3Rd Grade Curriculum / Unit Maps

2014 – 15 3rd Grade Math Concept Map – Unit 1 Big Idea – RT4: Multiplication and Division Computation Students understand the meanings of multiplication and division of whole numbers through the use of representations, such as equal-sized groups, arrays, area models and number lines for multiplication, and repeated subtraction, partitioning and sharing for division. They use properties of addition and multiplication (identity, zero, commutative, associative & distributive) to multiply whole numbers and apply increasingly sophisticated strategies to solve contextual problems. Through their work with multiple strategies, students relate multiplication and division as inverse operations. By the end of the unit the students should fluently multiply and divide within 100.* Connections to the Big Idea RT 1&2: Students extend their understanding of place value to multi-digit numbers in various situations, including understanding how place value relates to addition, subtraction, multiplication, and division. They compose and decompose numbers in multiple ways, such as 3420 = 3420 ones, 3 thousands + 4 hundreds + 2 tens, 342 tens, etc.

RT 3: Students continue to develop their understanding of addition and subtraction of multi-digit whole numbers including building their facility with mental arithmetic (e.g., 250 + 600 or 203-199) and by using computational estimation to judge the reasonableness of results. They select and apply appropriate methods to estimate sums and differences or calculate them mentally depending on the context and numbers involved. They apply their understanding of repeated addition and/or subtraction to multiplication and division. RT6: Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication and justify using multiplication to determine the area of a rectangle. RT 7: Students continue to develop an understanding of an unknown quantity represented as a symbol such as a box or picture, and solving for that unknown in computation situations including multiplication and division. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent equations in computation situations including multiplication and division. Students continue to develop their understanding of patterns by describing and extending them. Their work with multiplication and division strategies should involve analysis of the patterns that exist within these operations. Students work with various models such as number lines, ratio tables and arrays, and should embed the analysis of the patterns that exist.

* Fluency is defined under the CCSS as “the ability to use certain facts and procedures with enough facility that using them does not slow down or derail the problem solver as he or she works on more complex problems and being able to use relevant ideas or procedures in a wide range of context.”

July 25, 2014 2014 – 15 3rd Grade Math Concept Map – Unit 1

2014 – 15 3rd Grade Math Concept Map – Unit 2 Big Idea – RT 1&2: Number Systems, Relationships and Representations Students develop an understanding of fractions to represent part(s) of a whole, part(s) of a set, or distance(s) on a number line. They understand that the size of a fractional part is relative to the July 25, 2014 size of the whole (unitizing), and they use fractions to represent numbers that are equal to, less than or greater than one. They use models, such as benchmark fractions (halves, thirds, fourths, sixths and eighths) common numerators or denominators, and measurement tools (ruler) to solve problems that involve comparing, ordering and identifying equivalent fractions. Connections to the Big Idea RT 5: Students continue to develop their understanding that measurement systems utilize standardized tools and units to measure attributes of length. Students use rulers, yardsticks and meter sticks as distance models (number lines) in order to solidify their understanding of fractional parts. RT 7: Students continue to develop an understanding of equality around the equal sign (=) and generate equivalent fractions. Students continue to develop their understanding of patterns by describing and extending patterns.

RT 8: Students partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole. For example, partition a shape into four parts with equal area, and describe the area of each part as ¼ of the area of the shape.

RT9: Students continue to develop understanding of data representation and analysis by creating and using picture and bar graphs. They use measurement data to draw a scaled picture graph and a scaled bar graph that represent a data set with several categories. Students 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 animals in an ecosystem.

July 25, 2014 2014 – 15 3rd Grade Math Concept Map – Unit 2

2014 – 15 3rd Grade Math Concept Map – Unit 3 Big Idea – RT6: Dimensional Measurement Relationships Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same- size units of area required to cover the shape without gaps or overlaps, a square with

July 25, 2014 sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. Students develop an understanding of perimeter and area as an extension of measuring length and can select appropriate units, strategies and tools to solve problems related to perimeter and area. Connections to the Big Idea RT 3: Students use their understanding of addition and subtraction of whole numbers in order to solve problems involving perimeter of two-dimensional figures and use computational estimation to judge the reasonableness of results. They select and apply appropriate methods to estimate sums and differences or calculate them mentally depending on the context and numbers involved. RT4: Students relate area and array models to demonstrate an understanding of multiplication of whole numbers up to 10 x 10, including contextual situations.

RT 5: Students continue to develop their understanding that measurement systems utilize standardized tools and metric units to measure attributes of objects. They utilize formal units and tools to measure attributes of liquid volume, weight, and time. In addition, students work on estimating the number of units needed for a particular measurement. The majority of the work on measurement systems can be embedded within Science RT4 which focuses on changes and measures of matter. RT 7: Students continue to develop an understanding of an unknown quantity represented as a symbol such as a box or picture, and solving for that unknown in situations involving perimeter and area of two dimensional figures. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent equations in situations involving perimeter and area. RT 8: Students describe, analyze, compare and classify two dimensional shapes by their attributes to create definitions of shapes. They recognize area as an attribute of two-dimensional regions. 2014 – 15 3rd Grade Math Concept Map – Unit 3

July 25, 2014