Mathematical Thinking at Grade 5 (Introduction, Landmarks in the Number System)
Students extend their understanding of our base ten number system as they become familiar with important ways of thinking about and doing mathematics. They work with a variety of mathematical materials and methods as they explore factors and multiples of 100, 1,000, and 10,000, important landmarks in our number system. They use their knowledge of relationships among landmark numbers up to 10,000 to develop strategies for solving computation problems involving the four basic operations. This unit will help students become acclimated to a mathematics class in which the emphasis is on developing strategies, solving problems for which there is no one procedure, and constructing conjectures about mathematical ideas based on evidence that they gather themselves.
Picturing Polygons (2-D Geometry)
Students create polygons with shape pieces. They construct, apply, discuss, and evaluate mathematical definitions of these shapes. They analyze the properties of polygons so they can draw them on coordinate grids on and off the computer. They investigate various properties of triangles, quadrilaterals, and regular polygons, asking which remain constant and which change when making larger and smaller similar shapes. They write procedures for regular polygons using Geo-Logo turtle commands, measure lengths and angles of polygons off-computer, and look at patterns in sums of angles and of turns.
Name That Portion (Fractions, Percents, and Decimals)
Students use different models, including grids, arrays, number lines, and clocks, to find fraction, percent, and decimal equivalencies, to play games, and to solve word problems. They investigate and collect data about the participation of females and males, adults and children, in different activities and occupations. They interpret this data using fractions, percents, decimals, and circle graphs.
Between Never and Always (Probability)
Students develop a likelihood line on which they locate the probability of various events occurring, first using words such as "uncertain" and "impossible" as reference points on the line, and later the numbers 0, 1, and simple fractions. A major objective is that students learn to interpret a probability as saying something about how often a repeatable event will happen rather than as a predictor of whether or not it will happen on a particular occasion. This is accomplished by exploring a variety of spinners for which students compare what they expect to happen if they spin it, e.g., 50 times, with the different results obtained by students in the class. They investigate a number of games, such as rock-paper-scissors, determining whether or not they are "fair games," and if not, modifying them so that they are fair.
Building on Numbers You Know (Computation and Estimation Strategies)
This unit focuses on computation and estimation with multiplication, division, subtraction, and addition. Students learn to look at a problem such as 674 divided by 32 and use their knowledge of more familiar relationships, such as 10 x 32 = 320, as a starting point for finding the solution. Students also learn to use estimation to check the reasonableness of the results of their calculations. Throughout the unit, we encourage students to develop their own strategies, as we believe this can give them a deeper understanding of computation and estimation.
Measurement Benchmarks (Estimating and Measuring)
In this unit students learn about measures of time and about the Metric and US Standard measures of weight, volume, length, and distance. Students estimate measurements, and they take actual measurements with meter sticks, balance scales, liter measures, and other measuring tools. They also work with measurement information in a variety of ways: they compare estimates and measurements; they compare the sizes of measurement in different systems, they calculate with measurements; they analyze measurement data they have collected; and they investigate ways that people use measurement in their everyday lives. Throughout the unit, students find and use benchmarks. Benchmarks are familiar things that are about the same size as units of measure--two dollar bills placed end-to-end is about a foot, a fifth grader's little finger is about a centimeter wide, a can of kidney beans weighs about a pound.
Patterns of Change (Tables and Graphs)
Students make tile patterns (including square numbers, triangular numbers, multiples of two, and powers of two) and describe how they change, distinguishing among growth/shrinkage/oscillation as well as between steady and accelerated growth. Then students collect data about time and distances in trips along a straight line marked on the floor. Students distinguish between accumulated distance and distance between successive steps and learn to identify correspondences between number tables, graphs, and stories. In a final investigation, students use the TRIPS software environment which simulates a boy and a girl walking along two tracks. Off computer, they represent the steps of the boy and the girl along a Meter Stick. Students reflect on the trade off between step size and frequency of steps and investigate the relationship between graphs of position vs. time and graphs of step size vs. time.
Containers and Cubes (3-D Geometry: Volume)
By packing 3-D rectangular boxes with cubes, students develop strategies to determine how many cubes or packages fit inside boxes. They explore the concept of volume, inventing strategies for finding the volume of small paper boxes and their classroom. They investigate volume relationships between cylinders and cones, and pyramids and prisms, with the same base and height.
Kids, Cats, and Ads (Sampling and Comparing Data)
This unit provides students with additional tools to enhance their ability to work with data. Students have several opportunities to compare two data sets, using both "typical" values such as the median and calculating what fraction of each data set is above or below a particular value. Students also work with samples, beginning to experience how samples can be informative, yet not provide all the information a population would. The unit culminates with a student-designed survey of a sample of their school to explore data about playground injuries.
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