comparison problems using multiplication or division equations
4.OA.A.2.c Ability to distinguish and explain the difference between multiplicative comparison and additive comparison.
4.OA.A.3 Solve multi-step 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.
4.OA.A.3.a Ability to identify which of the four operations will be used to solve multi-step word problems and accurately represent the problem with the corresponding equations
4.OA.A.3.b Ability to use the context of the problem to interpret the remainder of a problem to appropriately determine if it should be discarded, replaced with the next highest whole number answer, or used as the answer to the question.
4.OA.A.3.d Ability to verbally and in writing provide evidence of reasonableness of answers using mental computation, properties of operations, relationships between operations, and estimation strategies.
4.OA.B Gain familiarity with factors and multiples.
4.OA.B.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 of 1-100 is prime or composite.
4.OA.B.4.a Knowledge of multiplication as arrays and its connection to area of rectangles to determine factor pairs
4.OA.B.4.b Knowledge of and ability to apply multiplication facts to determine multiples of one-digit numbers
4.NBT.A.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.
4.NBT.A.2.a Ability to flexibly read and write different number forms, base ten numerals (285) extended form (200 + 80 + 5), written form (two hundred eight-five)
4.NBT.B.5 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
4.NBT.B.5.a Apply to apply knowledge of multiplication and division facts of one digit whole numbers
4.NBT.B.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.
4.NBT.B.6.a Ability to apply knowledge of multiplication and division within 100
4.NF.A Extend understanding of fraction equivalence and ordering.
4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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.
4.NF.A.1.a Ability to use concrete materials to model fraction number concepts and values
4.NF.A.1.d Generate a rule for finding equivalent fractions based on conceptual understanding of using models to show equivalent fractions.
4.NF.A.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 ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.A.2.a Ability to apply knowledge factors (4.OA.B.4) to the strategies used to determine equivalent fractions as well as ordering fractions
4.NF.B.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation. Justify decompositions, e.g., by using a visual fraction model.
4.NF.B.3c 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.
4.NF.B.3c.1 Ability to change a mixed number into an improper fraction
4.NF.3d 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.
4.NF.3d.1 Ability to apply the understanding that the numerator tells us how many parts of the whole we are counting and the denominator tells us how many total parts there are in the whole,
4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, e.g., by using a visual model.
4.NF.C.7.a Ability to apply knowledge of place value as a strategy to compare decimals
4.MD.A Solve problems involving measurement and conversion of measurements for a larger unit to a smaller unit.
4.MD.A.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 in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
4.MD.A.1.a Knowledge of capacity units should also include cups, pints, quarts, and gallons.
4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.A.2.a Ability to use visual aids with conversion of measurement
4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
4.MD.A.3.a Ability to apply knowledge of the relationship between area and perimeter through the exploration of rectangles with the same area but different perimeters or rectangles with the same perimeter but different areas
4.MD.B.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.
4.MD.B.4.a See the skills and knowledge that are stated in the Standard.
4.MD.C.5a 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 the circle is called a "one-degree angle," and can be used to measure angles.
4.MD.C.5a.1 Knowledge of partitioning circles into equal shares
4.MD.C.5a.2 Ability to relate understanding of equal shares of a circle to angles
4.MD.C.5a.3 Ability to use visual aids and/or technology to apply the understanding of how a circle is divided into 360 degrees (e.g., circle protractor or geometry software)
4.MD.C.5a.4 Introduce the unit of measurement of a circle (degrees) Students need to understand that a whole circle is 360 degrees by taking a circle and dividing it into 1/2,1/4,1/8 etc. so that 1/2 is 360 divided by 4, etc.
4.MD.C.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.
4.MD.C.7.a Ability to apply knowledge of common whole number addition and subtraction situations to fractional problem situations
4.G.A.1.b Ability to apply a deep understanding of this vocabulary will assist with drawing and identifying these shapes within two- dimensional figures.
4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
4.G.A.2.a Ability to use concrete materials to model the lines and angles of two-dimensional figures to provide visual evidence of the relationship between various figures
4.G.A.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-symmetric figures and draw lines of symmetry.
4.G.A.3.a See the skills and knowledge that are stated in the Standard.