Balancing Equations and Counting Backwards

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Objective

SWBAT balance an equation for addition or subtraction and use counting on or counting back to find the answers.

Big Idea

The Common Core standards for second grade include being able to add and subtract with in 100. Students need practice with finding the solution even if it is not the answer that is missing.

Warm Up

10 minutes

To connect to prior knowledge I begin with putting the number sentence 200+ 40 + 6 on the board, leave a blank and put the number 246 on the other side. I ask students to choose an alligator mouth (inequality or equal sign < > =) to connect the two sides. 

The alligator mouth is a memory device that helps children connect the direction the sign is missing to its meaning. I remind students that the alligator always eats the greatest or biggest amount. I am deliberate in using both words - "kid friendly" biggest and math vocabulary greatest - so that students will learn mathematical vocabulary while being able to make sense of the symbols. So, they are constantly hearing the correct language as they are learning directionality of the sign. (I also remind students that if the 2 numbers are equal the alligator can't decide so he closes his mouth and gets 2 equal rows of teeth - the equal sign.)

I am careful to use the language greater than, less than or equal to when I read the problem. 

After students have recorded the number sentences in their math journals, we talk about which alligator mouth connected the two sides. We talk about the fact that even though the 2 sides don't look the same, they are equal.  This is an important point for students to remember. Equal means that the two quantities are the same amount (if I were to draw the two sides the pictures would be the same) even if/when the quantity is shown in a different way.

Example: 6+ 4 (if I draw the sum, I have 10 objects) is equal to 12 - 2 (if I draw the difference, I have 10 objects).

I ask if they remember finding equal parts last week? 

Today are looking for equal parts. We will look for equal math sentences and we will look for equal weights of things. 

I bring out the Balance Scale and ask students if they have ever used it. What does it do? I then show a spring scale and ask if they have ever seen one. What might it do?

I hang an object on the spring scale to demonstrate how the needle moves. Why is it moving? What do I now know about this object? I tell students that today we will be looking for things that balance and also for things that equal 1 pound.

I show some pennies and ask if anyone can guess how many pennies in a pound? I tell them they will have a chance to figure that out today. I ask if anyone knows what unit we use to measure things less than a pound. We talk about grams and ounces. I tell them that there are 16 ounces in a pound. 

I tell students that we will be working in small groups today to do some measurement, and to work with number sentences. I divide students into 3 groups, two for measuring and the third group will work independently on a practice page. 

Teaching the Lesson

45 minutes

The students work in 3 centers. This way I can adapt activities to differentiate for my students.

Center 1: Students work with an adult. They first use the pan balance to discover ways to make the pan balance even using small objects. They have a recorder make a word sentence, such as the pencils equal the staples, or the pencils are lighter than the staples. 

This is a concrete way to demonstrate "equal to". The station requires adult support, because students might otherwise just pile up objects. This activity is intended to develop understanding of what equal really means, but it is also important because I use of concept of a balance many times later in the year to scaffold other mathematical concepts.

Center 2: With an adult, each student works to solve a number sentence using blocks to find the missing addend. The students will see 6 + ___ = 5 + 7. The students walk through the process of taking 5 + 7 cubes and making a tower and counting it, and then taking 6 and setting it next to the tower of 12 and counting up or back to figure out how many blocks will make the sentence true. For students who grasp this concept, larger numbers will be used. These students will manipulate the base ten blocks to work with sets of double digit numbers. Again, the concrete examples help to solidify the understanding that there are numerous ways to get to the same amount. While students understand this with single numbers, seeing two equations compared is new and needs concrete reinforcement. 

Center 3:  Students complete equal number sentences using drawings or other models to solve the problems presented on the practice sheet.

Closing

5 minutes

Students have seen the idea of equal modeled with weights and number sentences and they have had a chance to practice this concept.

Now they are asked to create two equal number sentences in their math journals. These number sentences will be used to informally assess student understanding.