Mental Math and Multiplication with Tens

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Students will be able to observe patterns of multiplication with ones, and tens to solve multiplication problems mentally.

Big Idea

Students will find numeric patterns in multiplication with ones and tens and solve multiplication problems mentally by factoring tens.

Warm Up

5 minutes

Students begin with their math journals and a journal prompt. The journal prompt: Tom adds two three digit numbers and gets a correct answer of 829.  What might the two numbers be: Show 5 possible solutions.

I chose this journal prompt today to review the relationship between addition and subtraction.  From taking the practice Smarter Balanced Assessment (the test my state will take 2015) I know how prevalent these types of questions are.  Students need to be able to make connection between reciprocal operations and solve problems by working backwards. This journal prompt is one way for students to be able to practice this.

Click mental math warm up mental math lesson to see student sample 1 with my teacher observations and ideas about this students math progression and understanding.  Then watch mental math warm up only adding, to see another students work who is not as far along in her math progression and inverse operation understanding. 

Concept development

40 minutes

I start this lesson by having students add two more sections to their fold-able they started in the previous lesson.  Students will add prime numbers and composite numbers to their notes with definitions of those. I guide student to write a correct definition.

Students work at building their understanding of multiplying by tens, standard 4.NBT.5 using strategies based on place value and properties of operations in this lesson. I  begin by reviewing the concept from the day before by showing this mental math table.  I ask students what numbers are missing and to explain how they know. I review important vocabulary like factors and products.  Then students make two tables in their math notebooks similar to this one.  The numbers I use are: 6 x 3, 6 x 30, 60 x 30, and 5 x 8, 5 x 80, and 50 x 80.  Students fill in the sections like the first table.  In the past, this table has confused students that still needed the visual area model.  I instruct my students to use centimeter grid paper to draw area models if needed. About five of my students needed to use grid paper to complete the tables.

Math Practice Standard 7 is also at the heart of this lesson.  Students find patterns and repeated reasoning that can help solve more complex multiplication problems in the future.  They work to recognize the Associative Property and Commutative property of multiplication.  After students complete the above table, I ask them, like yesterday, about patterns they see with the zeros in the factors and the relationship to the zeros in the product, reminding them that math practice 7 is about looking at structures and patterns in problems and that doing so can help us with more complex ones.  Once students can verbalize that the number of zeros in the product is the sum of the zeros in the factors, I explicitly state this several times and point it out on the chart.

For the remainder of the lesson, I have students work on group or partner work I assign. Based on my observations from yesterday lesson and today's lesson, I differentiate students assignments. Students that seem to be grasping this concept of multiplying by tens and the Associative Property will solve a cross-number puzzle with a partner and create their own if time permits.  Students that finished creating their own puzzle, exchanged their puzzle with their learning partner to solve. 

For students who need more support and scaffolds, they work with me in a small group drawing area models and writing numerically what is happening when they multiply by tens. Click here to see how I help students rewrite 60 x 5.  I re-emphasize vocabulary, have students label the sides of the arrays, and have students practice explaining one anther's work in their own words. Explaining one another's  reasoning helps students deepen their own understanding of a concept. It also help students practice important speaking and listening skills as stated in the Common Core State Standards for English Language Arts. 

I went over the correct answers to to the number puzzle. As the students discussed strategies for figuring out the products, one student explained how he arrived at 90,000 as a product for 450 x 200.  I wrote down on the board what his thinking. You can see and hear about that by clicking here.

Students work with finding double digit by one digit products in the next lesson, using the area model, so it is imperative they are comfortable with this model and know how to find products of ones and tens.

Student debrief - Wrap up

15 minutes

This exit ticket is a check to see if students are understanding the Associative Property of multiplication. 

Exit ticket - Choose a two digit number ending in zero and multiply it by a one digit number of your choice.  Show your work by factoring the tens.

Most of my students completed this exit ticket with ease and proficiency.  I have four students who are struggling with this. These students also struggle with their basic multiplication fact recall, so I was not surprised that seeing the pattern of multiplying by multiples of ten was drowned in their thinking.  These students end up using large amounts of time to find the product of 6 x 7, thus making 6 x 70 seem very arduous.  These students are receiving one one tutor support with a high school volunteer tutor two days a week, during school hours.  They are also pulled each day for 10 minutes before lunch to work on a program called xtramath.  Click here if you want more information about this free computer based math facts program.  I remain optimistic that with extra practice and time, the students who are struggling with math facts will continue to make progress in math fact fluency.