download Bits and Pieces 2: Using Rational Numbers (Connected Mathematics Series: Number) Explore our editors' picks for the best kids' books of the month. Home · 5th Grade · 6th Grade · Advisory · Photos · Math Practice. Bits and Pieces 2. 1.) Problem 2.) Problem 3.) Problem 4.) Problem 5. The Murderous Maths books have been published in over 25 countries. . while trying to assemble a book shelf and now I need to separate 2 pieces of wood.

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BIts II Unit TEST STUDY GUIDE with Key (also Videos, Games, and Activities). Picture. Bits and Pieces II Student code amk Inv 2 Book Pages. Inform students and parents about CMP2 Math resources. More work with fractions Book >> of goals, specific questions to ask your students and examples of core concepts from the unit, go to Bits and Pieces II. CONNECTED MATHEMATICS BITS AND PIECES II STUDENT EDITION a subscription that delivers editorially hand-picked children's books every 1, 2, or 3 .

All newest products Schoolaid Math Spunky is a donkey pronounced dunkey in some parts , and young pupils will find him frolicking through the pages of the Schoolaid math series. Actually, learning math is rarely a frolic, but these workbooks provide exercises that will be familiar to rural farm and school life. Prepared for use in one-room schools, home schooling parents might take to them as well, where teaching time is a precious commodity. The teacher's manual gives the beginning teacher a good overview, and offers advice on routines, teaching aids, and ways to help your students work independantly. Each grade has a pair of workbooks to cover the year, and some specially-designed flash card sets are available to supplement the program.

For example, the three listed under Category VI all mean 'no tests, quizzes or worksheets'' and the two in Category III mean 'group work with manipulatives. None of these criteria assess what specific mathematics is covered. Thus the Connected Mathematics Project CMP can be the highest rated, even though the topics it covers in grade 8 are covered in grade 7 in competing programs, and covered in grade 6 in Japan, Korean, China, Singapore and Russia.

All that one should conclude from the Project report is that their top-rated programs are politically correct.

I have looked over the CMP program carefully. It definitely is politically correct. What criteria should be used? A good math program has several stages. Grades should be preparation for the real math that starts with a solid grade 8 algebra course focusing on quadratic equations and polynomials, and a grade 9 course in Euclidean geometry, with proofs. That is the plan followed by most countries, and the one recommended by the U. Department of Education.

Virtually all students find these two courses very hard; many find them TOO hard and drop out of math at that point.

But these courses are not intrinsically difficult. The problem lies in the US grade programs. There our children spend their time going over more arithmetic, instead of taking the first steps toward real algebra and geometry with proofs.

This last sentence exactly describes the problem with CMP and similar programs. The Project report does not reveal this fundamental deficiency because its criteria do not include real algebra and geometry with proofs. A study of their website is essential for understanding the battle lines in the current debate over mathematics education. I have young children in the Okemos schools.

I am VERY concerned about the mathematics programs. You should be very concerned also. If your daughter is taking 8th grade CMP rather than Honors Algebra I then she is not on track to take calculus in high school.

Calculus is the basic entry point to majoring in science, engineering and medicine.

In Korea all students, including the children of rice farmers, take calculus as juniors in high school. You should be asking Okemos officials why it is that your daughter, who is apparently a top student in a top school system, is two years behind the children of Korean rice farmers.

Mathematical Depth There is very little mathematical content in this book. Students leaving this course will have no background in or facility with analytic or pre-algebra skills. Quality of Presentation This book is completely dedicated to a constructivist philosophy of learning, with heavy emphasis on discovery exercises and rejection of whole class teacher directed instruction.

The introduction to Part 1 says "Connected Mathematics was developed with the belief that calculators should be available and that students should decide when to use them. Quality of Student Work Students are busy, but they are not productively busy. Most of their time is directed away from true understanding and useful skills.

Its purpose is to make you aware of a math program for 6th-8th grades. This program is called "Connected Mathematics". In a nutshell, this program is "discovery" learning.

The students "discover" the concepts in each unit through a variety of activities. The program sounds like a great idea in theory. The goal is to have students make sense of the mathematics they study and to be able to communicate their reasoning clearly. The teacher begins the unit by presenting the 'problem" to the students.

The kids then work in pairs or small groups to solve the problem by gathering data, sharing ideas, looking for patterns, making conjectures, or developing other types of problem solving strategies.

When most of the students have made sufficient progress toward solving the problem, the teacher helps the class to discuss ways they found to organize the data and look for patterns and related rules in the data. Below are concerns which every parent should consider. There are a lot of kids that simply will not want to "discover" the concept.

This kind of learning should begin in the elementary grades and progress to the middle school level. The program states that in classes that last less than 45 minutes, there is not sufficient time to make progress on a problem. Most classes are right around 45 minutes. The students are not taught any algorithms and they are allowed to arrive at an answer any way they wish with little or no work shown.

How are these kids going to adjust when they go into a traditional algebra curriculum in the 9th grade? Calculators are used entirely throughout the program.

How do teachers adapt this program for their special education and learning disabled students? How will teachers tutor their students? How will students who are absent make-up the lesson? Students need drill and practice in order to master most concepts. There is none of that in this program. There are some concepts, such as percents and computation of fractions, that middle school students need to see in all 3 years of middle school. There are very few units in CMP that are covered in all 3 years.

Several of the units have other units as prerequisites. What about those students that move to PIano in the middle of the year? Do you want your children to be used as guinea pigs for this radical experiment? The titles for the grade 6 booklets are underlined below. The indented comments are from a parent whose daughter was subjected to CMP. Prime Time -- factors and multiples Mainly a game book but unfortunately, a boring game book with factors.

For a curriculum that stresses on real world problems, most of the problems are not real life problems. For example, there are exercises to discover abundant, deficit and perfect number which are interesting numbers but have no application in life -- most scientists and mathematicians have not heard about them.

This is also the unit where students are asked to make posters about numbers including my favorite number. Shapes and Designs -- two-dimensional geometry After 6 weeks of playing around with polygons and triangles in 5th grade, similar activities are repeated again in this four week course. It is pathetic not to teach area of rectangle, squares and triangles in the 6th grade. Bits and Pieces I -- understanding rational numbers This unit contains a large overlap with fifth grade mathematics curriculum.

Students use paper strip to understand fractions. Most of the materials described here about fractions, decimals and percentage are so simple minded, a competent 6th grader would have known the material already. Covering and Surrounding -- two-dimensional measurement Discovering pi by cutting and pasting of circles is a waste of time. It took my daughter nearly two hours one evening to do such an activity.

What is wrong with just remembering pi as 3. How Likely is It? Bits and Pieces II -- using rational numbers It was my daughter's experience with this unit that I started tutoring her at home. She was an A student and was in 7th grade.

She was completely confused by the way CMP introduced fractions, decimals and percentages. She was frustrated by the tricks that she "discovered" which did not work in more general cases. Obviously she was not taught about formulas to convert one to the other.

A lot of students have problems learning addition and subtraction of fractions using this unit. Ruins of Montarek -- spatial visualization See quote from Professor Milgram below.

The philosophy used throughout the program is that the students should entirely construct their own knowledge and that calculators are to always be available for calculation. Precise definitions are never given. Repetitive practice for developing skills, such as basic manipulative skills is never given. As we go through these booklets and a few of the more advanced ones, I will constantly be pointing out areas where the problems above occur.

This is to help make the point that these are not isolated instances, but represent a consistent point of view towards the material, and the level at which it should be addressed. This booklet is concerned with prime factorization of whole numbers. In standards based curricula, such as that in California, this is a fourth and fifth grade topic. It takes 8 people to clear an acre of weeds in 4 hours.

How many acres can 16 people clear in 4 hours? How many acres can 2 people clear in 4 hours? How many people are needed to clear 3 acres in 4 hours? How many people are needed to clear 3 acres in 2 hours? The sixth-grade students at Cleveland Middle School are selling popcorn as a fundraiser. After Day 4, the sixth-graders are doing better. Mark this point on a copy of the number line. After Day 6, the sixth-graders are breaking even.

This means they are no longer losing any money, but they are not gaining any money either. Mark their progress on your number line. How much money have they raised? What fraction of their goal did they raise after they broke even?

Sometimes, instead of adding or subtracting fractions, you need to multiply them. For example, suppose you take inventory at the sporting goods store 1 where you work.

There are 13 2 boxes of footballs in the stock room, and there are 12 footballs in a full box. How can you find the total number of footballs without opening all the boxes? This situation requires multiplication.

In this investigation, you will relate what you already know about multiplication to situations involving fractions. Remember, to make sense of a situation you can draw a model or change a fraction to an equivalent form. You can also estimate to see if your answer makes sense.

Paulo and Shania work the brownie How much is booth at the school fair. Sometimes, 1 of 2? Williams asks to buy 2 of a pan that is 3 full. Use a copy of the brownie pan model Model of a Brownie Pan shown at the right.

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