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Putting Together Ten (Grades 2)
Master Teacher
Michael Ellis
Time Allotment
Two to three class periods
Overview
This lesson will provide students with a basis for making groups of ten. The lesson is mixed with concrete examples and algorithms; these activities lead the students to locate all the ways that ten can be made. Students use packages of objects and are led through discovery activities. Using concrete models (sets of objects where they have to determine what amount is needed to make a group of ten), students also make the connection between making tens and completing patterns. Before starting this lesson, students must have, at the very least, a notion of place value. Later this unit can be referenced as a study of subtraction with or without regrouping, and can be used in teaching fact families.
Subject Matter
Mathematics (Place Value, Missing Addends, Patterns)
Learning Objectives
Students will be able to:
- identify numbers whose sum is ten
- identify the missing addend in a mathematics sentence
- identify the pattern created as tens are made
- apply problem-solving strategies
- work cooperatively in groups and with partners
National Standards
Visit The National Council of Teachers of Mathematics Standards website.
Number and Operations
- Understand numbers, ways of representing
numbers, relationships among numbers, and number systems - Understand the meaning of operations and how they relate to each other
- Use computational tools and strategies and estimate appropriately
Patterns Functions and Algebra
- Understand various types of patterns and functional relationship
- Use symbolic forms to represent and analyze mathematical situations and structures
- Use mathematical models and analyze change in both real and abstract contexts
Process Standards
- Problem-Solving
- Reasoning and Proof
- Communication
- Connections
- Representation
South Carolina Standards
Visit the South Carolina Department of Education for the South Carolina Mathematics Standards.
Mathematics—Grade 2
I. Number and Numeration Systems
A. Establish a strong sense of numbers by exploring concepts such as counting, grouping, place value, and estimating.
6. The student will identify the place value of each digit in a four-digit numeral.
D. Relate the use and understanding of numeration systems to their world.
II. Numerical and Algebraic Concepts and Operations
A. Use concrete models to develop an understanding of the concepts of addition, subtraction, multiplication, and division of whole numbers.
B. Use models to allow students to construct their own algorithms for addition, subtraction, multiplication, and division of whole numbers.
C. Investigate, model, and compare different strategies for constructing basic arithmetic facts with whole numbers.
D. Model, explain, and develop reasonable proficiency in adding subtracting, and multiplying whole numbers and evaluating reasonableness of result.
3. The student will find the missing addends in an addition number sentence.
III. Patterns, Relationships, and Function
A. Recognize, describe, extend, and create a wide variety of patterns.
1. The student will identify, create, and extend a wide variety of patterns using symbols and objects.
C. Represent, discuss, and describe mathematical relationships and make generalizations based on observed patterns and relationships.
3. The student will use oral and/or writtencommunication to describe a general rule for the pattern.
Media Component
Video
Math Monsters, Lesson 6: The Making of Tens is an animated video where a group of monster operations signs are faced with providing gifts for friends. They struggle with the notion of how many ways the number 10 can be made.
Materials
- packages of items grouped in tens
- counters (two different colors)
- Math Journals (Students will use these to record Math Vocabulary and for the Cross-Curricular Extension which is a writing assignment.)
- chart of addition song
- Activity Sheets (for groups and individuals)
- packages with less than ten items
Prep for Teachers
- You should have exposed students to place value by now, so that they have an understanding of what tens are.
- Prior to this lesson, prepare several packages of different objects. These packages are put together for groups of three or four students. Each package should have ten items in it, but they should be in different combinations (e.g., a package of ten buttons—seven white and three black).
- Also prepare counters the same way for each pair of partners to use. Each partner should have enough counters in two different colors to complete a tens combination pattern. (Fast forward the video to the spot where all the monsters have filled all the boxes with gollywomples. Notice the pattern that has been created.)
- Also have available coins (dimes, nickels, and pennies). These can be used in an enrichment activity.
- Have available a dry erase board or a sheet that can be prepared in a way that it can be written on and then the answers wiped off for reuse.
- Chart the words to the song at the end of the video so that children can sing along. The lyrics are found on Activity Sheet 5.
Introductory Activity: Setting the Stage
Step 1
Introduce students to the vocabulary terms for this unit. Use the vocabulary worksheet provided. (See Activity Sheet 1.) Help students develop an understanding of the terms, which may be unfamiliar. Students should place these words in a mathematics journal (notebook). Tell students that they will see how these words will be used as this unit progresses.
Step 2
Ask discovery questions. Present the number 10 to students. Ask them how the number 10 is made. Accept all reasonable answers. A possible response might include "with a one and zero.
Step 3
Focus for Media Interaction: Before showing the first clip from Math Monsters, Lesson 6: The Making of Tens, ask students to watch for the different ways the monsters were able to make 10. START the tape from the beginning and STOP at the first break which is a large question mark (?) on the screen. See if the students have responses to the question: "Are there other ways to make 10?"
Step 4
Focus for Media Interaction: Ask students to see if the monsters have found all the ways to make 10. START the second clip where you left off in Step 3. STOP at the breaking point (the next large question mark) and allow students to brainstorm answers to the Monsters' question: "How can we make sure that we have all the ways of making 10?"
RESTART the tape where you left off and STOP again after the monsters have put seven green and three blue gollywomples in the box.
Focus for Media Interaction: Ask students if they can think of what will be in the next three boxes. START the tape again to see if predictions are correct.
START the tape again and STOP the tape one last time when the monsters think they are finished—but one asks, "Isn't something missing?" Focus for Media Interaction: Allow students to respond.
Step 5
Focus for Media Interaction: Ask students to see an example of how tens are used in real life. Have available the chart of the song as it plays at the end of the video. Rewind the tape and allow students to sing along.
Learning Activity 1: Discovering Ten
Step 1
Divide the class into groups of three or four.
Step 2
Give each group of students a bag containing ten items. Bags should have the number ten divided in different ways.
Step 3
Give students time to explore and think about the number of items they have.
Step 4
Ask students to report back to the whole group about what they found in their bags. (For example: "I have ten buttons. Three are white and seven are black.)
Step 5
After each group has reported, ask groups to work together one more time to see if they can write a mathematics sentence to illustrate what was in their bags. Write these where students can see them.
Learning Activity 2: Missing Addend
Step 1
Go back to the mathematical sentences that were recorded from the group activity. Take these numbers and prepare a chart where you have the problem showing with the answer, and then show a problem where one of the addends is missing. Have students try to guess what the correct answer is.
Step 2
Give students the missing addend practice sheet. (See Activity Sheet 2.) Allow students to work with partners to complete this sheet.
Step 3
When students have completed this activity, have them report their findings to the whole group.
Step 4
Ask students if they agree or disagree with the results. Why or why not?
Learning Activity 3: Patterns
Step 1
Give each pair of students counters of two different colors.
Step 2
Start the students off by placing a row of ten of the same color counters on the desk.
Step 3
Next, have students place nine of the same color counters in a row and one of the other color counters.
Step 4
Have students copy these rows on the pattern activity sheet (Activity Sheet 3) and write an algorithm on the line beside the row.
Step 5
Have students complete the pattern on their desks, and on the pattern activity sheet.
Enrichment Activity
Step 1
Give each student or pairs of students one dime, some nickels, and some pennies
Step 2
Have them make ten in as many different ways as possible.
Step 3
Talk with students about the activity in reference to the real-life experience that was at the end of the video. Review the end of the video, if necessary.
Culminating Activity/Assessment
Step 1
Provide each student with five bags with various numbers of objects less than ten.
Step 2
Provide students with an Activity Assessment Sheet. (See Activity Sheet 4.)
Step 3
On the Activity Assessment Sheet, have students log the number of items in the bag, and record how many more are needed to make ten. (This is continued for each of the five bags.)
Step 4
Have students fill in the missing addend.
Step 5
Observe and have students prove their findings using the objects they have been given.
Cross-Curricular Extensions
Language Connection: Lead students in the writing process with the topic "How Tens Are Used in the World." Have students do creative writing on this topic, using each of the steps in the writing process (first draft, revise, edit, proofread, and publish) in their work.
Community Connections
Plan a field experience to a neighborhood banking
institution. Have the bank personnel explain
to students how they use tens in their daily work.
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