Teaching Factoring With Flash Cards

Factoring is one of those abstract concepts that I often find it difficult to teach, and difficult to connect to students' lives.  I have a student now who is preparing for the FCAT, which is Florida's standardized test that is being fazed out with the implementation of the Common Core.  Factoring is one of the concepts he needs work on, and I believe I've discovered a more interactive way to teach it. 

First, I created some multiplication flash cards that contain most of the larger facts with which he still needs practice.  I will give them to him to take home and study.  But before that, I will ask him to carefully look at them, and see if some of them have the same answers on the back.  (Of course, numbers like 24, 36 and 48 will be products on multiple cards).  I will ask him to place like products in piles together.  Then, we will select one, for example, 24.  We will then review the three cards together; 12 X 2, 6 X 4, and 3 X 8.  I can then encourage my student to count out 24 2-color counters, and examine the varying ways that the set can be divided evenly, using the cards as an aid.  As each grouping is created, the student can record the fact on a chart.  I will also remind my student of the principle of multiplying a number by 1, and include that in the chart as well.  After this guided practice, I can introduce the related vocabulary.  If time permits, I can release more responsibility to my student, and let him try another number with multiple products with greater independence.  If anyone has any other fun, exciting ideas, I would love to hear them. 

Take care, and happy teaching. ;)

Prime and Composite lesson plan

Hello again!  Today, I'm sharing another lesson plan that I've written for my first "core curricular" class in Grad school.  I have adapted a typical math lesson on prime and composite numbers to include multiple modalities to suit varied learning styles.  Instead of creating a Google doc, I decided to just paste it into my blog post this time for easier access. 

My independent practice sheet was a freebie from Ms. Ashley's Resource Room  Thanks so much for sharing! 

Prime and Composite lesson plan

Content area:  Math          Grade level:  3 – 4          Date:  Winter 2013

Objective: 

Students will demonstrate understanding of, and classify prime and composite numbers with 80 percent accuracy. 

Standard Addressed:

CCSS.Math.Content.4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Purpose:

The goal of this lesson is to demonstrate the abstract concept of prime and composite numbers with varying modalities.  In addition to the teacher’s explanation and mental modeling, students will view and interact with the graphic organizer as well as manipulatives. These added visual and kinesthetic modalities, along with guided interaction, support English learners, as well as other learners with varied learning styles.  This lesson assumes that students are already fluent with many multiplication facts, and understand the concept of dividing a number into its subgroups of factors. 

Introduction & Guided Practice:

The teacher begins by passing out bags of two-color counters to each table, and asks students to model the number 16, as if they had just completed a multiplication problem.  Volunteers explain how they have grouped the counters, either in arrays or small clusters.  Then, all counters are returned to the bag, and the teacher asks that students model the number five.  The teacher encourages discussion among group members regarding how the counters will be grouped.  After students struggle for a few minutes with this dilemma, the teacher calls students’ attention to the graphic organizer that s/he has placed on the board or document camera (see below).  The chart has two columns for prime and composite respectively.  “What differences did you find when grouping five and sixteen?” asks the teacher, as s/he copies students’ replies on a list displayed for the class.  When the students voice the fact that five can’t be divided evenly, it is drawn on the Prime side of the chart, displaying 5 and 1 as its only factors.  Students then volunteer possible groupings for 16, which include 4 and 4, 8 and 2, and 16 and 1, and are drawn on the composite side of the chart.  Students then pick a number at random between 1 and 12, and the class decides together, using two-color counters whether it can be divided evenly.  Then, a student volunteers to draw its factors on the appropriate side of the chart.  This is repeated once again to provide additional guided practice.  The teacher asks students what important words they have used when discussing this process with group members, and adds any to the list which students have omitted.  These can include prime, composite, factor, multiple, etc.  This provides English learners with practive using the academic vocabulary surrounding this concept. 

Independent Practice:

   The teacher then distributes the independent practice sheet (see Here), which also contains a completed concept map at the top.  There are five or six exercises on this sheet which involve deciding whether numbers are prime or composite, and listing the factors of composite numbers.  Students are permitted to ask fellow table group members for clarification if they have questions.  They are also permitted to model with the counters if needed.  The teacher circulates to answer questions and monitor student activity.  S/he may need to provide additional scaffolding to some students. 

Closing:

Students will return to large-group setting after a predetermined time, and offer any conclusions or discoveries that occurred to them while practicing.  One or two volunteers may add another number or two to the graphic organizer.  The teacher collects the independent practice sheets, which do not need to be finished. 

Assessment & Extension:

The independent practice sheet will serve as a formative assessment to determine which students have successfully classified the attempted numbers with 80 % accuracy.  This concept, as with most others, will then be incorporated into future authentic problem-solving activities. It can also serve as a center activity for those who have met the objective, and a guided math group activity for those who have not.   Additional practice can be gained from textbook exercises assigned for homework for those comfortable with the concept. 

Enjoy!

My math group is in the groove

At long last, I have settled into a routine with regard to my elementary school interventions, and finally have a few minutes where I’m not feeling overwhelmed.  Since this is only my second year in this capacity, I still have so much to learn.  In particular, I’ve been planning for next week’s small group of fifth graders needing extra help in math.  The stated goal is to get them up to speed with measurement, converting units and data graphing.  However, I’m finding that they are also in need of extra instruction regarding fractions and number sense.  Last year, we’d spend our whole hour covering one topic together, strictly following the curriculum book and adding nothing creative.  I wanted to do something different this year. 

Two weeks ago, I thought, naively that I could cover three short mini lessons in the hour that I am with them twice a week.  But I failed to realize how much time the guided practice and scaffolding would take.  I now feel quite comfortable dividing our hour together by only two ways. 

The first half hour will focus on some concept of number sense.  This could include multiplication, divisibility rules, fractions,etc.  The second half will focus on some other data concept such as measuring, graphing, estimating or geometry.  This year, I’ve ben feeling much more confident about supplementing the provided curriculum book with extended, hands-on activities.  In two weeks, I’m going to be using Julie’s Hershey’s Hershey's Fraction Bar Activity.  One of my students is still a little foggy about rounding, so I used this freebie from The Math Coach’s Corner.  Most important, however, is that I want to facilitate meaningful discussions with students instead of just feeding them algorithms.  I must say that I’m not always so successful with this.  I only hope I can improve with practice.  If anyone has thoughts or suggestions, would love to hear them.  

Happy teaching.