3rd Grade - Gateway 1

The materials reviewed for Math Mammoth Grade 3, Light Blue Series, do not 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 in extensive work and/or do not provide opportunities for students to meet the full intent with grade-level-problems for standards including but not limited to: 3.OA.3, 3.OA.8, 3.OA.9, 3.MD.3, and 3.MD.6 . Some off-grade-level work negatively impacts students’ work with grade-level content.

The materials are divided into two Worktexts, 3-A and 3-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 3-A, Chapter 2: Multiplication Concept, Many Times the Same Group, Question 1, “Write the multiplication.” Pictures showing equal groups are shown, for example, e. shows five groups of two blue dots. “_____ x _____” Question 2, “Now it is your turn to draw! Notice the symbol x which is read ‘times’. c. 1 times 7 1 x 7” Students engage in extensive work with grade-level problems to meet the full intent of 3.OA.1 (Interpret products of whole numbers)

• Worktext 3-A, Chapter  3: Multiplication Tables, Multiplication Table of 2, Question 4, “Don’t write the answers down. Use these problems for random drill practice. _ x 2 = 14, _ x 2 = 12 ,  ___ x 2 = 6 …” Students fill in the missing number to make the equation true. In subsequent lessons, students solve similar problems with different factors. In the lesson, Multiplication Table of 5, Question 4, “Don’t write the answers down. Use these problems for random drill practice _ x 5 = 35, _ x 5 = 20 ,  ___ x 5 = 55 …” In Chapter 3: Multiplication Tables, lessons are available for Multiplication Tables 2 -12, with similar questions. Students engage in extensive work with grade-level problems to meet the full intent of 3.OA.4 (Determine the unknown whole number in a multiplication or division equation relating three whole numbers.)

• Worktext 3-B, Chapter 10: Fractions, Fractions on a Number Line, Question 1, “Fill in. You can also color a rectangle that goes up to the arrow, to help you.  a. The number line from 0 to 1 is divided into _____ parts.  The arrow marks the fraction .” Question 5, “Divide the number line from 0 to 1 into equal parts. Then mark the fraction on it.” There are ten problems where students are shown a number line from 0 to 1 and they identify where a fraction is on the line, for example e. asks them to find  \frac{3}{4}. Question 6, “Write all the fractions under the tick marks.” A number line from 0 to 3 is shown. There are dots at each \frac{1}{5}. Students engage in extensive work with grade-level problems to meet the full intent of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram.)

The materials provide limited opportunities for all students to engage in extensive work with grade-level problems and/or do not provide opportunities for students to meet the full intent of most of the standards. Examples include, but are not limited to: 

• Students do not have the opportunity to engage in extensive work with 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). In Worktext 3-A, Chapter 3: Multiplication Tables, Multiplication Table of 7, Question 4, “Solve. Write a number sentence for each problem, not just the answer! a. Jenny packed pretty stones in boxes.  She put seven stones in each box.  How many boxes did Jenny need to pack 28 stones?”  The material does not provide extensive work in solving word problems involving arrays.

• Students are not provided the opportunity to engage with the full intent of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs). In Worktext 3-A, Chapter 1: Addition and Subtraction, Graphs, Question 1, “The graph shows the number of books some children read during a vacation reading assignment. Read the graph and fill in the blanks. c. How many more books did Jack read than Jake?  ___ books f. Did the girls or the boys read more books? ___  How many more? ___ ” Students are not provided the opportunity to draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. 

• Students do not have the opportunity to engage in extensive work with 3.MD.6 (Measure area by counting square units). In Worktext 3-B, Chapter 7: Geometry, Getting Started with Area, Question 1, “How many square units is the area of these figures? a. The area is ___  square units. b. The area is ___  square units.” Students are provided four figures with colored squares to count and find the area. The material does not provide extensive work in measuring area by counting square units.

• Students do not have the opportunity to engage in extensive work with 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.) In Worktext 2-B, Chapter 7: Geometry, Some Special Quadrilaterals.  Question 2, “Draw three quadrilaterals that are NOT squares nor rectangles.”A square or a rhombus?  The material does not provide extensive work in drawing examples of quadrilaterals that do not belong to the subcategories of rhombuses, rectangles, and squares.

• Students are not provided the opportunity to engage with the full intent of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.). In Worktext 3-B, Chapter 10: Fractions, Understand Fractions, Question 7, “ Divide the shapes into equal parts. Shade ONE part. Write the area of that part as a fraction of the whole area. b. Divide the shape into three equal parts. shaded area = \frac{a}{b} of the whole area” Students are provided a picture of 3 by 4 rectangle on a grid. Students are not provided an opportunity to express the area of each part as a unit fraction of the whole.

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

• Worktext 3-B, Chapter 6: Place Value with Thousands, Add 4-Digit Numbers with Regrouping, Question 2, “Add. Be careful to line up the ones, tens, hundreds, and thousands. a. 34 + 2,382 +, 391 + 77 + 3,409 ” Throughout the lesson students are tasked to add numbers beyond 1000, which does not align to a third grade standard.

• Worktext 3-B, Chapter 6: Place Value with Thousands, Subtract 4-Digit Numbers with Regrouping, Question 3, “ a. 4,908 - 203 - 1,420 ”. Throughout the lesson students are tasked to subtract numbers beyond 1000, which does not align to a third grade standard.

The materials reviewed for Math Mammoth Grade 3, Light Blue Series, do not meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The materials do not devote at least 65$$\%$$ of instructional time to the major clusters of the grade: 

• The number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 10, approximately 60$$\%$$. 

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 79 out of 127, approximately 62$$\%$$ 

• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 103.5 out of 173, approximately 60$$\%$$. 

A day-level analysis is most representative of the instructional materials as the lessons typically cover multiple days that focus on major work of the grade. As a result, approximately 60$$\%$$ of the instructional materials focus on major work of the grade.

The materials reviewed for Math Mammoth Grade 3, Light Blue Series, do not meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. While some references to future or earlier grade work does occur in the introduction lesson, these references are limited, and are not always related to grade-level concepts or work. The materials include a Common Core Alignment Document that lists the grade-level standards addressed in each lesson, however, the document does not include information regarding the progression of the lesson standards between grade-level bands. 

There are some examples of references to future grade content, however these references are not always identified and/or related to grade-level work. Examples include, but are not limited to:

• Worktext 3-A, Chapter 4: Telling Time, Introduction, "We review the topic of reading the clock to the five-minute intervals, first using numbers in telling the time, such as 6:45 or 12:15. Then, children learn about quarter hours, such as a quarter till 6 or a quarter past 9. We also review the topic of using “past” and “till”, such as in 20 till 6 or 10 past 11. Next, we study elapsed time in the lessons How Many Minutes Pass and More on Elapsed Time. These lessons provide lots of visual aids (clock faces) for the children to be able to figure out how much time passes. You can also use a practice clock. The lessons don't yet cover the situation where we would need to figure out the elapsed time in several parts (such as, how much time passes from 9:13 AM to 1:45 PM?). That is studied in 4th grade."

• Worktext 3-B, Chapter 9: Division, Introduction, “...the student finds the remainder by using visual models (you could also use manipulatives), and then by calculating. This concept will be studied again in fourth grade.”

There are some examples of references to prior grade learning, however not all references relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include, but are not limited to:

• Worktext 3-A, Chapter 1: Addition and Subtraction, Introduction, “I have included several lessons on mental math, including review of many of the strategies from second grade,”

• Worktext 3-A, Chapter 4: Telling Time, Introduction, “ … The lesson Clock to the Minute completes the topic (begun in earlier grades) of reading the clock, because the student will now be able to tell the complete time.”