3.OA.A.1.f Knowledge that the example in Standard 3.0A.A.1 can also represent the total number of objects with 5 items in each of 7 groups (Commutative Property)
3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
3.OA.A.2.a Knowledge that division is the inverse of multiplication and the process of repeated subtraction
3.OA.A.2.d Knowledge that just as multiplication is related to repeated addition, division is related to of repeated subtraction
3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.A.3.a Ability to determine when to use multiplication or division to solve a given word problem situation.
3.OA.A.3.b Ability to represent a problem using drawings and equations without or with a symbol for the unknown number.
3.OA.A.3.c Ability to solve different types of multiplication and division word problems
3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.OA.C.7.a Knowledge of multiplication and division strategies and properties to achieve efficient recall of facts
3.OA.C.7.c Ability to model the various properties using concrete materials
3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.D.8 Solve two-step word problems using the four operations. 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.
3.OA.D.8.a Knowledge of strategies for word problems as established for addition and subtraction
3.NF.A.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
3.NF.A.3d.1 Ability to use benchmarks of 0, ½ and 1 to explain relative value of fractions
3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
3.MD.A.1.a Ability to tell time to the nearest 5- minute interval
3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
3.MD.A.2.a Participates in multiple hands-on experiences to understand the quantity of grams, kilograms, and liters, as well as how they compare with each other.
3.MD.A.2.b Ability to use the tools to measure mass and volume.
3.MD.A.2.c Ability to explain the differences between mass and volume.
3.MD.A.2.e Ability to solve one-step word problems involving masses or volumes using the four operations.
3.MD.B Represent and interpret data.
3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how may less" problems using information presented in scaled bar graphs.
3.MD.B.3.a Knowledge that the use of "square" is referring to interval on the scale and that not all graphs will include a "square" but all graphs should include intervals
3.MD.B.3.b Ability to apply experience with constructing and analyzing simple, single-unit scaled bar and picture graphs (pictograph) with no more than 4 categories
3.MD.B.3.c Knowledge of increased scale and intervals (moving to graphs representing more than one item and the intervals representing 2, 5, 10 on the graph, etc.) and expanding to one-step and two-step problem-solving with given data
3.MD.B.3.d Knowledge that the interval of scale is the amount from one tick mark to the next along the axis and that the scale would be determined based on the values being represented in the data
3.MD.B.3.e Knowledge of and ability to connect understanding of locating points on a number line with locating points between intervals on a given axis. (e.g., if given a scale counting by 5s students would need to be able to estimate the location of 13 between intervals of 10 and 15.)
3.MD.B.3.f Ability to apply the information in the Key when interpreting fractions of a symbol on a picture graph
3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units – whole numbers, halves, or quarters.
3.MD.B.4.a Ability to apply prior experience with the measurement of lengths being marked and recorded on line plots to the nearest whole unit
3.MD.C.7b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
3.MD.C.7b.1 Ability to apply the formula for area of a rectangle to solve word problems
3.MD.C.7b.3 Use understanding of area to identify false reasoning and explain how to correctly find the area of rectangles.
3.MD.C.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.C.7c.1 Ability to construct rectangles on grid paper and decompose them by cutting them up or color coding them to investigate area
3.MD.C.7c.2 Ability to use a pictorial model of the distributive property to solve area word problems
3.MD.C.7c.3 Knowledge that, for example, when working with a rectangle with side lengths of 7 units by 8 units, let a represent 7 and b + c represent a decomposition of 8 (e.g. 5 + 3, 6 + 2, 4 + 4, 7 + 1, etc.) In other words, 7 x 8 is the same as (7 x 2) + (7 x 6)
3.MD.C.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
3.MD.C.7d.1 This is an extension of 3.MD.C.7c.
3.MD.C.7d.2 Knowledge that rectilinear figures refer to any polygon with all right angles
3.MD.C.7d.3 Ability to apply knowledge of finding area of a single polygon to finding areas of two non-overlapping rectangles to find the area f the whole figure.
3.MD.D Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
3.MD.D.8.a Knowledge that the perimeter is the distance around a region
3.MD.D.8.b Ability to use manipulatives and visual models to find the perimeter of a polygon
3.MD.D.8.c Ability to apply a variety of strategies to find the perimeter of a polygon.
3.MD.D.8.e Use understanding of perimeter to identify false reasoning and explain how to correctly find the perimeter of plane figures
3.MD.D.8.f Knowledge that this is a geometry application of unit fractions (3.NF.A.1) and ability to make use of unit fraction understanding
3.MD.D.8.g Ability to use concrete materials to divide shapes into equal areas (e.g., pattern blocks, color tiles, geoboards)
3.G.A Reason with shapes and their attributes.
3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
3.G.A.1.a Ability to compare and sort polygons based on their attributes, extending beyond the number of sides