> y @/bjbj 7{{@'txfn$!\" -------c3MB-60f-!-!--!--f!: Grade 3How will we assess this?Related textbook pages Related additional resources and activitiesOperations and Algebraic Thinking (3.OA)Represent and solve problems involving multiplication and division.1. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7.
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. For example, describe a context in which a number of shares or a number of
groups can be expressed as 56 8.
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.
4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations
8 ? = 48, 5 = 3, 6 6 = ?.Understand properties of multiplication and the relationship between multiplication and division.5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive
property.)
6. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100. 7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 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.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.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.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.Number and Operations in Base Ten (3.NBT) Use place value understanding and properties of operations to perform multi-digit arithmetic.
1. Use place value understanding to round whole numbers to the nearest 10 or 100.
2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.3. Multiply one-digit whole numbers by multiples of 10 in the range 1090 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations.
Number and OperationsFractions (3.NF) Develop understanding of fractions as numbers.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number
line diagram by defining the interval
from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each
part has size 1/b and that the endpoint
of the part based at 0 locates the
number 1/b on the number line.
b. Represent a fraction a/b on a number
line diagram by marking off a lengths 1/b
from 0. Recognize that the resulting
interval has size a/b and that its
endpoint locates the number a/b on the
number line.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent
(equal) if they are the same size, or the
same point on a number line.
b. Recognize and generate simple
equivalent fractions, e.g., 1/2 = 2/4,
4/6 = 2/3). Explain why the fractions
are equivalent, e.g., by using a visual
fraction model.
c. Express whole numbers as fractions,
and recognize fractions that are
equivalent to whole numbers.
Examples: Express 3 in the form 3 =
3/1; recognize that 6/1 = 6; locate 4/4
and 1 at the same point of a number
line diagram.
d. 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.Measurement and Data (3.MD)Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.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.
2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 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.Represent and interpret data.
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 many less problems using information presented in scaled bar graphs.
For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
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 unitswhole numbers, halves, or quarters.
Geometric measurement: understand concepts of area and relate
area to multiplication and to addition.
5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called
a unit square, is said to have one
square unit of area, and can be used to
measure area.
b. A plane figure which can be covered
without gaps or overlaps by n unit
squares is said to have an area of n
square units.
6. Measure areas by counting unit squares
(square cm, square m, square in, square ft, and improvised units).
7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with
whole-number side lengths by tiling it,
and show that the area is the same as
would be found by multiplying the side
lengths.
b. 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.
c. 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 b and a c. Use area
models to represent the distributive
property in mathematical reasoning.
d. 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.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
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.
Geometry (3.G)Reason with shapes and their attributes.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.
2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
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