Gizmos for Arizona - Mathematics: 5th Grade (Academic Standards adopted 2016)

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

5.OA: : Operations and Algebraic Thinking

5.OA.A: : Write and interpret numerical expressions.

5.OA.A.1: : Use parentheses and brackets in numerical expressions, and evaluate expressions with these symbols (Order of Operations).

5.OA.B: : Analyze patterns and relationships.

5.OA.B.3: : Generate two numerical patterns using two given rules (e.g., generate terms in the resulting sequences). Identify and explain the 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 (e.g., 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).

5.OA.B.4: : Understand primes have only two factors and decompose numbers into prime factors.

5.NBT: : Number and Operations in Base Ten

5.NBT.A: : Understand the place value system.

5.NBT.A.1: : Apply concepts of place value, multiplication, and division to understand 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.A.3: : Read, write, and compare decimals to thousandths.

5.NBT.A.3a: : Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

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

5.NBT.B: : Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.B.5: : Fluently multiply multi-digit whole numbers using a standard algorithm.

5.NBT.B.6: : Apply and extend understanding of division to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

5.NBT.B.7: : Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations. Relate the strategy to a written form.

5.NF: : Number and Operations—Fractions

5.NF.A: : Use equivalent fractions to add and subtract fractions.

5.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 (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12).

5.NF.A.2: : Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using a variety of representations, equations, and visual models to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g. recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7

5.NF.B: : Use previous understandings of multiplication and division to multiply and divide fractions.

5.NF.B.3: : Interpret a fraction as the number that results from dividing the whole number numerator by the whole number denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

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

5.NF.B.4a: : Interpret the product (??/??) x ?? as a parts of a partition of ?? into ?? equal parts.

5.NF.B.4c: : 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.B.6: : Solve problems in real-world contexts involving multiplication of fractions, including mixed numbers, by using a variety of representations including equations and models.

5.MD: : Measurement and Data

5.MD.A: : Convert like measurement units within a given measurement system.

5.MD.A.1: : Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems.

5.MD.C: : Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition.

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

5.MD.C.3a: : 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.

5.MD.C.3b: : 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.C.4: : Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

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

5.MD.C.5a: : 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).

5.MD.C.5b: : Understand and use the formulas V = l x w x h and V = Bh, where in this case B is the area of the base (B = l x w), for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve mathematical problems and problems in real-world contexts.

5.G: : Geometry

5.G.A: : Graph points on the coordinate plane to solve mathematical problems as well as problems in real-world context.

5.G.A.1: : Understand and describe a coordinate system as perpendicular number lines, called axes, that intersect at the origin (0, 0). Identify a given point in the first quadrant of the coordinate plane using an ordered pair of numbers, called coordinates. Understand that the first number (x) indicates the distance traveled on the horizontal axis, and the second number (y) indicates the distance traveled on the vertical axis.

5.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.

5.G.B: : Classify two-dimensional figures into categories based on their properties.

5.G.B.3: : Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

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

5.MP: : Standards for Mathematical Practices

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

6.1.1: : Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?' to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others.

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

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

6.3.1: : Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

5.MP.4: : Model with mathematics.

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

6.5.1: : Mathematically proficient students consider available tools when solving a mathematical problem. They choose tools that are relevant and useful to the problem at hand. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful; recognizing both the insight to be gained and their limitations. Students deepen their understanding of mathematical concepts when using tools to visualize, explore, compare, communicate, make and test predictions, and understand the thinking of others.

5.MP.6: : Attend to precision.

6.6.1: : Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

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

6.7.1: : Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

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

6.8.1: : Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency.

Correlation last revised: 9/16/2020

Arizona - Mathematics: 5th Grade

Academic Standards | Adopted: 2016