1st Grade - Gateway 1

The materials reviewed for Math Mammoth Grade 1, 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: 1.OA.6, 1.OA.7, 1.NBT.2, 1.MD.1, 1.MD.3, 1.MD.4 and 1.G.3. Some off-grade-level work negatively impacts students’ work with grade-level content.

The materials are divided into two Worktexts, 1-A and 1-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 1-A, Chapter 2: Subtraction Within 0-10, Two Parts - One Total, Question 1, “Solve the word problems. Write an addition sentence AND a subtraction sentence. a. Mother put some blue and some red flowers in a case. Jen counted five red ones and a total of ten. How many of the flowers are blue?   ____ + ____ = _____ , ____ - ____ = _____ .” Question 2, “For each picture, make a word problem that is solved by subtraction.”  Students are given a picture of 4 dolls and 3 cars for part b. Question 5, “Draw a picture to solve these problems. b. Seven birds sat in a tree. One of them was black, two were blue, and the rest were brown. How many were brown?” Students engage in extensive work with grade-level problems to meet the full intent of 1.OA.1(Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions)   

• Worktext 1-A, Chapter 3: Place Value Within 0-100, Which Number is Greater?, Question 2, “Write < or > between the numbers. You can draw ten-sticks and one-dots to help. b. 34 ___ 24”. Question 3, “Write < or > between the numbers to compare them. Number line can help. c. 99 ___ 96”. Question 4, “Write < , > or =.  g. 40+5 ___  40+4”. Students engage in extensive work with grade-level problems to meet the full intent of 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < .) 

• Worktext 1-B, Chapter 6: Shapes and Measuring, Basic Shapes, Question 2, students are shown a picture of a circle for part h, “Write down how many corners each shape has.”  Question 3, Using the pictures of the various shapes above, “a. In the shapes above, there is one rectangle. Mark it with R.” Question 4, “a. Draw three dots anywhere in this space. Join them with lines. What shapes do you get?” Students engage in extensive work with grade-level problems to meet the full intent of 1.G.1 (Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes.)

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 are not provided the opportunity to engage with the full intent of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.) In Worktext 1-B, Chapter 4: Addition and Subtraction Facts, Addition and Subtraction Facts with 9, Question 1, “Write the fact families where the sum is 9.” One of the items has a picture of a group of 8 stars and a group of 1 star. “______ , _______ , 9 ____ + ____ = _____ ,____ + ____ = _____, ____ - ____ = _____ ,  ____ - ____ = _____ .”  Students are asked to complete two addition and two subtraction problems with the addends for 9. Question 3, “Write the addition facts with 9 and memorize them!” A box is given with ten incomplete equations for students to fill in missing addends for 9.  In Worktext 1-B, Chapter 7: Adding and Subtracting within 0-100, Going Over Ten, Question 2, “First circle ten marbles to make a ten. How many marbles are there in all? a. 7 + 8 = _____” There are a total of eight problems in this lesson that have sums between 11 and 20. Students are not provided with the opportunity to engage with the full intent due to the limited amount of problems presented to them in the materials.  Students have limited work with sums between 10 and 20. 

• Students do not have the opportunity to engage in extensive work with 1.OA.7 (Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.) In Worktext 1-A, Chapter 1: Addition Within 0-10, Comparisons, students are told that “= means ‘EQUALS’” and also told the meanings of the symbols  < and > . Question 1, “First add in your head. Then compare and write <, >, or =.  c. 6 ____ 2+3.” Question 6, “Are these additions right? Circle true or false.” “a. 7 + 3 = 10” Students are provided with limited opportunities to determine if equations involving addition and subtraction are true or false.

• Students do not have the opportunity to engage in extensive work with 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object.) In Worktext 1-B, Chapter 6: Shapes and Measuring, Measuring Length, Question 6, “Compare the things to the ‘measuring stick.’ Mark the longer of the two.”  For part a, students are shown a picture of a pen and a pencil, each with a measuring stick underneath.  The pen is longer.  Question 7, “Draw a picture to match the situation.  You can draw stick figures.”  Students draw a picture to solve, “b. The table is taller than little Kyle.  Little Mary is taller than the table.” Students are provided with limited opportunities to compare lengths indirectly using a third object. 

• Students are not provided the opportunity to engage with the full intent of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks.) In Worktext 1-B, Chapter 5: Time, Whole and Half Hours, Question 1, students are shown a clock with the hour hand only, “Write the time under each clock face. b.  ______ o’clock”  The clock has the hour pointing to 11:00. Question 2, Students are shown a picture of a blank clock, “Draw the hour hand. a. Five o’clock”  Question 8,  students are shown a clock with the hour hand pointing to 12, “Write the time that the clock shows. Then write what the time will be an hour later. b. ____ o’clock, An hour later _________.” Students are not given the opportunities to tell and write time on digital clocks and many of the analog clocks don’t have minute hands, only hour hands.   

• Students are not provided the opportunity to engage with the full intent of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.) In Worktext 1-A, Chapter 3: Place Value Within 0-100, Tally Marks, Question 3, “Count the fish. Use tally marks to keep track. Mark each fish you count and make a tally mark for it. That way you won’t count the same fish twice. Then write the number under ‘Count’.” Students count the number of each color (Red, Blue, and Yellow) of fish and record in the chart, but do not answer any questions about how many more or less. 

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 1-B, Chapter 5: Time, The Calendar, Question 2, “What do the letters Su Mo Tu We Th Fr Sa mean?” This question asks students to engage in the calendar which is not aligned to a first grade standard.

• Worktext 1-B, Chapter 7: Adding and Subtracting within 0-100, Pictographs, students work with these types of questions by analyzing picture graphs, which is a grade 2 standard (2.MD.10).

• Worktext 1-B, Chapter 8: Coins, Practicing with Money, Question 3, “Illustrate these amounts of money. Use two quarters in each problem. “c. 58¢” This question asks students to engage in counting money which is not aligned to a first grade standard.

The materials reviewed for Math Mammoth Grade 1, Light Blue Series, do not meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Throughout the Worktexts, standards are mostly taught in isolation from other standards.  There are missed opportunities to connect supporting work to major work throughout the materials. The materials include a Common Core Alignment Document that does not provide guidance for connections between supporting and major work of the grade.

Examples of connections between supporting and major work include: 

• Worktext 1-A, Chapter 2: Subtraction Within 0-10, “How Many More” Problems and Subtraction, connects the supporting work of 1.MD.4 (Organize, represent and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.) to the major work of 1.OA.1(Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions). For example, Question 8, “Zach and Mary want to make a graph of their toys. To complete the graph, draw one block for each toy. Draw them all the same size and lined up in a column, just like the ones for the dolls. d. How many more teddy bears do they have than dolls?” Students subtract based on data shown in the graph. 

Examples of connections between supporting work and major work of the grade that are entirely absent from the materials include, but are not limited to: 

• No connections are made between the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.), to the major work of 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.. 

• No connections are made between the supporting work of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks.) to the major work of 1.NBT.1(Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.) 

• No connections are made between the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.) 

• There are no connections between the supporting work of 1.G.1(Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes.) to any major standards in first grade.

The materials reviewed for Math Mammoth Grade 1, 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 1-A, Chapter 1: Addition Within 0-10, Introduction, “These same addition facts are studied again in the following chapter about subtraction. They are also used constantly in all later math work. I recommend that children become fluent with addition facts within 0-10 by the end of first grade.”

• Worktext 1-B, Chapter 5: Time, Introduction, “This lesson also includes a few exercises about reading clocks to five-minute intervals using a special clock that includes the numbers for the minute hand; however, these can be skipped if desired, because in second grade, the student will get a lot of practice reading the clock to the nearest five minutes.”

• Worktext 1-B, Chapter 7: Adding and Subtracting within 0-100, Introduction, “We study a trick with nine and eight, adding just one more than a known sum, and using the relationship between addition and subtraction to subtract. The actual memorization of the basic addition and subtraction facts within 0-18 is left for second grade.”

There is an example of a reference to prior grade learning, however this reference does not relate grade-level concepts explicitly to prior knowledge from earlier grades:

• Worktext 1-B, Chapter 4: Addition and Subtraction Facts, Introduction, “Mathematics builds upon previously learned concepts and facts and learning addition and subtraction facts is essential for later study, such as when students add 24 + 5 (in chapter 7 of this curriculum).