1. Solve two- and multi-step word problems involving addition, using a letter to represent the unknown (MP.4).
2. Assess the reasonableness of answers by choosing a place to round the given values to, rounding them, and using those to compute the solution (MP.1).

• Lesson 15 is the first lesson of the year where students will solve two- and multi-step word problems using a letter to represent the unknown. This begs the question: should students be able to represent a two- or multi-step problem with a single equation or are many equations acceptable? As Bill McCallum states, “it’s a good question and a good discussion, but the standards are largely silent on the answer… I don’t read the standard as requiring that every single word problem be accompanied by an equation, merely that students should have experience writing equations for word problems” (Parenthesis in equations that represent multi-step word problems, Mathematical Musings). As the Progressions state, “some problems might easily be represented with a single equation, and others will be more sensibly represented by more than one equation or a diagram and one or more equations” (OA Progression, p. 29). Thus, it is left to the teacher to decide what “easily” and “sensibly” means for your students, and when to make the transition to representing some two- and multi-step word problems with one step of representation/one equation, which you could do here or wait for subsequent lessons and units to do so. As some general guidance, it seems reasonable to expect every student to be able to write an equation for all one-step problems, two-step problems where the unknown is isolated on one side of the equal sign in the equation without needing to manipulate it, and some multi-step problems with the same parameters by the end of the year. For example, see #2 of Mathematics Common Core Sample Questions Grade 4, #5c of MCAS Spring 2016 Grade 4 Mathematics Test, and #11 of PARCC Math Spring 2017 Grade 4 Released Items.
• This lesson provides an opportunity to connect two domains in the grade, 4.OA and 4.NBT, since students will be solving multi-step word problems involving addition within 1,000,000 and assess the reasonableness of their answers using rounding, thus connecting standards 4.OA.3, 4.NBT.3, and 4.NBT.4.
• Let students work on each problem on the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram, then allow them to try again on their own. Encourage students to use a strategy of their choice to assess the reasonableness of their solution.

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In January, Scott earned $8,999. In February, he earned $2,387 more than in January. In March, Scott earned the same amount as in February. 

1. Choose a place value to round to, then use those rounded values to estimate the amount Scott earned altogether during those three months. 
2. Exactly how much did Scott earn in those three months?
3. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain. 

References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic D > Lesson 12 — Exit Ticket

Grade 4 Mathematics > Module 1 > Topic D > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..