**Question: **Why does 3rd grade start with a multiplication/division unit and not addition/subtraction?

**Answer: **We often hear from people who wonder why Grade 3 starts with a multiplication and division unit—just like it did in the 1st edition!—rather than an addition and subtraction unit. As we decided on the sequence of the units in any grade, we considered many different things. The most important was the development of mathematical content within and across grades.

In *Investigations 3*, multiplication and division is a major focus in Grade 3. We wanted 3rd graders to start the year with the important work of the grade and to begin developing a conceptual understanding of multiplication and division. Also, there are three units focused on multiplication and division; putting one first allowed us to spread them sensibly across the year. (The other units are Units 5 and 8.)

*Understanding Equal Groups* is a great way to start the year as it provides a level playing field. Ideas about multiplication and division are, for the most part, new for *all* students. The ideas are accessible to all, and most students get excited about starting the year digging into new mathematical ideas. In contrast, if the year starts with addition and subtraction, most students already have a history with these operations, and for some it has not been positive. Others may understand the concepts of addition and subtraction, but begin to struggle when they are asked to add and subtract larger numbers.

In fact, putting the 1st addition and subtraction unit 3rd in the sequence allowed us to include review of addition, subtraction, and place value ideas across Units 1 and 2, in the Ten-Minute Math Activity *Practicing Place Value* and through the Daily Practice Pages. Our intent was to provide teachers the opportunity to observe students doing this work, and enable them to identify those who might need additional support to be ready for Unit 3, which assumes students can fluently add and subtract within 100 and use representations to add and subtract within 1,000.

The question about why start the year with multiplication and division seems to suggest that third graders should work on addition and subtraction before multiplication and division. While 8- and 9-year olds are likely more familiar with addition and subtraction, there’s no reason it needs to come first.

*Understanding Equal Groups*** **focuses on the *meaning* of multiplication and division. The numbers are small, generally less than 100. Students use contexts and representations as they begin to develop strategies for solving multiplication and division problems. The focus is on coming to understand and visualize these operations through constructing equal groups or arrays. Later, students will build on this foundation as they develop efficient strategies. While *Travel Stories and Collections* is about understanding the operations of addition and subtraction, it’s much more about extending students’ understanding of those operations, especially subtraction, and beginning to refine addition and subtraction strategies. It’s a big difference.

By now, 3rd grade teachers have finished Unit 1. We’d be interested in hearing how it went!

*We are excited to have a space that offers us the opportunity to answer common questions from the field. Have questions you’d like to see answered? Email us.*

- Reflections on NCSM/NCTM, Part 2 - April 29, 2019
- Reflections on NCSM/NCTM, Part 1 - April 22, 2019
- A Grade 2 Q&A: The Size of the Numbers - November 28, 2018

I finished the first unit about two weeks ago, and this is my second year using teaching third grade and using these materials. I really liked the work of this unit and agree that starting this way has all of the students start on a level playing field. Last year I got really bogged down in this unit and as a result, didn’t have time to get to some other units. One thing that helped this year was knowing that I had to move on to be able to com back to Multiplication later in the year. I kept that idea of moving on in my head as I thought about whether we needed to spend more time with an activity or whether we had gotten out of it what we needed to for this time of the year, not necessarily not gotten everything out of it that it has to offer.

Something that I did when my students were having trouble visualizing things that come in groups was this: I noticed when I was grocery shopping many things that were in groups: juice boxes, toys, glue sticks, markers, etc. Because I have the technology in my classroom to easily show pictures from an Apple device, I took out my phone, took some photos, and projected them the next day. It only took 5 minutes but the photos showing things that come in groups helped them to think about more things that come in groups.

That’s great to hear, Karen-thanks! We’ve learned that the first time through a unit often does take longer, as you pointed out. Hopefully the math focus points, assessments, etc help guide teachers, but experience with the curriculum for an entire year makes a huge difference. That’s also a useful tip about pictures of groups, it seems a nice prompt to get students to started. I always enjoy seeing the lists 3rd graders come up with!

Hi, team Investigations,

I’m super excited to pilot Investigations 3 at my school. I especially love that third grade has three units in multiplication and division. I think that these experiences will help the children to develop deeper understanding in these vital operations. Why have the algebra units and probability lessons been taken out. I loved that K-2 kids explored algebra.

Hi Alicia, thanks for writing. We’re excited that you’ll be piloting Investigations too! We’ll put your question about algebra in K-2 on our list of Q&As, and will look forward to hearing about how things are going in your school – please keep us posted!

I loved starting the year with multiplication/division this yera…third graders know this is big, new work and they were really excited to jump right into it. The quizzes and assessments helped me quickly pull a subgroup for reteaching and extra help. So far, so good~! Was very happy that students performed really well on end of unit assessment. Best of all was student engagement in games and activities, as well as the student book….love the large font enough space for st to show their thinking when solving problems.

Thank you for sharing your experience starting the year with multiplication and division. We are glad to hear that your students were excited to start the year digging in to multiplication and division and that the assessments gave you some good opportunities to get a sense of where your students were in their understanding of these pretty new ideas. We would be curious to hear more about your students’ learning and thinking as they continue on their journey of working on multiplication and division throughout 3rd grade.