The materials reviewed for Math Mammoth Grade 6, Light Blue Series, partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide limited opportunities for all students to meet the full intent with grade-level-problems for standards including but not limited to: 6.RP.3a, 6.NS.1, and 6.NS.5. The materials provide limited opportunities for all students to engage with extensive work with the grade-level-problems for the following standard: 6.NS.6 . 

The materials are divided into two Worktexts, 6-A and 6-B. Each Worktext is divided into chapters. Each chapter is divided into lessons that contain content instruction, mental math problems, puzzle corners, and practice problems, in addition to chapter reviews and a chapter test.

Examples of extensive work with grade-level problems to meet the full intent of some grade-level standards include:

• Worktext 6-A, Chapter 2: Expressions and Equations, Expressions, Part 1, Question 1, “Evaluate the expressions when the value of the variable is given. f. $\frac{3}{5}$s when s = 25 h. $\frac{1}{9}$y - 4 when y = 81” In Expressions, Part 2, Question 3, “John uses the formula C = $\frac{mg}{22}$ to calculate how much it costs him in dollars to travel m miles, when the price of gas is g dollars per gallon (C is the cost). He gets 22 miles per gallon of gas. If gasoline costs $$\$3.25$$ per gallon, how much will it cost John to travel 380 miles?” In Worktext 6-B, Chapter 6: Prime Factorization, GCF and LCM, Chapter 6 Mixed Review, Question 11, “Write an expression. a. the quantity 5s plus 8, divided by 7 b. the quantity n plus 11, cubed”. Students engage in extensive work with grade-level problems to meet the full intent of 6.EE.2 (Write, read, and evaluate expressions in which letters stand for numbers).

• Worktext 6-A, Chapter 4: Ratios, Unit Rates, Question 3, “Change to unit rates. Give the rate using the word ‘per’ or the slash /. a. To paint 130 square meters, you need to use 15 liters of paint. b, Joanne’s Internet speed is 100 megabits in 25 seconds.” In Chapter 4 Review, Question 4, “A car traveled 480 kilometers in 6 hours at a constant speed. Fill in the table of equivalent rates: b. What is the unit rate?”. In Worktext 6-B, Chapter 8: Integers, Chapter 8 Mixed Review, Question 6, “Annabelle can type 70 words in two minutes. How many words can she type in 15 minutes?” Students engage in extensive work with grade-level problems to meet the full intent of 6.RP.2 (Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.)

• Worktext 6-B, Chapter 10: Statistics, Using Mean Median and Mode, Question 2, “Judith asked 55 teenagers about how much money they spent to purchase a Mother’s Day gift. a. The mean is $$\$11$$ and the median is $$\$9$$. Which of the two better describes this data? Also, explain how your choice relates to the shape of the distribution.  b. Approximately what percentage of these teenagers spent $$\$10$$ or less on a Mother’s Day gift?” A histogram is provided labeled “Money Spent for Mother’s Day Gift”. Question 3, “ a. Find the mean, median, and mode of this data set: 3, 4, 4, 5, 5, 5, 5, 6, 8, 25. Note that the distribution has an outlier at 25. mean_____ mode _____ median _____ b. Which of the three, mean, median, or mode, best describes the center of this data? Clearly, either the _____ or the _____, but not the _____ ! The _____ is off from the central peak of the distribution. c. Calculate the mean again if the outlier 25 is omitted After all, it is so different from the other data items, it could even be a typing error!” Students are given a dot plot of the data set. Question 4, “a. Describe the overall shape or pattern of this distribution. b. Find the mode and the median. mode _____ median _____ c. Which of the two better describes this distribution, and why?” A dot plot is given with the title, “The Ages of Website Class Participants” The scale is labeled years and counts by ones from 9 to 20. Students engage in extensive work with grade-level problems to meet the full intent of 6.SP.2 (Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.) and 6.SP.3 (Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.)

The materials do not provide opportunities for students to meet the full intent of most of the standards. Examples include, but not limited to: 

• Students are not provided the opportunity to engage with the full intent of 6.RP.3a (Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios).  In Worktext 6-A, Chapter 4: Ratios, Using Equivalent Rates, Question 7, “a. Three pairs of socks cost $$\$9$$. Fill in the table of rates. The varible C stands for cost, and p for pairs of socks.” A horizontal table is provided with C on the top row and p on the bottom row. The values 1-10 are filled in next to p  and the 3 has the corresponding value of 9 filled in above it. “b. Each number pair in the table is a rate, but we can also view them as points with two coordinates. Plot the number pairs in the coordinate grid. c. Write an equartion relating the cost (C) and the number of pairs of socks (p).” Students are not prompted to use tables to compare ratios.

• Students are not provided the opportunity to engage with the full intent of 6.NS.5 (Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation). In Worktext 6-B, Chapter 8: Integers, Integers, Question 2, “Write an integer appropriate to each situation. a. Daniel owes $$\$23$$.  b. Mary earned $$\$250$$. c. The airplane flew at the altitude of 8800 meters. …” Students are not prompted to explain the meaning of 0 in any of these situations.

The materials provide limited opportunities for all students to engage in extensive work with the following standard:

• Students do not have the opportunity to engage in extensive work with 6.NS.6 (Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.). In Worktext 6-B, Chapter 8: Integers, Integers, Question 1, “Plot the integers on the number-line. a. -7, b. +6, c. -4, d. -2.” A horizontal number line ranging from -10 to 10 is given.   In Coordinate Grid, Question 4, “Two vertices of a rectangle are (-5, -3) and (-2, 4). What are the other two vertices?” A coordinate plane is given. Students are provided with limited opportunities to work with positive or negative rational numbers such as decimals and fractions on number lines and the coordinate plane