In this unit, students use buttons to explore logical and numerical relationships. The unit begins with two lessons that focus on the two basic logical thinking skills, classification and serration, which are the foundation for understanding numbers and number relationships. These abilities in turn form the basis for understanding addition and subtraction. In the next six lessons, students explore the relationships between numbers and model addition and subtraction sentences with buttons.
In this unit, students explore the operations of addition and all three meanings of subtraction (take away, comparative, and missing addend). A set model is used for both operations.
http://illuminations.nctm.org/LessonDetail.aspx?ID=U31
Individual Lessons
In this lesson, students describe order by using vocabulary such as before, after, and between. They also review and use both cardinal and ordinal numbers.
Students classify buttons and make disjoint and overlapping Venn diagrams. In an extension, they make and record linear patterns.
In this lesson, students review classification, make sets of a given number, explore relationships between numbers, and find numbers that are one more and one less than a given number. They apply their knowledge of classification as they play a game similar to bingo.
Students use buttons to create, model, and record addition sentences. They also explore commutative in addition contexts.
Students work with subtraction at the intuitive level as they explore number families and ways to decompose numbers to 10. They will also identify members of 'fact families.' [A fact family is a set of three (or two) numbers that can be related by addition and subtraction, for example: 7 = 4 + 3, 7 = 3 + 4, 7 - 4 = 3, and 7 - - 3 = 4. When the number is a double, there are only two members of the fact family. An example would be 10 - 5 = 5, and 5 + 5 = 10.]
In this lesson and the following one, students investigate subtraction more directly, beginning with the easier “take away” mode. They model “take away” subtraction with buttons and write subtraction sentences. They also work with the additive identity (0) as an addend and as a difference and find missing addends.
Students explore subtraction in the comparative mode by answering questions of “How many more?” and “How many less?” as they match sets of buttons. They also make and discuss bar graphs based on the number of buttons they are wearing.
More and More Buttons
| Students use buttons to create, model, and record addition sentences. They also explore commutative in addition contexts. |
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| Learning Objectives |
| | Students will:
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| Materials |
| | Buttons
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Instructional Plan
To review rational counting and to prepare for the exploration of addition, distribute a bag of buttons and one number cube to each student. Ask the students to roll their number cube and then make a set with as many buttons as the number of spots showing on the number cube. Ask for volunteers to say the number in their set of buttons and then write it. Now tell the students to make a set of one more and one less button than the set they first made.
Group the students into pairs and give each pair two number cubes, a bag of buttons, and a strip of paper. Ask them to fold the strip in half, and then color one side of the paper red and the other side blue.
Display a class chart that is labeled “Number of Buttons on the Red Side,” “Number of Buttons on the Blue Side,” and “Number of Buttons in All.” Now ask the students to each roll a number cube and make a set containing the same number of buttons as there are spots showing on the number cube, with one student placing his or her set of buttons on the red side of the chart and the other student placing his or her set on the blue side. Then ask them to determine how many buttons they have when they join the two sets together.
To make the joining action more obvious, assign one student in each pair to place his or her hands around the two sets and say “whoosh” while bringing both sets of buttons together. On scrap paper, the other student writes in red the number of buttons on the red side, in blue the number of buttons on the blue side, and in purple the number of buttons in all. Then have the students switch roles. Repeat several times.
When they have identified several sums, help each group to enter two or three of their findings on a class chart. After the students have made their entries, ask them to give examples of the terms “addend” and “sum.” Call on a volunteer to read one row of the chart. Then call on other volunteers to read other rows. Next demonstrate how to write the entries on the chart as addition sentences. Encourage the students to record a few of their “whooshes” as addition sentences.
3 + 4 = 7
Now ask the students to put three buttons on the red side of their paper and four buttons on the blue side. Ask them to whoosh them together and record the addition sentence that tells what they did, using red and blue numerals for the addends and purple for the sum. Next, ask them to put four buttons on the red side and three buttons on the blue side and to predict how large the set will be when they whoosh the two sides together. Ask them to use red, blue, and purple numerals to write the addition sentences.
3 + 4 = 7 4 + 3 = 7
Repeat with other number pairs until the students are comfortable with the idea that order does not matter when they are joining two sets and recording the results
Ask the students to choose one of the rows from the chart and draw a picture illustrating that number fact, writing under it the addition sentence that the picture illustrates. Then distribute a copy of the Sums to 10 chart to each student and ask the students to find the addends they just used, putting one finger on each addend. Demonstrate how they can bring their fingers together on the sum. [Note that the addends and sum are color coded to match the chart they worked with earlier.] Now ask them to find the same addends in the other color and see if they get the same sum. Now have several children use their drawings and the Sums to 10 chart to explain the commutativity property in their own words. You may wish to display the drawings in the classroom or in a more public place before adding the records to their portfolio.
Questions for Students
How can you show you are joining two sets?
| How can you show you are joining two sets? How many buttons are on the red side of this sheet? On the blue side? How many in all? Which sum on the classroom chart was listed first? What addends were used to get it? Which sum on the Sums to 10 chart was the greatest? Which pairs of addends were used to get it? Which pairs of addends on the Sums to 10 chart were used to get 8? 5? Look at this row. Does any other row have the same sum? Are the addends the same? Would you get the same sum if you had two buttons on the blue side and five on the red side as you would if five were on the blue side and two were on the red side? Can you show why?
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- At this stage of the unit, it is important for students to know how to:
- model addition using the set model
- identify sums and addends
- record addition sentences
- recognize and use the order principle
- identify addends and sums on an addition chart
Teacher Reflection
- Were all students able to model the addition of sets?
- Could they record the addition in a number sentence?
- Could they find addends and sums on an addition chart?
- Did they use the terms “addend” and ‘sum” correctly?
- Are all students able to explain in their own words the commutative property of addition?
- Did some students exhibit special strengths? Did some students exhibit reluctance to participate? Why?
- Which students met all the objectives of this lesson? What extension activities are appropriate for these students?
- Which students did not meet the objectives of this lesson? What misconceptions did they demonstrate?
NCTM Standards and Expectations
- 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.
- Understand the effects of adding and subtracting whole numbers.
- Count with understanding and recognize "how many" in sets of objects.
- Connect number words and numerals to the quantities they represent, using various physical models and representations.
- Use multiple models to develop initial understandings of place value and the base-ten number system.
References
The idea of “whooshing” was shared by Janet Sharp of the University of Iowa during a summer institute in El Paso, Texas
Please include the entire activity and answer the following questions: * What introductory information is necessary for children to have prior to starting this activity? Students need to have a basic understanding of math concepts, addition facts, and have a basic number sense. * What grade level/s is appropriate for this activity? Please use appropriate justification for your answers here. This activity is suitable for PreK – Grade 2. You can make this activity as easy as you want it or as hard as you want to. This activity would be easy to make adjustments for the group of students that you are working with. * How will you engage students with different learning styles? This activity will touch on all different learning styles. There will be hands on learning, so they can touch and see the buttons and the die. For the students that are not at the same level as the other students, they can have a hand out with easier problems. For an ELL student, the teacher can pair them up with a friend that can speak English or have a Para with assist student. This activity would also allow for group work for the students to learn from each other. * How does this activity connect to the real world for students? Be specific. The students are able to work with the numbers in a couple of different ways, they see the number on the die, and they work with that many buttons. The activity is giving them opportunities to “see” numbers in different ways. This will reinforce the skills more. The students are able to relate this activity to the real world; they will have a chance to create word problems that have meaning to them. * Why is this activity with its concepts important for student learning? Be specific. When students are able to read a math statement and then be able to see the example(s) i.e the die and the buttons, they are able to directly relate the information. They are able to put it all together in one big picture. This activity is allowing students to work in with many different forms of number sense, to see the dots on the die, to see the numbers of buttons, to see the words written out on the paper, to verbally express their number sense out loud. * What are your comments on this activity? I found this activity and think it would be great to use in the classroom. A teacher can go many different directions with this lesson. They can start very basic and get harder as they go. They can incorporate so many different word problems into this lesson; it shows the students visually Would you use it in your classroom? Yes, I would. I think the more hands on activities a teacher can have for students the better. They are going to retain the information so much longer, and they will be able to recall the information longer. I did not have a chance to do this with any students. I would have done it with my preschoolers, but it is just a little over there head.
| 2 | Number & Operation | Compare and represent whole numbers up to 1000 with an emphasis on place value and equality. | 2.1.1.1 | Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. |
| 2.1.1.2 | Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. For example: Writing 853 is a shorter way of writing 8 hundreds + 5 tens + 3 ones. | |||
| 2.1.1.3 | Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. For example: Find the number that is 10 less than 382 and the number that is 100 more than 382. | |||
| 2.1.1.4 | Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100. For example: If there are 17 students in the class and granola bars come 10 to a box, you need to buy 20 bars (2 boxes) in order to have enough bars for everyone. | |||
| 2.1.1.5 | Compare and order whole numbers up to 1000. | |||
| Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems. | 2.1.2.1 | Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. For example: Use the associative property to make tens when adding 5 + 8 = (3 + 2) + 8 = 3 + (2 + 8) = 3 + 10 = 13. | ||
| 2.1.2.2 | Demonstrate fluency with basic addition facts and related subtraction facts. |
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