# Summary of Skills

Age 7-9 - Concept 5: Math

## Unit 1: Multiplication and Division I

### Math

• Apply properties of operations as strategies to multiply and divide
• Determine the unknown whole number in a multiplication or division equation relating three whole numbers
• Fluently multiply and divide within 100
• Identify arithmetic patterns, and explain them using properties of operations
• Identify equal groups
• Interpret and create arrays that model multiplication
• Interpret products of whole numbers (for example, interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each)
• Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each)
• Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each).
• Interpret whole-number quotients of whole numbers (for example, 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)
• Skip count
• Understand division as an unknown-factor problem
• Use arrays to create addition sentences
• Use equal groups to model multiplication
• Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities
• Use repeated addition and number lines to model multiplication.
• Use the language of multiplication

## Unit 2: Place Value

### Math

• Assess the reasonableness of answers using mental computation and estimation strategies including rounding
• Count to 10,000
• Fluently add and subtract beyond 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction
• Read and write numbers to 10,000 using base-10 numerals, number names, and expanded form
• Read, write, and skip count to 1000
• Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
• Use place value understanding to round whole numbers to the nearest 10 or 100

## Unit 3: Measurement

### Math

• Add, subtract, multiply, or divide to solve one-step word problems involving weights or volumes that are given in the same units
• Measure and estimate liquid volumes (capacities) using standard units
• Measure and estimate liquid volumes and weights of objects using standard units
• Measure and estimate liquid volumes using standard units
• Measure and estimate weight using standard units
• Measure and estimate weights of objects using standard units
• Solve word problems involving addition and subtraction of time intervals in minutes
• Tell and write time to the nearest minute
• Tell and write time to the nearest minute and measure time intervals in minutes
• Tell, show, and talk about time to 5 minutes

## Unit 4: Multiplication and Division II

### Math

• Apply properties of operations as strategies to multiply and divide
• Determine the unknown whole number in a multiplication or division equation relating three whole numbers
• Fluently multiply and divide within 100
• Identify arithmetic patterns
• Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each
• 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
• Multiply one-digit whole numbers by multiples of 10 in the range 10-90
• Solve two-step word problems using the four operations
• Understand division as an unknown-factor problem
• Use multiplication and division to solve word problems
• Use multiplication and division within 100 to solve word problems

## Unit 5: Area and Perimeter

### Math

• Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts
• 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
• 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
• Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
• Measure length
• Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems
• Name, describe, and create polygons
• Recognize area as an attribute of plane figures and understand concepts of area measurement
• Relate area to the operations of multiplication and addition
• Solve real world and mathematical problems involving perimeters of polygons
• Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths
• Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length
• 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
• Understand that 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

## Unit 6: Fractions

### Math

• Compare two fractions with the same numerator or the same denominator
• Compare two fractions with the same numerator or the same denominator by reasoning about their size
• Discuss the use of fractions in the real world
• Explain equivalence of fractions in special cases
• Identify and compare wholes and parts
• Recognize and generate simple equivalent fractions
• Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3
• Recognize fractions that are equivalent to whole numbers
• Recognize parts of fractions: numerator and denominator
• Record the results of comparisons with the symbols >, =, or <, and justify the conclusions
• 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
• 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
• Show fractional parts of shapes
• Understand a fraction a/b as the quantity formed by a parts of size 1/b
• Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts
• 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
• Understand a fraction as a number on the number line; represent fractions on a number line diagram
• Understand two fractions as equivalent (equal) if they are the same size

## Unit 7: Geometry

### Math

• Define the attributes of polygons
• Express the area of each part as a unit fraction of the whole
• Identify and create parallel, intersecting, and perpendicular lines
• Identify congruent shapes
• Identify polygons and non-polygons
• Partition shapes into parts with equal areas
• Recognize rhombuses, rectangles, and squares as examples of quadrilaterals
• 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)

## Unit 8: Graphing Data

### Math

• Collect data
• Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories
• Draw conclusions
• Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
• Measure to half and quarter inches
• Read and interpret line plots
• Show data by making a line plot, where the horizontal scale is marked off in appropriate units
• Show data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters
• Solve one- and two-step "how many more" and "how many less" problems using information presented in graphs

## Unit 9: Skills Review

### Math

• Apply properties of operations as strategies to multiply and divide
• Divide shapes into parts with equal areas and express each area as a fraction of the whole
• Find areas of given shapes
• Find perimeters of given shapes
• Fluently multiply and divide within 100
• Identify units of measure
• Identify, represent, and compare fractions
• Recognize and generate simple equivalent fractions