Alternate strategies


This week in math methods class my Pre-service Teachers (PST) were introduced to alternative strategies for multiplication and division. According to Common Core State Standard/ College and Career Readiness Standards(CCSS/CCRS), students learn the standard US algorithm for multi digit multiplication in fifth grade.
   Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NBT5]     
  Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5-NBT6]
 
This mean teachers use inventive strategies and strategies involving place value understanding for multidigit multiplication.
 
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 the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4-NBT5]

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4-NBT6]
 
We discuss area model for multiplication and division with repeated subtraction.
One group presented multiplication using the area model. They were given the problem
47 x 36 using the open area model.
 
                                              47 x 36
                 40 x 30
 
                  1200
30x7
 
 
210
                        40 x6
            240
7x6
42
 









The one group explain this concept thoroughly and the importance of choosing this method. I asked them to notice the size of the partitioned rectangles. the size of the rectangle is related to the size of the number quantity. Therefore, students can see multiplication in terms of finding the area of rectangles.

Another group presenting on multiplication use partial product for 84 x6.

From their analysis, PST saw the connection between  partial product and standard algorithm. They determined that teaching students the standard algorithm first lends to errors in computation. The common error is not regrouping the 2 tens when multiplying 8 tens by 6. Using the problem 357 x 8, PST determined that they can start with any one of the place values digits to multiply and at the end you will get the same product. With this discovery, PST realized the importance of learning place value in the lower grades and building upon this foundation in fourth and fifth grades. The revelation with division with repeated subtraction was the same. Their enthusiasm for teaching math using  alternative strategies  has changed from the beginning of the semester. My students went from comments such as "CCSS is just dumbing down the curriculum" to "This makes more sense. I wish I learned it this way". For the next two  weeks. I will have to teach fraction using alternative strategies. I can't wait!      
                     
        
 
 
  
 

Comments

Post a Comment

Popular posts from this blog

Let’s Talk about Numbers! Embedding Number Talks into Pre-service Teachers Mathematics Methods Course As a classroom teacher, I saw the essential benefits of including mathematical discourse in my mathematics classroom. My elementary students were engaged with solving problems and having discussions about their approaches. As a faculty member, allowing my preservice teachers to have conversations about numbers is even more essential. Preservice teachers come with diverse experience and preconceived feelings about mathematics. They bring their feelings into college and into their teaching practices. These feelings include the following: ·          I can’t stand math! I don’t want to teach it. ·          I love math. It was my favorite subject in school! ·          There is only one way to do math!   My goal is to help develop mathematical thinkers, and, in turn, give them the necessary pedagogy to build mathematically thinkers. Hopefully, my preservice teache
Read more

My Answer is Five!

Several times a week I offer study sessions to my pre-service teachers for Praxis Multiple Subject Mathematics, one of five tests elementary teacher candidates have to pass to teach.   My preservice teacher came across the following practice problem from Math Made Easy:   Jan ran 30 blocks in 6 minutes. Assuming that she ran at a constant speed, how long did it take Jan to run one block? My student commenced to solving the problem. She said so I divide 30 by 6 to find out how much time it will take to run 1 block and the answer is 5. After reading the problem again. I ask her to notice the problem. Remember if the speed is constant, should it take her 5 minutes to run 1 block?   She thought about and decided it did not make sense. I am writing this in support of one of the Standards for Mathematical Practices from the Common Core State Standards . Reason abstractly and quantitatively.   Students proficient in mathematics make sense of the relationship of quantities in p
Read more

Number Talks with Fraction

Image
This post is based on the last class session for this semester. We went out with a bang. We tackled NT with fractions. We actually started our talk about fractions the previous class session. Today was more of a review for the final. After much practice order fractions without determining alike denominators and operations with fractions using models, my PST (Pre-service Teachers) engaged in a NT involving fractions. The following is a conversation with adding fractions:   1/4 +1/2 Teacher: How did you get 3/4/ ? PST 1: I know that 1/2   is equal to 1/4 + 1/4which is 2/4.  So I used 1 /4  + 1/4 + 1/4. Therefore   it equals to 3/4.   PST 2: I just found that common denominator which is fourths. Since the first fraction already has fourth, I don’t have to change that fraction. But the second fraction is ½. The second fraction has to be changed to the new fractions that is equivalent. The equivalent fraction is 2/4 . So 1/4 + 2/4   is 3/4  .   Both student used equivalenc
Read more