Multiplication arrays

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SWBAT understand area models of multiplication for ones and tens.

Big Idea

Students model arrays and make connections to the associative property when multiplying ones and tens.

Number Hook - Magic Trick

4 minutes
This number trick uses the knowledge of prime numbers students learned yesterday.
Take any two consecutive numbers less than 41, calculate their product and add 41 to it. The result is a prime!!
For instance Take 7 & 8
7 X 8 + 41 = 97 

Warm Up

5 minutes

Students will start today's lesson with a fluency assessment.  This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.

This is an assessment I have my students do each week and then graph their results. 

It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions.  (It also happens to be the quietest time in my math classroom all week!!)

I do not start my students with the fourth grade skills. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards.  By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics.  I want to make clear that this assessment ONLY measures basic math computation.  It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year.  Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.

Concept development

40 minutes

I start this lesson with a vocabulary review and have students record notes in their math notebooks.  See photo.  I like this fold-able for notebook vocabulary because they are basically 3-D graphic organizers. Graphic organizers are great tools to help English Language Learners (and all students) categorize content in a way to make it more accessible to them .

The words students use for their fold-able are: factors, multiples, prime numbers, and composite. It is extremely important I continue to use these words throughout this unit in order for students to fully understand them and be able to use them.  In order for students to be proficient in 4.OA.4 and find factor pairs for whole numbers..., they need to fully understand that factors, multiples, prime numbers and composite numbers are. I find this a necessary step in their progression of mastering CCSS 4.OA.4.  Due to the amount of time in my lessons, students only complete the top two sections in the fold-able today, factors and multiples.  They will work to finish it each day this week. (see resources for how to make a fold-able)

Then I play this song for students as a review. 

Perimeter and area are words that students still get confused about. Since I will be using the word "area" a lot during this lesson and future lessons, I wanted to spend just a few minutes reviewing the term and it's relationship to multiplication.

I spend much of this lesson modeling arrays with students. I have found from previous experience, student need review about which rows and columns and naming array correctly. Students work in deepening their understanding of multiplication in this lesson and standard 4.NBT.5. Since the standard states that students will multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and properties of operations, this lesson allows students to use the Commutative Property and Associative Property with a visual model. Students draw arrays on centimeter grid paper, while I model the arrays on the smartboard.  Math practice standard 4 is a critical component of this lessons as students draw arrays to visually see the area of that array and make sense of what is happening numerically. We start by drawing a 2 x 3 array, then a 2 x 30 array, and then finally a 20 x 30 array.  I ask students to make connections between all three arrays by asking them about the number of zeros in the products compared with the number of zeros in the factors.

When I model the above arrays, I show students how to factor out the tens in the factors so students can see 2 x 30 = (2 x 1) x (3 x 10)  which equals (2 x 3) x (1 x 10) which equals 6 x 10 = 60.  See this example from the resources section - array 2.notebook

The resources in this lesson are notebook files which I use with my smartboard.  If you are unable to open the resources this is a photo that is similar to how I model the number properties. 

Some students find the process of rewriting 2 x 30 as (2 x 3) x (1 x 10) to be tedious and confusing or unnecessary.  This is, however, important to understand for solving more difficult products later.  Again, math practice standard 4 is at the heart of this understanding for students.  When students can see how the tens are factored out, the numerical equation begins to make sense. Understanding the Associative Property and Commutative Property is part of CCSS 4.NBT.5 when students use strategies based on place value and the properties of operations.  At my school, students spent time in third grade learning about the Commutative Property. The Associative Property is new to them this year. This one lesson alone, is not enough time for students to fully understand the Associate Property, rather it is just a start. I do not expect my students to be proficient in writing equations to factor out tens and ones at this point. I do expect them to be able to model, with their centimeter paper, factoring out the tens to compute the area of an array.

I end this lesson by writing 2 x 3 = 6, 2 x 30 = 60, 20 x 30 = 600 on the board and ask students what they notice.  Students use math practice 8 when they notice patterns about the zeros in the factors make the sum of the zeros in the product.  When students look for patterns, generalize results, monitor the solving process, check the reasonableness of answers, make discoveries, and devise new avenues to explore, they exhibit the habits of mind math practice standard 8 embodies. 




Student debrief - Wrap up

10 minutes

This is an exit strategy I call footprints. I ask students to write down some new knowledge they are walking out the door with today. They write this on a sticky note and then place it on a giant footprint outside our door.  See photo. Later I look at these to determine if there are misconceptions that need cleared up.