The materials reviewed for Math Mammoth Grade 5, 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 engage with extensive work with grade-level-problems for standards including but not limited to: 5.NBT.1, 5.NBT.6, and 5.NF.5a . The materials provide limited opportunities for all students to meet the full intent with grade-level-problems for the following standard: 5.NF.5b . Some off-grade-level work negatively impacts students’ work with grade-level content.

The materials are divided into two Worktexts, 5-A and 5-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 5-A, Chapter 1:  The Four Operations, The Multiplication Algorithm, Question 2, students use the standard algorithm to solve multiplication problems of multi-digit by one whole number. “Multiply 5- and 6-digit numbers. a. 17552 x 7  b.  27805 x 3  c.  144123 x 5 “ In More Multiplication, Questions 1 and 2, students use the standard algorithm to solve multiplication problems of multi-digit by multi-digit numbers. Question 1, “Multiply. Remember: you will need to place two zeros in the third line. b. 409 x 228 c. 246 x 137” Question 2, “Practice 4-digit by 2-digit and 5-digit by 2-digit multiplications. d. 20516 x 37 e. 31447 x 29” Students engage in extensive work with grade-level problems to meet the full intent of 5.NBT.5 (Fluidly multiply multi-digit whole numbers using the standard algorithm.)

• Worktext 5-A, Chapter 4: Decimals, Part 1, Comparing Decimals, Question 2, “Write these numbers in order, from the smallest to the greatest. The number line above can help. ___<___<___<___<___<___<___<___<___” The numbers the students are given are the following: 5.01, 5.3, 5.03, 4.8, 5.24, 4.92, 5.1, 5.15 and 5.19. Question 3, “Compare the numbers and write <, =, or >. You can use the place value charts to help. a 0.6 ___ 0.006 b. 0.03 ___ 0.3” Question 4, “Compare the numbers and write <, =, or >. c. 5.007 ___ 5.4 d. 3.004 ___ 3.400” Students engage in extensive work with grade-level problems to meet the full intent of 5.NBT.3 (Read, write, and compare decimals to the thousandths.)

• Worktext 5-B, Chapter 9: Geometry, Volume, Question 1, “Find the Volume of these figures in cubic units. “V” means volume. a.  V = ______ cubic units, b  V = ______ cubic units” For part “a” a picture of six cubic are provided arranged side by side in rows of three and for part “b” a picture of a rectangular prism is provided made out of cubes two layers of 2x4 cubes” Students are provided the information before the problem that, “This little cube is 1 cubic unit.” Question 2, “Find the total volume of each figure when the edge length of the little cube is given. Remember to include the unit! c. The edge of each cube is 1cm. V = ______ d. The edge of each cube is 1 m. V = ______” Students are given pictures of cubic units in various configurations. Question 3, “Find the volume of these rectangular prisms by finding the amount of cubic units in the bottom layer and multiplying that by the height (how many layers there are). b. Cubes in the bottom layer ______ Height ______ Volume ______” Students are given a picture of rectangular prisms that has a length of 2, width of six, and height of four. Students engage in extensive work with grade-level problems to meet the full intent of 5.MD.4 (Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.)

The materials provide limited opportunities for all students to engage in extensive work with grade-level-problems for standards including, but not limited to:

• Students do not have the opportunity to engage in extensive work with 5.NBT.1 (Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left). In Worktext 5-A, Chapter 4: Decimals, Part 1, More Decimals: Thousandths, Question 3, “Fill in, following the model. Note: the phrase “copies of” corresponds to multiplication, and “makes” corresponds to the equal sign. b.  ____copies of $\frac{1}{100}$ makes one tenth.  ____ x  = … f.  ____copies of $\frac{1}{1000}$ makes one whole.  ____ x  = ” Students are not provided extensive work with recognizing that in a multi-digit number, a digit in one place is 1/10 of what it represents in the place to its left.

• Students do not have the opportunity to engage in extensive work with 5.NF.5a (Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication). In Worktext 5-B, Chapter 8: Fractions: Multiply and Divide, Multiplication as Scaling/Resizing Decimals, Question 3, “ Will the resulting stick be longer or shorter than the original —- or equally long? You do not have to calculate anything. Compare. a. $\frac{9}{8}$ x —- is longer/shorther than —- … d. $\frac{99}{100}$ x —- is longer/shorter than —-.” Students are not provided extensive work with comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

The materials does not provide for all students the opportunity to engage in the full intent of the following standard:

• Students are not provided the opportunity to engage with the full intent of 5.NF.5b (Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1). Throughout the materials students are not provided the opportunity to explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number or explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

The materials include some off-grade-level content that negatively impacts students’ work with the grade-level standards. An example includes, but is not limited to:  

• Worktext 5-A, Chapter 1: The Four Operations, Review: Addition and Subtraction, Question 1,  “Write one addition equation and one subtraction equation to match each bar model.  Then solve for x. a. Addition: Subtraction: x = ______” A bar model is shown one part is labeled x the other is labeled 1,057. Below the bar the total is labeled 2,370. Students are asked to solve equations with variables, which does not align to a fifth grade standard.

The materials reviewed for Math Mammoth Grade 5, Light Blue Series, partially meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Materials contain multiple connections of supporting work to supporting work throughout, however, some connections of major work to major work are entirely absent from the grade-level materials.  Included within the materials is a Common Core Alignment document, however, the document does not provide explicit guidance for connections between or among domains and clusters. 

There are some connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Worktext 5-A, Chapter 2: Large Numbers and the Calculator, Multiplying Numbers by Powers of Ten, connects the major work of 5.NBT.A (Understand the place value system.) to the major work of 5.NBT.B (Perform operations with multi-digit numbers and with decimals to hundredths.). For example, Question 4, “Explain how the power of ten, number of zeros, and the digits shifting relate in these types of multiplication. Use 10⁴ x 758 for an example.” Students use their understanding of the place value system to perform operations with multi-digit numbers and explain the placement of the decimal point.

• Worktext 5-A, Chapter 5: Graphing, Number Patterns in the Coordinate Grid, connects the supporting work of 5.OA.B (Analyze patterns and relationships.) to the supporting work of 5.G.A (Graph points on the coordinate plane to solve real-world and mathematical problems.). For example, Question 1, “a. Fill in the x and y values according to the given rules. The rule for x-values: start at 0, and add 1 each time. The rule for y-values: start at 0, and add 2 each time. b. Plot the points formed by the number pairs. c. What simple relationship exists between each x and y coordinate? d. Why do you think this relationship is there? (Where does it stem from?)” Students use number patterns to create coordinates that they then plot on the coordinate plane.

• Worktext 5-B, Chapter 7: Fractions: Add and Subtract, Mixed Review Chapter 7, connects the supporting work of 5.MD.A (Convert like measurement units within a given measurement system.) to the supporting work of 5.G.A (Graph points on the coordinate plane to solve real-world and mathematical problems.). For example, Question 4, “Make a line graph of the baby’s weight.” A 3 column table is provided . Column 1 is labeled “Week” and has the following information: 0, 1, 2, 3, 4, 5, 6, and 7. Column 2 is labeled “Weight” and has the following information: 6 lb 14 oz, 6 lb 12 oz, 6 lb 14 oz, 7 lb, 7lb 2 oz, 7 lb 4 oz, 7 lb 6 oz, and 7 lb 7 oz . Column 3 is labeled “Weight in ounces” and is blank.  Students convert the weights into ounces and then graph the data on the chart.

• Worktext 5-B, Chapter 9: Geometry, Volume of Rectangular Prisms, connects the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to the hundredths.) to the major work of 5.MD.C (Geometric measurement: understand concepts of volume.). For Example, Question 11, “John’s room is 12 ft x 18 ft and it is 9 ft high. The family plans to lower the ceiling by 1 foot. a. What will the volume of the room be after that?  b. How much volume will the room lose?” Students use the standard algorithm for multiplication to solve multi-digit whole number volume problems.

The following connections are entirely absent from the materials:

• No connection is made between the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths) to the major work of 5.NF.B (Apply and extend previous understanding of multiplication and division.).

• No connections are made to the major work of 5.NF.A (Use equivalent fractions as a strategy to add and subtract fractions.).