Slide Rule We Put Men on the Moon with These Calculators!

Slide Rule We Put Men on the Moon with these Calculators!

Topics: Estimation, Multiplication, Historic These math tools of the past allowed mathematicians and scientists to calculate faster Math Tools, Logarithms and easier, without batteries! Students of today’s electronic calculator age can hone their estimation skills while using these simplified replicas. Materials List  2 Large craft sticks Assembly  2 Small craft sticks 1. Cut out and adhere the 2 log scales templates onto large craft sticks. The rules  1 Piece transparent (i.e. - long lines) should be as close to the edge of the craft sticks as possible. plastic 1 cm x 5 cm 2. Glue the “C” scale craft stick to the matte board. (½” x 2”) 3. Place the “D” scale craft stick on the matte board underneath the “C” scale, but  Permanent marker leave this scale unglued so that it can slide.  Hot or white glue 4. Create the sliding cursor assembly by placing a small craft stick above the “C”  Matte board 8 cm x scale and another below the “D” scale. Glue the transparent plastic strip to the 25 cm (3” x 10”) small craft sticks (as shown). Use a permanent marker to draw the cursor line.

This activity can be used to teach: Common Core Math C Scale – Standards: (Glued to matte board) Cursor  Multiplication and Assembly Division (Number and (Free to Slide) D Scale – Operations in Base (Free to Slide) Ten, Grade 4, 5 & 6; Grade 5, 5-7; Number System, Grade 6, 2 & The Content Behind the Activity 3; Grade 7, 2 & 3) The slide rule is a tool that uses logarithms (logs, for short) to solve multiplication,  Factors (Grade 6, division, and complex math problems. Slide rules do not perform addition and Number System, 4) subtraction, and they require the user to estimate the answer and place a decimal point  Problem Solving accordingly. John Napier, a 17th century Scottish mathematician, developed (Mathematical logarithms, the inverse of exponentiation (for example, alogaX = X; or, the number 10 Practices Grades 4-12) is assigned the log value of 1, and 100 becomes 2, and so on). Adding logarithms National Curriculum for equates to multiplying the base numbers. For example, multiplying 10 x 100 can be Social Studies: achieved by simply adding their log numbers (1 + 2); the log answer is 3, or the log of  Knowledge and 1000. In 1625, William Oughtred mounted log scales onto sliding rules, creating the understanding of the first true Slide Rule. This helped the user visualize the process. This tool assisted in a past (Theme 2, Time, wide range of mathematical applications, ranging from simple algebra problems to Continuity, & Kepler’s astronomical and NASA’s Apollo mission computations. The slide rule was Change) used in mathematics instruction well into the 20th century until the advent of  Influence of science electronic calculators and computers. & technology (Theme

8, Science, Technology, & Why show students how to use a slide rule now that we have electronic calculators? Society) Aside from the historical significance, using a slide rule requires an important skill: estimation. Rather than just writing down the number that appears on a screen, a slide rule user must be aware of what could be a reasonable answer. A slide rule can also be used to teach the concepts of scientific notation, significant digits, and… logarithms.

Designed and written by Coral Clark (RAFT) Copyright 2015, RAFT Multiplying with the Slide Rule 1. Multiplying with a slide rule is essentially measuring and adding 2 lengths on log scales. Begin by aligning the cursor assembly to the “C” Scale. Use significant digits. In the first example below, the “C” Scale is marked off at 124. In the second example, the “C” Scale is marked off at 24.3 2. Align “1” on the “D” Scale to the cursor. Leave the scales in this configuration. 3. Measure out the second multiplier onto the “D” Scale with the cursor. 4. Find the answer by reading the cursor’s location on the “C” Scale.

“C” Scale 124 = ~ 500

1 2 3 4 5 500 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8

1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8 “D” Scale 1 2 3 4 5 6 7 8 9 1

x 4

= ~ 780 “C” Scale 24.3 500 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8

1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8 “D” Scale 1 2 3 4 5 6 7 8 9 1

x 32 Taking it Further For more historical mathematical activities, see RAFT Idea Sheets Calculating Bones, Abacus Primer, and Abacus Variations.

Web Resources (Visit www.raft.net/raft-idea?isid=387 for more resources!)  For more information on slide rules, visit - http://www.sliderule.ca/intro.htm, http://www.hpmuseum.org/sliderul.htm, and http://www.ualr.edu/lasmoller/napier.html  Teacher designed math courses from the New Jersey Center for Teaching & Learning – https://njctl.org/courses/math

Slide Rule Templates 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8

1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8 1 2 3 4 5 6 7 8 9 1

1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8

1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8 1 2 3 4 5 6 7 8 9 1

1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8

1 2 3 4 5 6 7 8 9 2 4 6 8 2 4 6 8 1 2 3 4 5 6 7 8 9 1