How Many Pennies?

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Summary

Students will estimate the number of pennies it takes to fill outlines of various basic shapes.

Objectives

Student will identify different shapes.
Students will estimate based on a penny as being a standard unit.
Students will record and test their estimates.

Subject Area

Math

Grades

Class Time

Total Time: 0-45 Minutes minutes

Materials

Math Journals
20 to 30 pennies for each group of 3 or 4 students
Sheets of paper with large outlines of different shapes (circle, triangle, square, rectangle, etc) for each group

Lesson Steps

Have your students fold a page in their math journal or a sheet of paper into 3 columns, then label the columns “Shape,” “My estimate,” and “Actual number.”
Form groups of 3 or 4 students and give each group a set of supplies. Each group needs a set of pennies and one copy of the papers with the outlines of different shapes. There should be one paper for each student.
Have your students write in their math journals the name (or draw a picture) of their shape (in the first column) followed by their estimate of how many pennies they think it will take to fill up the shape (column 2). Students can look at the pennies and the shapes to help decide how many they think might fill each shape.
Each student should create an estimate for each shape, and then the students should compare their estimates. Each group can discuss how they arrived at their estimates, and if any of the estimates seem far off.
Have each student take one of the shape outlines and see how many pennies will fill each shape. Each student in the group can record the actual amount in their math journals.
Together the class can discuss the results. Students can share how they came up with their estimations.

Differentiated Learning Options

After each group has determined the number of coins that fill the first shape (decide on a common shape for each group to test), you may wish to review the estimates made earlier. Do any of the groups believe that their estimates were far off? Can they make a better estimate now that they have a stronger knowledge of the amount of space filled by a penny?

Assess

Students can be evaluated on the information they recorded in their math journals and their participation in the group discussion.

Common Core Standards

Discipline: Math Domain: 1.G Geometry Grade(s): Grade 1 Cluster: Reason with shapes and their attributes Standards:

1.G.1. Distinguish between defining attributes (eg, triangles are closed and three-sided) versus non-defining attributes (eg, color, orientation, overall size); build and draw shapes to possess defining attributes.
1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape.
1.G.3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters and use the phrases half of, fourth of and quarter of. Describe the whole as two of or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Discipline: Math Domain: K.CC Counting and Cardinality Grade(s): Grade 1 Cluster: Compare numbers Standards:

K.CC.6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, eg, by using matching and counting strategies.
K.CC.7. Compare two numbers between 1 and 10 presented as written numerals.

Discipline: Math Domain: K.CC Counting and Cardinality Grade(s): Grade 1 Cluster: Know number names and the count sequence Standards:

K.CC.1. Count to 100 by ones and by tens.
K.CC.2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Discipline: Math Domain: K.CC Counting and Cardinality Grade(s): Grade 1 Cluster: Count to tell the number of objects Standards:

K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality.
- When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
- Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
- Understand that each successive number name refers to a quantity that is one larger.
K.CC.5. Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

National Standards

Discipline: Mathematics Domain: K-2 Number and Operations Cluster: Compute fluently and make reasonable estimates. Grade(s): Grades K–2 Standards: In K through grade 2 all students should

develop and use strategies for whole-number computations, with a focus on addition and subtraction;
develop fluency with basic number combinations for addition and subtraction; and
use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Discipline: Mathematics Domain: K-2 Number and Operations Cluster: Understand meanings of operations and how they relate to one another. Grade(s): Grades K–2 Standards: In K through grade 2 all students should

understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;
understand the effects of adding and subtracting whole numbers; and
understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

Discipline: Mathematics Domain: K-2 Geometry Cluster: Use visualization, spatial reasoning, and geometric modeling to solve problems. Grade(s): Grades K–2 Standards: In K through grade 2 all students should

create mental images of geometric shapes using spatial memory and spatial visualization;
recognize and represent shapes from different perspectives;
relate ideas in geometry to ideas in number and measurement; and
recognize geometric shapes and structures in the environment and specify their location.

Discipline: Mathematics Domain: K-2 Measurement Cluster: Apply appropriate techniques, tools, and formulas to determine measurements. Grade(s): Grades K–2 Standards: In K through grade 2 all students should

measure with multiple copies of units of the same size, such as paper clips laid end to end;
use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick;
use tools to measure; and
develop common referents for measures to make comparisons and estimates.

Discipline: Mathematics Domain: K-2 Number and Operations Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Grade(s): Grades K–2 Standards: In K through grade 2 all students should

count with understanding and recognize "how many" in sets of objects;
use multiple models to develop initial understandings of place value and the base-ten number system;
develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;
develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;
connect number words and numerals to the quantities they represent, using various physical models and representations; and
understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.