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5-A contents and samples

5-B contents and samples

Here's a summary of the changes between the old and the new. You can also find this information here.

The biggest changes in grade 5 are that the two optional chapters (percent and integers) have been removed, and the topics in geometry chapter are different. However, overall, the structure and contents of this grade is very similar to the old.

**Chapter 1**starts out like the old version, with some review topics and multi-digit multiplication. There is now more focus and practice problems on long division with two-digit divisors. One big change is that the lessons on problem solving and equations were moved to their own chapter (chapter 3 in the revised version). Another is that I have now included the topics of divisibility, factors and primes, and prime factorization (used to be in the old version grade 6).

**Chapter 2**(large numbers) is also very similar to the old version. The lesson*A Little Bit of Millions*was added (it used to be in 4th grade).

**Chapter 3**is about problem solving and simple equations (originally these lessons were in the 1st chapter).

**Chapter 4**(decimals) is very similar to the old version in its contents. The topic of writing decimals in expanded form was added to one of the lessons. Other changes are cosmetic - improved layout, images, scaffolding of concepts, and order of presentation (in some lessons).

**Chapter 5**(graphing and statistics) is very similar to the old version. I added one more lesson on patterns in the coordinate grid. This chapter is now Chapter 5 (used to be chapter 4), and is moved to the part B.

It actually exceeds Common Core standards (line graphs, histograms, analyzing graphs, mean, and mode). However, I feel students will need this as a background before the statistics topics of 6th grade, which are somewhat advanced. For example, in 6th grade students will study interquartile range and/or mean absolute deviation, and will need to relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. I do not feel that you can read Common Core Standards as "include this and nothing else", because the standards are not all-inclusive: there are many topics they do not explicitly mention. In my opinion, for students to be able to make sense of mean absolute deviation and relate the choice of measures of center and variability to the shape of the data distribution in 6th grade, they need to analyze and study statistical graphs in easier manners in 5th grade.

**Chapter 6**is fraction addition and subtraction. It is, again, very similar to the earlier version in its contents. I have added a few new problems about how to spot calculation errors using "fraction number sensen" and about line plots.

**Chapter 7**is fraction multiplication and division. It is similar to the earlier version, but has some changes as well. The lesson*Fraction Multiplication and Area*is expanded to include problems where the student extends the sides of the given rectangle to get a square unit, and then write a multiplication for the area of the original rectangle. There are two new lesson*Multiplication as Scaling/Resizing*and*Fractions are Divisions*. Line plots are included in several of the lessons.Fraction division is only dealt in these special cases: sharing divisions (such as 4/6 ÷ 2), dividing unit fractions by whole numbers (1/5 ÷ 3) and dividing whole numbers by unit fractions (such as 5 ÷ (1/3)). These types of divisions can be solved with mental reasoning, without using the "rule". The general case of fraction division is left for 6th grade.

**Chapter 8**is geometry, and its topics are different from the older version. Now, it includes a review of angles, a review of area and perimeter, drawing circles, classifying triangles, classifying quadrilaterals, and volume of rectangular prisms. It used to include many lessons about the area of polygons, which will be moving to 6th grade.

For example, rounding and estimating are not mentioned in the standards for 5th grade. However, since students learn and use bigger numbers in this grade than they did in 4th grade, I feel it is good to review and practice them one more time.

In number theory topics, CCS mention that in grade 4, students are to "gain familiarity with factors and multiples." Then in 6th grade, students find common factors and multiples. However, CCS do not mention in which grade students should study prime factorization. Obviously you cannot leave that out, and so I put it in 5th grade.

Then, problem solving or word problems are not mentioned in any of the numbered individual standards for 5th grade. I included a whole chapter on problem solving, and I feel obviously word problems are to be included in 5th grade mathematics. Common Core Standards mention as one of the recommended mathematical practices that students are to "Make sense of problems and persevere in solving them."

Yet one more: 5th grade standards do not include any statistics topics. However, I feel students will benefit from being introduced to some of the concepts (line graph, histogram, mean, and mode), and from being used to analyzing graphs in order to prepare them for 6th grade statistics topics, which are somewhat advanced. In 6th grade, students will study for example interquartile range and/or mean absolute deviation, and will need to relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

See also: Math Mammoth Common Core alignment, Grade 5 - a list of lessons and the corresponding Common Core Standards in Math Mammoth grade 5 (a PDF file).