4th Grade - Gateway 1

The instructional materials for Into Math Florida Grade 4 meet the expectations for assessing grade-level content. An Assessment Guide, included in the materials, contains two parallel versions of each Module assessment, and the assessments include a variety of question types. In addition, there is a Performance Task for each Unit, and there are Beginning, Middle, and End-of-Year Interim Growth assessments.

Examples of assessment items aligned to grade-level standards include:

• Unit 2 Performance Task, Question 2, “Hannah flies over the country and makes a round trip from California to New Hampshire. Raoul says the miles she traveled is equal to the quotient for 5286 ÷ 3. How many digits will the number of miles she traveled have? Explain your reasoning.” (4.NBT.2.6)
• Module 12, Form A, Question 6, students determine if two fractions with denominators of 10 and 100 are equivalent to a given decimal. The choices are $$\frac{9}{10}$$, $$\frac{9}{100}$$, .009; $$\frac{2}{10}$$, $$\frac{2}{100}$$, .20; and $$\frac{8}{10}$$, $$\frac{8}{100}$$, .80. (4.NF.3.6)
• Module 14, Form A, Question 5, students solve a story problem requiring addition and subtraction of fractions with like denominators. (4.NF.2.3d)
• Module 19, Form A, Question 9, “Marcus buys an 8-pound pumpkin. He takes it home and removes 12 ounces of seeds and pulp. How many ounces does his pumpkin weigh now?” (4.MD.1.2)
• End-of-Year-Test, Question 12, “The city council where Antonio lives is planning to make the downtown area a better place to visit. The city council plans to spend $59 each on 48 small lamp posts and $63 each on 55 park benches. How much more is Antonio’s city council planning to spend on park benches than on lamp posts?” (4.OA.1.3)

Above grade-level assessment items are present, but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. These items include:

• Modules 11 and 13, the following problems use denominators outside of the range of possible denominators for 4.NF: Module 11, Form A, Questions 2 and 13; Module 11, Form B Questions 2, 3, and 13; and Module 13, Forms A and B, Question 6.
• Module 20, Form A, Questions 10 and 13, students convert from millimeters to centimeters and from milliliters to liters. This is converting from smaller units to larger units and aligns to 5.MD.1.1.

The instructional materials reviewed for Into Math Florida Grade 4 meet the expectations for spending a majority of instructional time on major work of grade.

• The number of Modules devoted to major work of the grade is 13 out of 21, which is approximately 62%.
• The number of Lessons devoted to major work of the grade (including supporting work connected to the major work) is 71 out of 108, which is approximately 66%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 108 out of 175 days, which is approximately 62%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and isn’t dependent on pacing suggestions. As a result, approximately 66% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Into Math Florida Grade 4 meet the expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of how the materials connect supporting standards to the major work of the grade include:

• Module 10, Teacher Manual, Lessons 1-4, 4.OA.2.4 supports the major work of 4.NBT.2. For example, Lesson 2, Question 7, students decide if seven is a factor of 91 and justify their answer by using division. Lesson 3, Question 4, students solve a story problem by using four as a factor.
• Module 11, Teacher Manual, Lesson 4, connections are made between the major work of 4.NF.1 and the supporting work of 4.OA.2.4. In Question 2, students list the factors of eight and 12, referring to the fraction $$\frac{8}{12}$$. Students use common factors between eight and 12 to write equivalent fractions.
• Module 19, Teacher Manual, Lesson 5, 4.MD.2.4 supports the major work of 4.NF.1.2. For example, in Question 1, students plot fractions on a line plot requiring students to first create equivalent fractions, then compare and order them correctly along the line plot.
• Module 19, Lesson 5, On My Own, Question 7, 4.MD.2.4 supports the major work of 4.NF.2.3d when students solve fraction addition and subtraction problems with data given in line plots. For example, “A local pizzeria held a pizza eating contest. The fractions below (all with a denominator of 8) represent the amount of pizza each contestant ate in 5 minutes. Make a line plot to display the data. How much more pizza did the winner eat than the person who came in last place?”

The instructional materials for Into Math Florida Grade 4 meet the expectations that the amount of content designated for one grade-level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 175 days, 123 days for lessons and 52 days for assessments.

• The Planning and Pacing Guide and Planning pages at the beginning of each module in the Teacher's Edition provide the same pacing information.
• Grade 4 has 7 Units, with 21 Modules containing 108 lessons.
• The pacing guide designates 8 lessons as two-day lessons and 100 as one-day lessons, leading to a total of 116 days. The materials do not define the number of minutes in a lesson or instructional day.
• Each Unit includes a Unit Opener, there are seven Openers for Grade 4 (seven days).
• Each lesson includes a variety of supplemental instruction such as: reteaching lessons, Flipbook lessons, etc. There is no guidance around building in days for differentiation, therefore no additional days were added.
• This is a total of 123 lesson days.

Assessments include:

• The Planning and Pacing Guide indicates a Beginning, Middle, and End of Year Interim Growth assessment that would require one day each (three days).
• Each Unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are seven Performance Tasks for Grade 4 (seven days).
• Each Module has both a review and an assessment. There are 21 Modules (42 days). Based on this, 52 assessment days can be added.

The instructional materials for Into Math Florida Grade 4 meet the expectations for the materials being consistent with the progressions in the Standards. In general, the materials identify content from prior and future grade-levels, as well as relating grade-level concepts explicitly to prior knowledge from earlier grades. In addition, the instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

The introduction for every Module in the Teacher Edition includes “Mathematical Progressions Across the Grades” identifying standards under the areas of Prior Learning, for Current Development, and Future Connections, as well as clarifying student learning statements in these categories. For example, Module 18, Lesson 2, builds upon work done on 2.MD.1.1 during Grade 2. The work will continue in 5th grade, Module 12, Lesson 1, with a focus on standards 5.MD.1.1. In Activate Prior Knowledge at the beginning of each lesson, content is explicitly related to prior knowledge to help students scaffold new concepts. Additional features of the materials further support the progressions of the standards. These include:

• In the beginning of each module includes a diagnostic assessment called “Are You Ready?” identifying prior knowledge needed for the current module. Module 5 shows the link to prior learning for Multiplication Facts as Grade 3, Modules 4 and 5 (3.OA.3.7) in the Data-Driven Intervention Chart. A narrative is provided for each skill on the page. “Multiplication Facts:  These items assess whether students are able to find the product of two 1-digit numbers using a variety of strategies. In upcoming lessons, students may use these strategies to multiply larger numbers.”
• Each lesson the standard of focus is explicitly connected to work in future and prior grades.  For instance, Module 20 Lesson 2 identifies the lesson focus as standard 4.MD.1.1.

There is one instance of off-grade level work that is not clearly marked:

• Module 20, Lesson 2, On My Own, Problems 3, 4, and 6, students convert from a larger unit to a smaller unit.  For example, 9 kilometers = ____ meters. Question 5 asks students to convert from a smaller unit to a larger one, 70mm = ___ cm.  Additionally, homework practice, Question 5, students convert from 6,000 m = ______ km (5.MD.1.1)

The materials give all students extensive work with grade-level problems. Students spend four to eight days within each module and one day per lesson. Each lesson includes a Problem of the Day to activate prior knowledge, a Spark your Learning portion as an introduction to the day’s learning goals that usually embeds partner or group work to solve a problem.  Each lesson includes grade level work in the Build Your Understanding, Step It Out, and On My Own. Additionally, Reteach and Challenge pages are available for each lesson which provide more practice with grade level work. For example:

• Module 8, Lesson 3, Build Understanding, students relate area models to partial products to multiply two-digit by two-digit numbers. For example, Question 1B,  “How can you use an area model to show the product?” Question 1C, “How can you write multiplication sentences to find the partial products?” During On My Own, students solve Question 2: “Write and solve an equation for the area model.” Additional practice is provided in More Practice/Homework (4.NBT.2.5).
• Module 12, Lesson 4, Step It Out, students compare decimals to hundredths using hundredths grids, number lines, and place value charts. During On My Own, students solve Question 3, “Chris has two kittens, Oscar and Tiger. Which kitten is heavier? Shade the hundredths model for each weight, and locate the weights on the number line.” (4.NF.3.7)
• Module 19, Lesson 5, Step it Out, students represent and interpret measurement data in line plots. Question 1, “The weights of some cell phones and tablets are shown. How can you display these data using a line plot?” On My Own has six questions where students create line plots and interpret the data.  Question 7, “A local pizzeria held a pizza-eating contest. The fractions below represent the amount of pizza each contestant ate in 5 minutes. Make a line plot to display the data. How much more pizza did the winner eat than the person who came in last place?” (4.MD.2.4)

The materials relate grade-level concepts to prior knowledge from earlier grades. Example includes: 

• Module 6, Lesson 2, Investigate Remainders, students build upon their prior knowledge of understanding division as separating objects into equal groups (3.OA.1.2) and representing division using arrays and bar models (3.OA.1.3). Students apply this knowledge to investigate remainders (4.NBT.2.6). For example, Module 6, Lesson 2, Question 2, students solve a word problem where 35 pencils are needed to make 8 party favor bags. Students create a drawing to show how all the pencils can be divided. Then, describe how many total pencils were drawn, how many pencils went into each bag, and how many pencils were left over (remainder) and to tell why.

The instructional materials reviewed for Into Math Florida Grade 4 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, and examples of this include:

• In Lesson 1.2, the learning objective, place value relationships to read and write multi-digit whole numbers to 1,000,000 in different forms is shaped by 4.NBT.1: Generalize place value understanding for multi-digit whole numbers.
• Lesson 11.7, the learning objective, comparisons to order fractions is shaped by 4.NF.1: Extend understanding of fraction equivalence and ordering.
  
• In Lesson 12.4 the learning objective, compare decimals using visual models, number lines, or place value is shaped by 4.NF.3: Understand decimal notation for fractions, and compare decimal fractions.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

• Module 11, Lesson 3, connects 4.NF.2 to 4.OA.1. For example, Question 2, students create a fraction equivalent to $$\frac{1}{2}$$, with 6 as the denominator. Then, students describe the relationship between the numerator and denominator of each fraction.
• Lesson 14.6, connects 4.NF.3 with 4.NF.1 when students use equivalent fractions to write fractions with denominators of 10 as denominators of 100, and then add like denominators. For example, On My Own, Question 9, “$$\frac{22}{100}$$ + $$\frac{7}{10}$$”.