This unit introduces the important processes of doing mathematics that students will use all year: mathematical reasoning, using a variety of tools and models to explore mathematics, and communicating about mathematical ideas through drawing, writing, and talking. Students use interlocking cubes and play money to show 100 and $1 in many ways, estimate and determine how many hundreds there are in a box of cubes, and play games involving money and hundreds. Students complete and find patterns on a 300 chart, and work on related problem sets involving addition, subtraction, and money. Also, students make symmetrical patterns on a geoboard and use pattern blocks to make patterns with mirror and rotational symmetry and build designs from oral descriptions.
This unit focuses on the process and application of multiplication and division. To model multiplication, students skip count on the 100 chart, and they make arrays using cubes and graph paper to represent all multiplication combinations with factors 2 through 12. They solve multiplication and division word problems and discuss the relationship between the situations and the standard notation. Students solve related multiplication problems, some with two digits, and discuss and write about various strategies they use to solve them. Students work in cluster problems, sets of groups to generate a list of "hard" multiplication pairs to learn, and they solve and share strategies for solving two-digit multiplication problems.
Students explore the relationship between three-dimensional objects and their two-dimensional representations and also explore what objects look like from different perspectives. Students use interlocking cubes to construct cube buildings shown in drawings and describe how they mentally see the buildings. Students investigate the shapes of silhouettes projected by geometric solids, and they draw silhouettes of cube buildings as viewed from different perspectives. They write instructions that tell others how to put together simple cube buildings, and they evaluate the effectiveness of several different types of building instructions. Students create their own toys out of 50-60 interlocking cubes and write instruction booklets that will enable a younger child to build their toys.
Students explore the structure of our number system through activities involving landmarks--numbers that are familiar landing places, such as multiples of 10 or 25, that make for simple calculations, and to which other numbers can be related. Students work with 100 by skip counting on the 100 chart to find factors of 100, and by making one layer and multi-layer "boxes" using 100 cubes (for example, four layers of 5 by 5 squares). They find factors of multiples of 100 and use landmarks to solve addition and subtraction problems. Students make books of the numbers 1 to 1000, use the books to locate different numbers, and find factors of 1000. They do several choice time activities involving estimating and adding and subtracting numbers to 1000. The class makes a 10,000 chart for the wall and locates numbers on the chart.
In this unit, which uses an area model for fractions, students represent fractions, find equivalent fractions, and order fractions. Students divide the area on a geoboard into halves, fourths, and eighths and compare various-shaped fourths to show they are the same size. They divide dot paper rectangles into thirds, sixths, and twelfths and make designs by coloring in specified fractions of the area. Students make decks of fraction cards and play games with the cards to practice finding equivalent fractions and ordering fractions.
Students use some tools to define questions, and to record, represent, and analyze simple data sets about familiar situations. They collect data on questions, such as, "How many people in a family?" and "How tall are fourth graders?" Then they organize the data in rough draft and presentation graphs. They look at the shape of the data--the patterns and special features--identifying places where there are concentrations of data (clumps) or where there are no data (holes). Students describe what seems to be typical for a set of data and are introduced to the median. As a final project, students divide into small research teams and investigate a question about sleep. They represent the data they have collected in several ways and prepare a written report and/or make a class presentation of their findings.
Students add and subtract decimal numbers and numbers in the hundreds and thousands. Students solve problems related to everyday uses of money. For example, they recommend $100.00 worth of children's books for the school library. They investigate distances in miles and tenths of a mile and use a map of their city or town to plan a tour of the area. Students discuss strategies for combining and comparing larger numbers, and they plan a trip around the United States of no more than 10,000 miles.
Students explore the ways things change over time and look at ways to represent these changes. Students plant seeds and measure and record plant heights throughout the unit. Students find their own ways to show the changing population of their homes during a 24-hour period. They examine a variety of items from newspapers, magazines, and other sources that relate to changing situations. Students make charts and line graphs to show changing speed, changing heights of plants, and changing population. They interpret a variety of graphical shapes, describing in words how the graphs relate to the situations.
Students continue to build on their understanding of multiplication and division, extending concepts and skills studied earlier in the year in Arrays and Shares. Using Array Cards, students make multiplication tables and look for patterns in their tables. Students discuss strategies for estimating and solving double-digit multiplication problems. They use 300 charts, rectangular arrays, cubes, calculators, and games to find factors of large numbers and solve multi-step problems that represent both multiplication and division.
Students name and locate points on a coordinate grid with ordered pairs of numbers, both positive and negative. They make coordinate mystery pictures and measure distances on the grid using "taxicab paths." They play Sunken Ships, identifying points on the grid and using distance feedback in their strategy for selecting a next possible location. Students discuss properties of rectangles and write rectangle procedures for the computer using Geo-Logo. They place rectangles symmetrically on a computer bulletin board. They analyze a general Geo-Logo procedure for making rectangles and use the procedure to draw and create complex rectangle patterns.
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