Pre-K-2, 3-5
A key goal for instruction on algebra at the elementary level is to analyze change, and to understand how change in one variable can relate to change in a second variable. The goal of this lesson is for students to explore how changes in students’ ages relate to changes in their heights.
Pre-K-2, 3-5
Students often view linear measurement as a procedure in which a number is simply read off a ruler. The goal of this lesson is to have students gain experience in linear measurement by using a variety of measuring instruments to measure the heights of classmates, to discover the error inherent in measurement, and to search for patterns in data that are represented on a table. In this lesson, students compare results of measuring the same height using different methods, and discuss measurement error. They measure the heights of classmates and the heights of older students in their school, and construct a table of height and age data. The lesson is also designed to serve as a springboard for a second lesson in which students relate measurement to algebra and data analysis concepts.
9-12
Students are presented with a problem: two bowls are suspended from the ceiling by springs. One bowl is lower than the other. In one bowl, you can only place marbles; in the other bowl, you can only place bingo chips. How many items must be placed in each bowl so that the heights of the bowls are the same?
9-12
Students learn about the repeated subtraction and repeated division methods for converting a decimal number
N to a numeral in base
b, provided
b
is an integer other than ‑1, 0, or 1. Students also learn about the
Fibonacci representation, which is a method for representing a numeral
as a sum of Fibonacci numbers. The Fibonacci representation will be
useful in later lessons in this unit when exploring Nim games.
9-12
Students discover the algorithm for solving linear programming problems and gain conceptual understanding by solving a real-world problem and using graphing calculator applications.
9-12
Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
9-12
This lesson allows students to apply their knowledge of linear equations and graphs in an authentic situation. Students plot data points corresponding to the cost of DVD rentals and interpret the results.
6-8
Using a balance in the classroom is a first step to algebraic understanding. Use this pan balance (numbers) applet to practice the order of operations in simplifying numerical expressions and to demonstrate the conventions of using algebraic logic in simplifying expressions.
6-8
Students use the Balance Pans Applet- Expressions Tool to explore algebraic expressions. They determine if algebraic expressions are equal. They balance pans to solve a system of equations and use graphing to find the solutions to a system of equations.
6-8
Using spreadsheets, students will explore another pattern, that of the triangular numbers. This exploration will enhance students’ ability to generalize a pattern with variables.
