Rounding up, Rounding down

        Rounding numbers is a necessary math skill and a useful skill we use all through our lives. Rounding means changing a given number to the nearest tens, hundreds, thousands, and so on. This is a concept that is sometimes hard for younger students to grasp, but with practice they will be able to master the skill of rounding.

How to Round Whole Numbers                                  

Step 1: Choose the place value that you want to round a number to-meaning 10's, 100's, 1000's or another place value.
Round 231 to the nearest ten-so in this case we are rounding to the ten's place. 


Step 2: Decide what two multiples the number you are rounding is between.
We are rounding to the hundred's place in this example so we would choose multiples of 100. 7251 is between 7200 and 7300.

Step 3: Look to the digit in the place immediately right of the place you are rounding to and use the rounding rules to decide whether you move it up to the higher multiple or round to the lower multiple.
Look in the tens place of the number 7251. We see a 5, so we must round to the higher number. Rounding 7251 to the nearest hundred = 7300.

There are many fun ways to help children learn how to master the skill of rounding. Here is a rounding rhyme that I think would be helpful.
1 through 4 stay on the floor
5 through 9 climb the vine.

Another fun activity I found was, I draw a mountain. 

 

        In this activity the teacher draws a mountain  on the white board and uses magnets on a cut out car to show the visual of rounding numbers. If the number ends in 1-4, you drive the car to that number, get out and look at the view and forget to put the car in park. You then discuss with the children what happens to the car if it's not in park. Of course it will roll back to the lower number. If the number ends in 6-9 you repeat the process with the car discussing whether it will roll forwards or backward when they are looking at the view. If the number is 5, it is determined the car will roll to the higher number. The teacher had a great idea because then she would give each of her students a piece of construction paper with a mountain and a small toy car so they could work at their own problems.

         There are many activities and fun ways children can learn about rounding numbers to keep reinforcing this skill. Here is a website that has an activity for children on a hundreds chart that I think would be helpful, also.
Hundreds Charts Activities 

Early Start is a Good Start in Math

        I am always amazed at how much children learn as they start building their foundation in the concepts of math. Preschool education is one of my greatest joys and teaching all of these concepts is so important in building that foundation. The Standards for Math Education for preschool through second grade are made up of five Content Standards and five Process Standards.

Content Standards                                                    
1. Number and operation                                            
2.Geometry and spatial sense                                       
3. Measurement                                                          
4. Patterns, functions,and algebra                                
5. Data analysis, statistics, and probability                   

Process Standards
1. Problem solving
2. Reasoning and proof
3. Communication
4. Connections
5. Representation

        All these standards for content and process are interconnected and interwoven throughout the curriculum in designing mathematical experience for young children. Developmentally Appropriate Practice is the key to quality mathematical education for three to six year-old children. Children at this age love to learn and explore. All we have to do is give them the right tools to use for their exploration. Math explorations can be something that is done all through the day from counting crackers at snack to making a chart on the weather. Math can be explored during play in games and activities. Children can explore math through literature and learn as they manipulate objects and create relationships among and between objects. When I stop and think about how different math is for elementary students now I realize how important building that foundation is in the preschool years.

Here is a video on preschoolers learning geometry.

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Using Lattice Multiplication Post#3 Math 1510

        Lattice multiplication is a way of doing multiplication using a grid that looks similar to a lattice. It has been around for centuries and was first introduced in Europe in the early 1200's by Fibonacci. With practice this method can be quick and efficient in solving multiplication problems. When I first saw this method my daughter was in fourth grade and I wondered what in the world it was. I never took the time to find out so this chapter has really helped me to understand this method.
        Primary grade students have difficulty keeping the math columns aligned when they start to learn multiplication.  Lattice multiplication can help students who are struggling with this problem achieve success. By demonstrating the technique and process of this new math skill the students will be able to separate the multiplication from the addition in first filling in the lattice and then adding the contents. Some of the important points in this method are that it can be easily learned, keeps their work organized, and is diagnostic in that if they do get a wrong answer the student  can easily see where the mistake was made. This method breaks down the process into smaller steps which can help some students grasp the concept of multiplication easier because it is so visual. Here is how you use this method:

1. If you are multiplying two digits by two digits, you need a grid two squares across and two squares down. A three digit by two digit problem takes a two by three grid.

2. Divide each box diagonally from the upper right corner to the lower left corner. Start at the top left corner and write one of the numbers you are multiplying across the top edge of the grid ( around the outer edge, not inside the boxes), one digit per space. Write the second number down the right edge in the same manner.

3. In each box multiply the number at the top of the column with the number at the right of the row. Write the result in the corresponding box with the ones below the diagonal and the tens above the diagonal (if it is a single digit number, write "0" for the tens).

4. Add the numbers along each diagonal row from right to left and record the sums along the lower or left outer each. Carry the tens to the next diagonal when the sum is 10 or greater. Read your answer around the outer edge from top left to lower right.
        The only time consuming part of the lattice method is making the grid. The more activities the students do, the more proficient they will become at using this method in multiplying large numbers.

Lattice Multiplication

Strategies for Problem Solving #2 Math 1510

        There are a number of ways to teach math but the textbook should not be the only resource that we use. Projects, small groups, modeling, and investigation were some of the tools mentioned in the video I watched this week. Students learn in a variety of different ways so using different strategies in the classroom will help reach more children. All these different classroom strategies help the student find different solutions to different problems.
        In problem solving we are teaching our students to look for a solution.These are steps that children learn so that the can become successful in their problem solving strategies. First we want them to understand the problem by asking important questions like: What does the situation involve? What has to be determined? What are the key data and conditions? What are some assumptions? After asking these questions we have to develop a plan by finding out what strategies will be useful are there subproblems, should we estimate or calculate the problem, and what method of calculation should be used. Then it is time to implement the problem  using the strategy and finding the answer. Always remember to look back to make sure the interpretation is correct, the calculation is correct, ask yourself if the answer is reasonable, or if there is another way to solve the problem.
        Problem solving is one of the Mathematical Process Standards that start in prekindergarten and follow children through grade 12. These standards help to enable students to build mathematical knowledge through problem solving, solve problems that arise, apply and adapt  a variety of strategies to solve problems, and monitor and reflect on the process of solving mathematical problems. Teaching the students problem solving strategies helps them to better understand  the problem solving process. Here is a video on strategies for problem solving that I found fun to view.

Authentic Assessment Post #1 Math 1510

        What does Authentic Assessment look like? This is a question that I have asked myself several time because there seems to be so many assessments out there. Authentic Assessment includes a task for students to perform and a rubric that evaluates the students performance. There are other names that are used for Authentic Assessment which are Performance Assessment, Alternative Assessment, and Direct Assessment.                      
         How are Authentic Assessment and Traditional Assessment similar and yet different. Both assessments have a belief that the primary mission of schools is to help develop productive citizens, but after this there is a difference. In the Traditional Assessment curriculum drives assessment. The body of knowledge is determined first and that becomes the curriculum that is delivered. In Authentic Assessment the assessment drives the curriculum. The teacher determines what task the students will perform to demonstrate their mastery, and the curriculum is developed to enable students to perform tasks well.
        Authentic or Performance Assessment has been gaining acceptance among early childhood and primary grade teachers. There are many benefits to this assessment one being that teachers document what they know and do based on activities the students engage in. The teachers can evaluate students progress from ongoing classroom interaction with materials and their peers. They can also plan a developmental curriculum based on what they know about each student. The teachers carry the responsibility for monitoring what the children are learning and what the teachers are teaching. Assessments are made on a daily basis, using reflective activities in math to make sure the students are building on previous lessons, performance tasks, and problem based learning. They have a full picture of their students and assess not only their answers but the way they communicate the answer, and solve problems. Communication, process, and solution are key in teaching math concepts. In Authentic Assessment it is brought to the forefront that this is a marriage between curriculum and assessment.

Hello to everyone in my group!

Hello to everyone! This has been a very interesting experience for me because I have never created a blog before. I am looking forward to the challenge and looking forward to seeing and sharing all our knowledge on the best ways to help children learn the concepts of math.