Equal Amounts

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SWBAT identify and create equal amounts and equations for a single number. Students measure an object using 2 different units of measure.

Big Idea

Students are expected to grasp that measuring the same object with different units can yield a different number, but represent the same quantity.

Warm Up

10 minutes

Students have been working with partners of ten and doubles, as well as adding 10 to a number. Today I ask students to find a different number sentence to equal the one I put on the board. I ask them to write the sentence in their math journals.

In first grade they should have met the Common Core Standard, "Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false." Students may understand the equal sign in a single equation such as 8 + 5 = 13, but if I were to write 8 + 5 = 10 + 3, they might have more trouble understanding that there can be more than one thing on the other side of the equal sign. Today's lesson helps to expand the student's understanding of what the equal sign really means.

As students work, I circulate around and choose 2 - 3 students, with different equations, to show their work on the board, so we can see that there are numerous ways to compose a given number.

I start with 5 + 5 = 10. One of the reasons I select this is that the concept of making ten in different ways should be in place, so it makes a good starting point for this lesson. Starting in kindergarten, students should be developing fluency within ten, and in making ten. I call making ten "partners of ten". I hope students will quickly recall another partner of ten equation.

After we share out, I put the equation 13 + 7 = 20 on the board. Again I ask for students to write their own equations that make 20 on their individual white boards. 

I do a subtraction equation as well 18 - 9 = 9. (Here I watch to see if the students attempt another subtraction problem, or find an addition problem that will equal 9.)

I keep track of students who may be having difficulty with the concept of composing true number sentences for a given number. 

I give students a stretch break and ask them to come to the rug.

Teaching The Lesson

35 minutes

I tell the students that today we will be working at 2 different centers, as well as completing a practice page. 

I explain that at the first center we will be taking dominos and looking at the two sides. We will write an addition sentence by adding the bottom and the top of the domino and putting the number sentence under the correct total. We will also write a subtraction sentence by counting the total, subtracting one side and writing the equation under the answer that is left.

Together we practice on the interactive white board until students are comfortable with what they will be doing.

I tell them that at the second center they will be measuring the objects already set out on the table. They will use inches and centimeters. We discuss which side of the ruler is inches and which is centimeters. I choose all objects that are less than 12 inches, but are full inches in length to avoid half or quarter. I tell them to measure to the closest centimeter. We practice together on the interactive white board how to hold the ruler so the zero point is at the end of the object and then to read to the nearest inch or centimeter. We record our answers on the chart.

I tell students that they will also complete a practice page where they will write as many ways as they can think of to represent a given number, just as we did when we started the day. 

I divide the children in heterogeneous groupings and send them to one of the three centers. After about 10 minutes I ring the bell and have students progress to a new center. Students will visit all 3 centers.


10 minutes

At the end of the center time I ask all children to return to their seats. I ask them to respond in their journals to the questions, "Can 2 hundreds, 3 tens and 9 ones be the same as 239, or 200 + 30 + 9? Why?"

Some students respond in words, others use pictures, or representations with blocks or tally marks to explain their thinking. 

Can I measure an object and find it is 3 inches long, when my partner says it is  about 8 centimeters long? How is that possible?

Again, some responses will be in words, but others use drawings to explain their thinking.

I use student responses to assess their understanding of it being possible to have 2 different numbers or representations of a number represent the same amount.