Counting on Bridges
Lesson material adapted from Under Construction, Aims Education Foundation
by Cyndi Blankenship, Educator, MathScience Innovation Center
Developed with funding from the MathScience Innovation Center
Explore engineering bridges through the fable the Three Billy Goats Gruff. Students
Major
Understanding will work in pairs to engineer a bridge and test the strength of their bridge under
various weights. Students will compare objects based on relative size and weight.
After recording their observations, students will redesign their bridge and create an
illustration of their work.
Grade/Subject
Objectives
Grade K; Mathematics and Physical Science
Describe and compare an object by relative size and weight.
Investigate and record observations through pictorial charts.
Identify the position of an object in relation to other objects.
Orally count a concrete number of items.
Identify and describe a set as having more, fewer, or the same number
of members.
Use nonstandard measures to compare objects weight and height.
Time
Materials
Anticipatory Set: Three Billy Goats Gruff
Who is the biggest Billy goat?
Activity: Building Bridges
Activity: Testing Bridges
Practice
Closure: Bridges around the world
Assessments
For the Class:
The Three Billy Goats Gruff storybook
Three model Billy goats
Examples of Bridges
For the Instructor:
Enlarged version of Counting on
Bridges Graphing Worksheet
Dry erase marker
Folder – lesson, handouts, background
Counting on Bridges
10 min
10 min
15 min
15 min
Variable
10 min.
Variable
For Each Group of Students:
Set of 10 unifix cubes
Model bridge beam
4 building blocks
Model river
Model troll
Extra blocks for redesigning bridges
Counting on Bridges Observation Worksheet
Counting on Bridges Graphing Worksheet
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©MathScience Innovation Center, 2011
State and
National
Correlations
Virginia Standards of Learning: 2010 Science K (K.1, K.4); 2009 Math K (K.1, K.2,
K.10, K.12)
National Science Education Standards: Exhibit understanding of inquiry. Explore
properties and position of objects.
NCTM Standards: Demonstrate correct oral counting sequence. Utilize non-standard
units of measurement. Sequence items according to their quantity.
Instructional
Strategies
1. Anticipatory Set: Three Billy Goats Gruff
1.1. Read or act out the story the Three Billy Goats Gruff with the class. As you
read the story, reinforce the positional words: over, under, on. The goats are
on the bridge. What is living under the bridge? The goats are using the
bridge to cross over the river. Using objects in the classroom, reinforce the
concepts of over, under, and on with the students at the end of the story.
1.2. After the role play, show the students the picture of the bridge from the story.
Define the purpose of a bridge with the class. Introduce the term engineer to
the class. Explain that creating useful things, like bridges, and making them
safe is the job of an engineer. Ask the students if they have traveled over a
bridge. Do they remember what was under the bridge they traveled over?
2. Activity: Who is the Biggest Billy Goat?
2.1. Now have the students describe the three Billy goats from the story. Are all
of the Billy goats the same size? Do you think they all weigh the same?
Introduce the students to the term model. Using the model Billy goats, have
the children order them from least to greatest in size and weight. Ask the
students if it makes a difference to the bridge if something light or heavy
passes over it? Remind the students that the bridge moved and creaked when
the largest Billy goat passed over. Let the students know that an engineer
needs to make bridges safe for both heavy and light objects.
2.2. Explain to students that today we will be creating model bridges and testing
how many Billy goats can safely walk across it. We will create an “I” beam
bridge that flexes. Show the students the model beam and demonstrate how
it can flex. Ask the students to predict what will happen to the beam as more
weight is placed on it.
2.3. Show students the block sets that represent the Billy goats for the Building
Bridges Activity. Allow the students to explore the properties of the blocks
that represent the Billy goats. Have the students order the blocks from
lightest to heaviest. Review with the students which block represents each of
the three Billy goats.
3. Activity: Building Bridges
Counting on Bridges
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©MathScience Innovation Center, 2011
3.1. Have the children sit around the edge of the carpet to demonstrate how to
construct and test their bridge. Explain that we will use a unifix tower to
measure the distance the bridge must span. Have the students orally count
out ten cubes as you stack the cubes together to create a tower. Lay the unifix
cube tower on its side. At each end of the tower, place a block in an “I”
formation. Remove the unifix cube tower and lay the beam across both
blocks to form a bridge. Lay an additional block on top of each support block
for stability. Explain to the students that this “I” shape is used when
constructing beam bridges for extra support. Now place the model river
under the bridge along with the troll doll. As you place the river under the
bridge, remind students that the support blocks (abutments) should not be
moved in closer to the river. The bridge is ready to be tested.
3.2. Send students back to their seats and break them into pairs. Provide each pair
of students with four blocks, a flexible beam, ten unifix cubes, model river
and troll doll. Allow teams to construct their bridge.
4. Activity: Testing Bridges
4.1. Pass out the model Billy goat block sets to each group of students and remind
them that they will use these models to test the strength of their bridges.
Review with the class which block will represent each of the three Billy
goats.
4.2. Pass out the Counting on Bridges Observation Worksheet to students.
Explain how to use the worksheet to record their findings as they test each
Billy goat. Tell students that the bridge is safe if the goat can sit in the
middle of the bridge, and the beam does not touch the troll under the bridge.
It is important to remind students that it is alright for their model bridge to
fail the safety test.
4.3. After each Billy goat has been tested, provide students with additional
building blocks. Encourage students to redesign their bridge to make it
stronger. Challenge students to create a bridge that will hold all three Billy
goats at once. Remind students that the abutments cannot touch the river, and
that the bridge beam should not bend enough to touch the troll under the
bridge.
4.4. As students finalize their bridges, have them draw a picture of the redesigned
bridge on the Counting on Bridges Observation Worksheet.
Practice
Counting on Bridges
Design and Engineer: Draw a road map on paper that can cover a large area of the
classroom floor. Provide students with blocks or LEGO bricks and challenge them to
construct bridges that toy cars can travel on. Remind students that other cars or
people may need to pass under the bridges, so they should not put supports in the
middle of the bridge. Do not give too much instruction so students will learn through
testing their bridges and can make adjustments, if needed.
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©MathScience Innovation Center, 2011
Closure
Using the photographs of different bridges from around the world, review the purpose
for bridges. Explain that bridges are built to help us safely travel from one place to
another by carrying us over an object. Bridges also allow for travel underneath.
Remind students that building bridges requires engineers to consider the weight of
the objects that will use them. The heavier an object is the stronger the bridge must be
to support the weight.
Extensions
1. Activity: Testing Bridges Extension
Students will use the unifix cube tower to measure how the weight of the model
Billy goat affects their bridge.
1.1. After the students have constructed their bridge, instruct the students to stand
the unifix cube tower in the river next to the bridge. Explain to the students
that we will be measuring the amount of blocks we see under the bridge as
we test each Billy goat.
1.2. Pass out the Counting on Bridges Graphing Worksheet and measure the
height of the bridge before placing any Billy goats on it for testing. The class
will have the same measurement. Show the student how to record this
information on their worksheet using the enlarged teacher version of the
graphing worksheet.
1.3. Allow students to test each Billy goat as it crosses the bridge. Students
should record the height of the bridge on the worksheet for each Billy goat.
Students will record the height of the bridge by coloring in the number of
unifix cubes on the worksheet that they can see under the bridge. If students
are having difficulty determining over and under, you may have the students
remove the blocks they see above the bridge and count the remaining blocks.
Students should place each Billy goat in the middle of the bridge for testing.
Each Billy goat should be tested one at a time.
Assessment
Sample items are provided for use in checking students’ understanding. The following
table shows how the assessment items are related to specific objectives.
 Counting on Bridges Pencil and Paper Test
 Counting on Bridges Pencil and Paper Test Key
 Counting on Bridges Project
 Counting on Bridges Project Rubric
Objective
Describe and compare an object by relative size
and weight.
Identify the position of an object in relation to
other objects.
Counting on Bridges
http://MathinScience.info
Pencil and
Paper Test
Product/
Performance
1, 7, 9
3,4
©MathScience Innovation Center, 2011
Orally count a concrete number of items.
Identify and describe a set as having more,
fewer, or the same number of members.
5, 6
Use nonstandard measures to compare objects
weight and height.
7, 9
Investigate and record observations through
pictorial charts.
Students will engineer a bridge and test
the strength of their bridge under various
weights. Students will compare
objects based on relative size and weight. After
making their observations,
students will test their bridge and create an
illustration depicting their results.
Teaching Tips
2
8
Counting on
Bridges Project
Key Terms that should be defined with the class: engineer, weight, height,
over, under, on, beam, model, heavy, light, abutments, distance.
Some tips about the materials used in this lesson: The support and
stabilizing blocks used for this lesson are math manipulative base ten blocks.
Thousand blocks are used as the abutments and hundreds blocks are used as
the support blocks. Classroom blocks or books can be used as the abutments
for constructing the bridge.
Where do we get the supplies?
 Base ten blocks were purchased at http://www.etacuisenaire.com/
 Model Billy goats were purchased at https://toysthatteachonline.com
Resources
Bridges! Amazing Structures To Design, Build & Test, Carol A. Johmann
and Elizabeth J. Reich
Aims Education Foundation
A resource for teachers providing relevant material for elementary teachers in
the areas of math, science, and engineering.
Some activities for this lesson were adapted from Under Construction
Exploring Technology, Materials, Tools and Design.
www.aimsedu.org
Discover Engineering
Learn the latest in engineering and the difference it is making in our everyday
lives. Educators will find activities, games, and information that is appropriate
for use in the classroom
http://www.discoverengineering.org
Counting on Bridges
http://MathinScience.info
©MathScience Innovation Center, 2011
Design Squad
This PBS website uses videos and design challenges to explore the role of an
engineer and the engineer design process. Education tools and lesson plans are
provided.
http://pbskids.org/designsquad
MathScience Innovation Center
Information on educational programs available to students, teachers and school
divisions, and procedures for registering for programs.
http://msinnovation.info
MathScience Innovation Center: On-Line Educational Programs
Learn through on-line virtual classrooms, web-based lessons, and on-line
courses. Access proven lesson plans and instructional modules.
http://msinnovation.info
Counting on Bridges
http://MathinScience.info
©MathScience Innovation Center, 2011