• Math Fun

    Knows are words the students should use when explaining problems or answers. (Vocabulary)

    Does are skills the student have to perform. (Tasks/Skills)

    August 10 - September 9

    Unit 1: Pace Value 

    Standards:

    • 3.NBT.1.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
    • 3.NBT.1.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties or operations, and/or the relationship between addition and subtraction. 

    Know:

     

    • round 
    • estimate 
    • place value (ones, tens, hundreds, thousands) 
    • sum 
    • difference 
    • properties of operations 
    • equation 
    • expanded form

    Do:

    • Use a number line to support answers when rounding. 
    • Use place value to round numbers to the nearest 10 or 100. 
    • Fluently add or subtract within 1000 using multiple strategies and algorithms. (Decompose/Compose using place value strategies) 
    • Apply associative, commutative, distributive, and inverse properties to add and subtract within 1000. 
    • Use vertical and horizontal forms when adding and subtracting. 
    • Explain a strategy selected to solve a problem. (See Number Talks resource bk.)

     

     September 12 - November 11

    Unit 2: Multiplication and Division Strategies

    Standards:

    • 3.OA.1.1 – Interpret products of whole numbers, e.g., interpret 5x7 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 5x7. 
    • 3.OA.1.2 – Interpret whole-number quotients of whole number 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.OA.1.3 – 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.1.4 – 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 x ? = 48, 5 =_ ÷ 3, 6 x 6 = ?.
    • 3.OA.2.5 – Apply properties of operations as strategies to multiply and divide. 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.) 
    • 3.OA.2.6 – Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that makes 32 when multiplied by 8. 
    • 3.OA.3.7 – Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8x5=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.4.8 – 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.4.9 – 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. 
    • 3.NBT.1.3 – Multiply one-digit whole numbers by multiples of 10 in the range of 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

    Know:

     

    • groups of 
    • equal groups, group size 
    • proportioned equally 
    • operation 
    • multiply, product, factor, multiple 
    • times as many 
    • divide, dividend, divisor, quotient 
    • equation 
    • inverse operations
    • unknown  
    • properties
    • identity property of multiplication: zero property of multiplication, commutative property of multiplication, distributive property, and associative property of multiplication  
    • patterns ( Ex: even x even = even, etc.)
    • arrays

     

    Do:

     

    • Use manipulatives to demonstrate equal groups and arrays. 
    • Represent expressions using various objects, pictures, words and symbols in order to develop their understanding of properties. 
    • Interpret products and quotients of whole numbers (e.g.5x7 is 5 groups of 7 objects, 56÷8 is 56 objects partitioned into 8 shares). 
    • Solve word problems up to 100 using multiplication and division, involving equal groups or shares, arrays, drawings, and symbols for unknown numbers. 
    • Use multiple strategies to fluently multiply and divide within 100. 
    • Multiply 1-digit numbers by multiples of 10 in the range of 10-90 using multiple strategies. NOTE: DO NOT teach the zero trick! Instead, teach 9 x 80 is equal to 9 x 8 tens = 72 tens.
    • Find the missing number in the multiplication and division equation. (e.g., 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 = ?) See Table 2 for common situations for multiplication and division at the end of this curriculum map. 
    • Use repeated subtraction with equal groups. 
    • Explore the inverse operation of multiplication and division using manipulatives. 
    • Identify patterns in multiplication and addition. 
    • Identify patterns in an addition table or multiplication table. 
    • Apply the commutative property of multiplication (e.g., 6 x 4 = 24, 4 x 6 = 24). 
    • Apply the associative property of multiplication (e.g., 3 x 5 x 2 is 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 10 x 3 = 30). 
    • Apply the distributive property 8 x 5 = 40 and 8 x 2 =16 is 8 x 7 as 8 x (5 + 2)=(8 x 5)+(8 x 2)=40 + 16 = 56. See Table 3 for a description of each of the properties at the end of this curriculum map. 
    • Use mental math to estimate an answer and check for reasonableness. 
    • Know from memory all products of two one-digit numbers by the end of Grade 3. 
    • Solve two-step word problems using the four operations. 
    • Investigate how the order of operations might change the answer when given an equation.

     

     

     

    November 14 - December 2

    Unit 3: Area and Perimeter 

    Standards:

     

    • 3.MD 3.5 – Recognize area as an attribute of plane figures and understand concepts of area measurement.  
      1. 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.
      2. 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.
    • 3.MD.3.6 – Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units). DOK 1 3.MD.3.7 – Relate area to the operations of multiplication and addition.  

     

      1. 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.
      2. 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. 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.
      4. 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.

     

    • 3.MD.4.8 – 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.

     

    Know:

    • square inch, square foot 
    • non-standard unit 
    • tiling 
    • recti-linear (polygon that has all right 
    • angles, e.g., L-shaped or T-shaped) 
    • gap 
    • overlap 
    • length, width 
    • base, height 
    • perimeter 
    • linear
    • polygon
    • side length
    • unit of measure
    • area
    • square unit (sq units)/unit square
    • square centimeter
    • square meter
    • distributive property
    • plane figures

    Do:

    • Strategically use tools such as geoboards, tiles, and graph paper to find all the possible rectangles that have a given perimeter. 
    • Add the sides of a variety of shapes to determine the perimeter. 
    • Use pictures to find the unknown side lengths or widths of polygons 
    • Fill a region with square tiles to determine the area. 
    • Use graph paper to depict the area of a shape. 
    • Use skip counting and multiplication to determine the number of squares in the array. 
    • Use square tiles to represent how different shapes can have the same area. 
    • Use area models to represent the distributive property (e.g., lengths a and b + c is the sum of a x b and a x c). 
    • Explain why multiplying the side lengths of a rectangle gives the same measurement of area as counting the number of tiles with the same unit length (e.g., one length tells how many unit squares in a row, and the other length tells how many rows there are). 
    • Decompose a figure to find an area (rectilinear). 
    • Compare polygons that have the same perimeter but different area. 
    • Compare and analyze polygons that have the same area but different perimeters. 
    • Justify solutions using words, diagrams, or pictures. 
    • Solve real world and mathematical problems involving area and perimeter of polygons.

    December 5 - January 13

    Unit 4: Geometry

    Standards:

    • 3.G.1.1 – 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.1.2 – 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 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

    Know:

    • angle, right angle
    • greater than a right angle
    • less than a right angle
    • rhombus
    • quadrilateral
    • parallelogram
    • polygon
    • triangle
    • trapezoid
    • unit fraction
    • equal side lengths

    Do: 

    • Classify shapes as quadrilaterals by examining their attributes. 
    • Classify squares, rectangles, and rhombuses as quadrilaterals. 
    • Classify shapes that fit certain categories, such as, equal side lengths, same number of sides, 4 right angles, etc. 
    • Draw examples of quadrilaterals that are not in the subcategories (such as: rhombi, rectangles and squares). 
    • Partition shapes into 1/2 , 1/3 , 1/4 , 1/6 , and 1/8 and express as halves, thirds, fourths, sixths and eighths. 
    • Partition a shape into equal parts that all have the same area. 
    • Partition a shape into parts with equal areas in several different ways.

    January 17 - February 24

    Unit 5: Frations

    Standards:

    • 3.NF.1.1 – 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. 
    • 3.NF.1.2 – Understand a fraction as a number on the number line; represent fractions on a number line diagram.
      1. 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.
      2. 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.NF.1.3 – Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
      1. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
      2. 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.
      3. 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.
      4. 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.

    Knows: 

    • equal parts
    • whole, halves, thirds,
    • fraction greater than 1 whole
    • fraction fourths, sixths, and eighths
    • visual fraction models
    • numerator
    • equal distance (intervals on a number line)
    • number lines 
    • denominator  
    • unit fraction (fraction with a numerator of 1)
    • compare (using greater than > and less than < symbols)

    Do:

    • Partition a whole into equal parts.
    • Understand that a fraction is part of a whole or part of a group.
    • Represent a fraction on a number line and label the intervals.
    • Use a variety of models to represent fractions.
    • Identify a unit fraction.
    • Write whole numbers as fractions (4/4, 8/8, 2/1, 4/2, 6/3).
    • Understand equivalent fractions using visual fraction models and number lines.
    • Understand equivalent fractions using reasoning skills without the use of models.
    • Compare two fractions with the same numerator or the same denominator. o Compare shaded models of two fractions o Compare unshaded (left over) areas of two fractions.  Ex. 2/3 compared to ¾ is also 1/3 away from 1 whole compared to ¼ away from 1 whole
    • Recognize that comparisons are valid only when the two fractions refer to the same whole. (e.g. ½ of a small pizza is not equal to ½ of a large pizza.)
    • Record the results of comparisons with the symbols <, >, =.
    • Justify conclusions when comparing two fractions using a visual fraction model.

    Feburary 27 - April 7

    Unit 6: Time, Measurement, Data

    • 3.MD.1.1 – 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.1.2 – 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.2.3 – 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. 
    • 3.MD.2.4 – 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. 

    Know:

    • frequency table 
    • data 
    • key 
    • horizontal bar graph 
    • vertical bar graph 
    • time interval (elapsed time) 
    • kilogram (kg) 
    • liter (l)
    • line plot
    • halves
    • quarters
    • liquid 
    • volume
    • mass
    • metric
    • gram (g)
    • picture graph
    • data set
    • inch/inches
    • scale
    • fourths
    • minutes
    • quarter after (:15) 
    • quarter before (:45)

     

    Do:

    • Draw a scaled picture graph to represent data using several categories. 
    • Draw a scaled bar graph to represent data using several categories. 
    • Solve one- and two-step word problems using “how many more” and “how many less”. 
    • Collect data, analyze data and interpret data that is relevant to their lives (e.g., A class survey on their favorite subject, favorite meal, sports, siblings, pets). 
    • Construct and interpret horizontal and vertical bar graphs using various scale intervals. (ex. Going up by 2’s, 5’s, 10’s, etc.) 
    • Generate a line plot using measurement data  Show data in a line plot, where the horizontal scale is marked off in appropriate units (whole numbers, halves, quarters). 
    • Tell and write time to the nearest minute.  Use clock models and number lines to solve addition and subtraction word problems with time intervals. 
    • Measure objects using rulers marked with ½ and ¼ inch. 
    • Measure and estimate multiple objects’ mass using gram and kilogram. 
    • Measure and estimate liquid volume using liters. 
    • Identify multiple objects that weigh about 1g, 5g, 10g (e.g., five different pieces of candy that all have the same weight).
    • Partition larger units into smaller equivalent units. 
    • Use the four operations to solve word problems with mass and volume.

    NOTE: Students DO NOT need to do conversions between units of measure