Exploring Place Value – Number Architects and Demolition Crews!
- Students will explain place value through the tens place.
- Students will investigate how place value can be used to compose and decompose numbers.
- Students will understand that ten ones can be grouped together to make a ten.
- Students will work together to creatively problem solve.
COMMON CORE STANDARDS ADDRESSED: Work with numbers 11-19 to gain foundations for place value.
- K.NBT.1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
TIME REQUIRED FOR LESSON:
45 minutes to one hour
TIME REQUIRED FOR TEACHER PREPARATION:
Less than ten minutes
MATERIALS FOR LESSON:
- Set of at least nineteen unifix cubes for each student
- Teacher-created worksheets for recording unifix work; see step 5 of lesson overview
- Paper, pencil and crayons or markers
OVERVIEW OF LESSON:
- Tell students, “Today we are going to explore the relationship between ones and tens.” As a pre-assessment, ask the students what they know about how ones and tens relate to one another. Put a two-digit number on the board, for example, 26. Ask the students, “What does the number two mean in this number? What does the number six mean? Which is bigger?” Record their ideas on a piece of chart paper that can be posted in the classroom at the end of the lesson.
- Count with the students from one to twenty-six. Tell students, “We are going to clap our hands every time that we complete a full set of ten.” You will probably need to model this initially. Practice clapping out sets of tens for other two-digit numbers. Now tell the class that you are going to record a stroke on the board for each clap or group of ten. Ask the students, “How much was left over?” For example, in twenty-six, there would be six left. Tell the students, “For however many are left over, we will pat out that number on our legs.” Demonstrate with the six in twenty-six. Show them that you are going to record a star on the board for every pat or group of one. Explain to the students that you are now going to put your movements together, again demonstrating with twenty-six, clapping twice and patting six times on your legs. Practice this with other two digit numbers. As they clap and pat out the numbers, record with strokes and stars on the board. Highlight with students the significance of the strokes and stars and their relationship to tens and ones in a two-digit number.
- Ask the group to stand up. Tell the students, “Now, instead of claps and pats, we are going to create larger movements to signify the ones and tens. This time we will take one large jump in place for the tens and several tiny hops on one foot for the ones.” Allow them to practice this with various numbers that you write on the board.
- Tell students, “Today you are going to be number architects and demolition crews. You are going to build numbers and break them apart.” Have students sit at their desks and demonstrate with them how to compose and decompose numbers using unifix cubes. Show them how to connect ten ones to make a ten and that the individual cubes represent ones. Demonstrate with the number twenty-six how to create two towers of ten and six ones. Then draw a picture of your cubes on the board with the number 2 under the two tens and the number 6 under the six ones. To the left of the picture write the number 26. Ask the students, “How does my picture relate to the numbers I have written on the board?” Allow time for discussion.
- Give each child a set of unifix cubes and a worksheet. On the top four spaces of the worksheet will be written a two-digit number. The students should decompose the number with their cubes into tens and ones and then draw a picture of their cubes to the right of the number like you did on the board with the number of tens written under the tens and the number of ones written under the ones. On the bottom four spaces of the worksheet there will be drawings of cubes representing tens and ones. The students need to count the number of tens and number of ones and write the number in standard form to the right of the drawings. Walk around and monitor students as they work.
- Divide students into two groups. *If you do not have enough students in your class, you may need to do this exercise as one large group. Tell the students, “Now we are going to represent decomposed numbers, in their tens and ones format, with our bodies. Tell them that one person in their group will be the creator and the other students will be the tools. The students will take turns being the creator. The teacher will write numbers on the board and the creator will use the students in their group to make a number. For each ten, the creator will choose a student to sit on the floor crossed-legged and for each one, they will choose a student to stand with their arms crossed. For example, for twenty-six, the creator will arrange their group so that two students are sitting with their legs crossed and six students are standing with their arms crossed. Once the creator is finished with their number decomposition, they will present it to the other group to evaluate. The other group will give a thumbs up or thumbs down depending on the accuracy of the decomposition. Take turns practicing this so that every student has a chance to be the creator.
- Have students meet back as a group in the front of the room. Reread what you recorded on the board at the beginning of the lesson. For a post-assessment, ask students how their ideas have changed and what they have learned about the relationship between tens and ones. Record their new findings/ideas on the chart paper making sure to reinforce the core standards addressed in this lesson.