Math in Focus - 5th grade
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General Recommendations
5th grade – I worked with a few students who are struggling with fractions. Students do not understand what a fraction is, that it represents a quantity. They do not understand the fractions we were working with were less than one, could be placed on a number line, or approximate values. The rules they were trying to do to add and subtract fractions had no meaning.
What to do - download both files below!
- Provide more opportunities for students to interact with the problems by presenting as open-ended problems (not the teacher demonstrating right away how to solve it) – put up the problem and let students begin to think about how to solve it. Try not to show everything first. Students need to begin developing a sense of learning mathematics by trying different strategies, not just learning steps to get to a right answer.
- Fluency is a problem for students. Teachers can spend some time – about 15 minutes only- building fluency with higher level games, number talks, fluency practice. The focus should be on the strategies. Students need to be able to explain the strategy, show how it works with concrete materials, before applying to “naked” math. Send home some of the fluency practice sheets or the transition guide resources for homework.
- Try to keep the book closed during the teach/learn. Have students work on brainstorming different methods to do the mathematics. Elicit “lots” of student telling and describing.
- Use visuals – concrete, pictorial, abstract – to build understanding of the concepts. Students have to be able to manipulate the concrete, then draw it on their own, before going to abstract. Do not pull the old naked math worksheets. Students need more time with the concrete and describing the processes.
- IEP students or the struggling students – much more time developing the concept of the mathematics (apply fractions to real-life problems), estimation, placing numbers on the number line.
5th grade – I worked with a few students who are struggling with fractions. Students do not understand what a fraction is, that it represents a quantity. They do not understand the fractions we were working with were less than one, could be placed on a number line, or approximate values. The rules they were trying to do to add and subtract fractions had no meaning.
What to do - download both files below!
- Spend much more time with concrete models, especially having the students make their own fraction kit may help. If time is an issue, have them just cut apart a fraction kit. I have posted the ideas on by website. This document provides the basis for building understanding of fractions. It includes a copy of the fraction bars, how to make them, and games that can help build understanding. It also lists the concepts that should be developed first.
- The article posted here, also describes how to develop concrete, pictorial, and abstract representations of fractions. It includes a nice comparison game of fractions. Remember to keep using the number line as a strategy besides the fraction notation and the visual fraction strips.
2012-13 School Year
February 2013
Look at the 4th grade notes, since we discussed the same topic.
For multiplying with decimals, reinforce the quantities of the places. We can write in showing the distributive property, 3 x 8.75 = 3 (8.00 + 0.70 + 0.05) and put in a matrix or table format. Students need to focus on the quantity of the numbers multiplied. Help by using money examples and using the chip models.
January 2013
We discussed the need for the number talks to develop fluency in students. The students have not been taught the strategies for learning their facts and computation.
50 Fact Times Drill - Students do not worry about how many, but practice using the strategies to complete this timed drill. There are one minute and three minute sections on this drill. One minute must follow down the columns equentially with no skipping. Then students switch to a different color pen or pencil. They now have 3 minutes to hop around and use their strategies to aswers problems.
Times Table - is a Excel workbook with different sheets to help students learn the strategies for multiplication. One is to fill in the multiplication table. This is to be used with the Strategies sheet. Students record the strategies and how many facts that relates to. This activity is to show students that there are not 169 facts to memorize, but much less when we learn out strategies. One sheet has different sets of times tables that students have to fill in using their strategies.
Multiplication strings will help build fluency and use strategies of doubles and making tens to help build fluency. The visuals of arrays, area model, and dots build understanding. Here are some problems for Number Talks that begins with strings and continues to build. Choose the problems that work for your grade level.
For our after school training, this is the PPT that I used with reference to Chapter 4, Lesson 5. In addition, here is the Fraction PPT that was given the past couple years.
November 2012
Tape diagrams provide students with a visual that will lead to solving the problem. Tape diagrams represent quantitities and the relationships between quantitites in a problem. Here is an explanation of Problem 4 on page 108, Chapter 2.
Here is an explanation of the 5th grade Chicken and Duck Problem. This was in Chapter 2 on the Enrichment Workbook.
Fractions - Understanding the unit fraction is a good review for students. The model to use is the number line. Here is an explanation of how to show how to compare fractions using the unit fraction.
October 2012
Chapter 2 - Operations with whole numbers - Multiplication and Division
Students struggle with all operations, understanding the concepts, vocabulary, and necessary estimation skills. Click here for the semantic map of operations. For the struggles with estimation skills, we can do number talks each day to help build computational fluency for the students.
In addition, show the partial sum, partial differences, partial quotient, partial product algorithms to build understanding and fluency. For examples, click on the Let's Stick to Math link above.
September 2012
Chapter 1 - Place Value with Whole Numbers
Look at the 4th grade notes, since we discussed the same topic.
For multiplying with decimals, reinforce the quantities of the places. We can write in showing the distributive property, 3 x 8.75 = 3 (8.00 + 0.70 + 0.05) and put in a matrix or table format. Students need to focus on the quantity of the numbers multiplied. Help by using money examples and using the chip models.
January 2013
We discussed the need for the number talks to develop fluency in students. The students have not been taught the strategies for learning their facts and computation.
50 Fact Times Drill - Students do not worry about how many, but practice using the strategies to complete this timed drill. There are one minute and three minute sections on this drill. One minute must follow down the columns equentially with no skipping. Then students switch to a different color pen or pencil. They now have 3 minutes to hop around and use their strategies to aswers problems.
Times Table - is a Excel workbook with different sheets to help students learn the strategies for multiplication. One is to fill in the multiplication table. This is to be used with the Strategies sheet. Students record the strategies and how many facts that relates to. This activity is to show students that there are not 169 facts to memorize, but much less when we learn out strategies. One sheet has different sets of times tables that students have to fill in using their strategies.
Multiplication strings will help build fluency and use strategies of doubles and making tens to help build fluency. The visuals of arrays, area model, and dots build understanding. Here are some problems for Number Talks that begins with strings and continues to build. Choose the problems that work for your grade level.
For our after school training, this is the PPT that I used with reference to Chapter 4, Lesson 5. In addition, here is the Fraction PPT that was given the past couple years.
November 2012
Tape diagrams provide students with a visual that will lead to solving the problem. Tape diagrams represent quantitities and the relationships between quantitites in a problem. Here is an explanation of Problem 4 on page 108, Chapter 2.
Here is an explanation of the 5th grade Chicken and Duck Problem. This was in Chapter 2 on the Enrichment Workbook.
Fractions - Understanding the unit fraction is a good review for students. The model to use is the number line. Here is an explanation of how to show how to compare fractions using the unit fraction.
October 2012
Chapter 2 - Operations with whole numbers - Multiplication and Division
Students struggle with all operations, understanding the concepts, vocabulary, and necessary estimation skills. Click here for the semantic map of operations. For the struggles with estimation skills, we can do number talks each day to help build computational fluency for the students.
In addition, show the partial sum, partial differences, partial quotient, partial product algorithms to build understanding and fluency. For examples, click on the Let's Stick to Math link above.
September 2012
Chapter 1 - Place Value with Whole Numbers
Estimation - two strategies are introduced - rounding and front-end estimation
with adjustments. When students encounter the numbers, they should consider the
situation and look at the numbers to decide which estimation strategy would get
the closest approximation. Students should discuss not only the strategies, but
why and when would these be used.
Subtraction
with front-end estimation will have different results, depending on the back end
numbers. This is due to the fact that subtraction is not commutative. So, let's
show 7,568 - 2,345.
Rounding - 8,000-2,000 = 6,000.
Front-End Estimation with adjustments.
7,000 -
2,000 = 5,000; then look at the back end numbers. 568 rounds to 600 and 345
rounds to 300. Subtract 600 - 300 = 300. So put those parts back together,
5,000 + 300 = 5,300.
If the back end numbers
are reversed, 7,345 - 2,568, then the problem will be different.
Rounding - 7,000 - 3,000 = 4,000
Front-End
Estimation with adjustments.
7,000 - 2,000 = 5,000; then again
look at the back end numbers. 345 rounds to 300 and 568 rounds to 600. So,
then 300 - 600 = -300. In the book, the numbers are switched, taking 600 - 300
= 300 and then subtracting the 300 from 5,000. This is because of the negative
number generated with the subtraction on the back end adjustment. Showing the
-300 with the subtraction of 300 - 600 would help show why we are subtracting.
The final result is the 5,000 - 300 = 4,700.
Which method give
the closes approximation? When would you need a closer
approximation?
The Frayer model can be used to help understand terminology. For example, compatible numbers is a new term.Click here for an example of the Frayer Model for Compatible Numbers.
with adjustments. When students encounter the numbers, they should consider the
situation and look at the numbers to decide which estimation strategy would get
the closest approximation. Students should discuss not only the strategies, but
why and when would these be used.
Subtraction
with front-end estimation will have different results, depending on the back end
numbers. This is due to the fact that subtraction is not commutative. So, let's
show 7,568 - 2,345.
Rounding - 8,000-2,000 = 6,000.
Front-End Estimation with adjustments.
7,000 -
2,000 = 5,000; then look at the back end numbers. 568 rounds to 600 and 345
rounds to 300. Subtract 600 - 300 = 300. So put those parts back together,
5,000 + 300 = 5,300.
If the back end numbers
are reversed, 7,345 - 2,568, then the problem will be different.
Rounding - 7,000 - 3,000 = 4,000
Front-End
Estimation with adjustments.
7,000 - 2,000 = 5,000; then again
look at the back end numbers. 345 rounds to 300 and 568 rounds to 600. So,
then 300 - 600 = -300. In the book, the numbers are switched, taking 600 - 300
= 300 and then subtracting the 300 from 5,000. This is because of the negative
number generated with the subtraction on the back end adjustment. Showing the
-300 with the subtraction of 300 - 600 would help show why we are subtracting.
The final result is the 5,000 - 300 = 4,700.
Which method give
the closes approximation? When would you need a closer
approximation?
The Frayer model can be used to help understand terminology. For example, compatible numbers is a new term.Click here for an example of the Frayer Model for Compatible Numbers.
