Class overview

In Math, Unit 1 focuses on the concepts of volume, multi-digit multiplication and division, and fluency with whole number multiplication. Learners begin to develop fluency for multiplication strategies by building on work done in 4th grade with the area model. They continue work building fluency with multiplication of whole numbers using the standard algorithm. These concepts lay the foundation for introducing learners to multiplication of decimals to hundredths. Similarly, learners extend the work done in 4th grade with the area model for division and divide whole numbers by using concrete models, drawings, and various strategies to divide. Learners build upon earlier work in grade 3 tiling rectangular figures to develop the concept of area. Now in grade 5, learners pack rectangular prisms with unit cubes to develop the concept of volume. They recognize volume as an attribute of solid figures, understand foundational concepts of volume measurement, and measure volumes by counting unit cubes of various standard and non-standard units. They relate volume to the operations of multiplication and addition and solve real world and mathematical problems by applying volume formulas V = l × w × h and V = B × h to rectangular prisms with whole number edge lengths. Learners recognize volume as additive and use the concept to determine volumes of composite solid figures composed of right rectangular prisms.

The focus of unit 2 is to understand place value to the thousandths place and apply that knowledge to various decimal concepts. This concept builds on students' grade 4 understanding of decimals to the hundredths place.  After examining the quantitative relationships that exist between the digits in place value positions of a multi-digit number (analyzing and explaining patterns in the number of zeros and the placement of the decimal point in the context of multiplying by powers of 10), learners read, write, and compare decimals to the thousandths place.  Learners use base-ten numerals, number names, and expanded form to represent multi-digit numbers with decimals. Later on in the unit, learners apply their previous understandings of adding and subtracting to add and subtract decimals to the hundredths place using models and reasoning about decimals.  Using knowledge gained through decimal operations, learners build upon many fraction concepts developed in earlier grades. They use fraction equivalence from grades 3 and 4 to add and subtract fractions with unlike denominators.  Learners solve word problems involving addition and subtraction of fractions, using benchmark fractions and number sense of fractions to estimate mentally and to assess the reasonableness of their answers.

Unit 3 focuses on fraction ideas and introduces a number of fractions concepts.  Learners first use what they know about multiplication and division of whole numbers while they work with multiplying and dividing with decimal numbers.   Learners then extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Building on their grade 3 work with area, they find the area of a rectangle with fractional side lengths by using concrete tools (tiling areas with unit squares) of the appropriate unit fraction side lengths.  They show that the area is the same as would be found by multiplying the side lengths and represent fraction products as rectangular areas. Learners continue to explore multiplication and division with fractions. They interpret multiplication as scaling and compare the size of the product to the size of the factors. They come to understand and explain that multiplying a given factor by a number greater than 1 leads to a product that is greater than the given factor. Learners solve real world problems involving multiplication of fractions and represent problems using visual fraction models and equations.  To conclude this unit, learners are introduced to a new interpretation of fraction. They interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). They solve word problems involving division of whole numbers that lead to answers in fraction form. Learners then extend these previous understandings of division to divide unit fractions by whole numbers and to divide whole numbers by unit fractions.

In Unit 4, learners use what they know about place value understanding from previous units and apply that knowledge to convert measurement units within a given system of measurement.  They use these conversions to solve word problems and create line plots involving fractional measurements.  After working with measurement and data, learners  extend their understanding of classifying geometric figures into categories to understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. They use this new understanding of categories and subcategories to classify two-dimensional figures in a hierarchy based on their properties.

This final unit in Grade 5 focuses on the additional and supporting concepts and skills to engage learners in analyzing the structure of numerical expressions.  Learners expand on what they learned in 4th grade about numerical expressions involving multiplicative and additive comparisons and apply that knowledge to evaluate and write numerical expressions with grouping symbols, write numerical expressions from a description, and interpret numerical expressions.  Learners move on to define a coordinate system and understand the relationship between coordinates and axes.  Learners define the first quadrant of the coordinate system and represent real world and mathematical problems by graphing points in that quadrant.   They also  form ordered pairs that they have generated using two given rules to generate two numerical patterns using two given rules.  They analyze and identify apparent relationships between corresponding terms.