It's important to explain to students that they use language every day that expresses calculations with numbers. For example, when students ask someone for "three more chips," they are expressing the operation "add 3". For today's warm up, I encourage dialogue about expressing calculations in words.
To start, I review a word problem that focuses on comparing with an unknown factor, a foundational skills learned in fourth grade.
Tracie waits 21 minutes for mom to pick her up from school. Tracie's waiting time is 3 times as long as Gwen's waiting time. How long does Gwen wait for the bus?
To find how long Tracie waits for the bus, I first model the problem. Then we write and solve an equation together. We use "g" to represent the unknown quantity, Gwen's waiting time.
21= 3 times as long as Gwen's waiting time.
21= 3 x g
We then write and solve a related division equation to find "g", the unknown factor.
21 divided by 3 = g
21 divided by 3= g
Gwen's waits 7 minutes for the bus.
I want to make sure that my students understand the concept of inverse relationships. My students and I quickly reviewed this because they caught on quickly and remembered this.
This lesson focuses on the use of grouping symbols in expressions. I point out to my students examples of the key words and phrases that indicate that parentheses should be used, such as "the result" and "twice the sum". I also make sure that my students know that there's more than one way to write a numerical expression.
You can support your ELL's by explaining that triple means three times, and double means 2 times. You can further model this if needed giving out counters to students and comparing numbers between students. You can use sentence frames as well.
I have each student divide their paper into quarters and label each box. One expression is written in each box. The students work with their table partner to attempt to solve these expressions.
We then walk through writing numerical expressions for the following:
a) twice the sum of five and seven
b) three times the result of subtracting four from nine
c) two less then the result of dividing fifteen by three
d) one more then five groups of two-fifths
As I rotate and facilitate, I remind my students that when necessary, they should use parentheses to group the operation that need to be performed first. (Parentheses are not needed in the last two expressions because multiplication and division are done before addition and subtraction.) I then use cold calling to call upon students to model using the document camera how to solve these expressions.
Using MP3, students construct viable arguments and critique the reasoning of others in the next few problems. In the first problem, students evaluate a claim involving numerical expressions and share their reasoning with their table partner. In the second problem, students explain why two verbal expressions represent the same numerical calculations. This is also building up their endurance to solve longer, more complicated math problems.
1) Lilly said that "three divided by twenty-one" is the same as "twenty-one divided by three". Is Lilly right? Explain why or why not.
(Students sometimes confuse the divisor and the dividend when interpreting statements involving division. I remind my students that the divisor (the number we are dividing by) is stated second when saying divided by, and first when saying divided into.)
2) Is "seven and one seventh less than the product of two times five" the same as "two multiplied by five and then decreased by seven and one seventh"? Explain why or why not?
(If students have trouble with #2, be sure that students break up the problem into 3 steps. 1) Write the word phrases as numerical expressions. 2) Look for equivalent expressions or equivalent parts of the expressions, 3) Compare the expressions.)
Using cold calling, I call upon random students to discuss how they came upon their answers in the independent practice. I also have students write as an exit ticket to the following:
What is another way to write "one more than five groups of two-fifths" in words? (Students will be eager to solve this, rather than re-write it in another way.)