Gizmos for Utah - Mathematics: 5th Grade (UT--Core Standards adopted 2016)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

5.MP: : Mathematical Practices

(Framing Text): : Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

5.MP.1: : Make sense of problems and persevere in solving them.

5.MP.1.a: : Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.

5.MP.2: : Reason abstractly and quantitatively.

5.MP.3: : Construct viable arguments and critique the reasoning of others.

5.MP.3.a: : Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.

5.MP.4: : Model with mathematics.

5.MP.5: : Use appropriate tools strategically.

5.MP.5.a: : Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.

5.MP.6: : Attend to precision.

5.MP.6.a: : Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.

5.MP.7: : Look for and make use of structure.

5.MP.7.a: : Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.

5.MP.8: : Look for and express regularity in repeated reasoning.

5.MP.8.a: : Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.

5.OA: : Operations and Algebraic Thinking

(Framing Text): : Write and interpret numerical expressions.

5.OA.1: : Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

(Framing Text): : Write and interpret numerical expressions, and analyze patterns and relationships.

5.OA.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.

5.NBT: : Number and Operations in Base Ten

(Framing Text): : Understand the place value system.

5.NBT.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.

5.NBT.3: : Read, write, and compare decimals to thousandths.

5.NBT.3.a: : Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. For example, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

5.NBT.3.b: : Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

(Framing Text): : Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.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.

5.NBT.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. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor.

5.NF: : Number and Operations—Fractions

(Framing Text): : Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.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.

5.NF.2: : Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by, for example, 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.

(Framing Text): : Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3: : Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve real-world problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, through the use of visual fraction models or equations to represent the problem.

5.NF.4: : Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.4.a: : Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b using a visual fraction model.

5.NF.4.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.

5.NF.6: : Solve real-world problems involving multiplication of fractions and mixed numbers, for example, by using visual fraction models or equations to represent the problem.

5.MD: : Measurement and Data

(Framing Text): : Convert like measurement units within a given measurement system.

5.MD.1: : Convert among different-sized standard measurement units within a given measurement system (for example, convert 5 cm to 0.05 m); use these conversions in solving multi-step, real-world problems.

(Framing Text): : Understand concepts of geometric measurement and volume, as well as how multiplication and addition relate to volume.

5.MD.3: : Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

5.MD.3.a: : A cube with side length one unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

5.MD.3.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.

5.MD.4: : Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units.

5.MD.5: : Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.

5.MD.5.a: : 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, for example, to represent the associative property of multiplication.

5.MD.5.b: : Apply the formulas V = l x w x h and V = b x 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.

5.G: : Geometry

(Framing Text): : Graph points on the coordinate plane to solve real-world and mathematical problems in quadrant one.

5.G.1: : Compose and understand the coordinate plane.

5.G.1.a: : 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 zero on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates.

5.G.1.b: : Using quadrant one on the coordinate plane, understand that the first number in a coordinate pair indicates how far to travel from the origin in the direction of the horizontal axis, and the second number indicates how far to travel in the direction of the vertical axis, with the convention that the names of the two axes and the coordinates correspond (x-axis and x-coordinate, y-axis and y-coordinate).

5.G.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.

(Framing Text): : Classify two-dimensional figures into categories based on their properties.

5.G.3: : 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 all squares are rectangles, so all squares have four right angles.

5.G.4: : Classify two-dimensional figures in a hierarchy based on properties.

Correlation last revised: 9/16/2020

Utah - Mathematics: 5th Grade

UT--Core Standards | Adopted: 2016