3rd Grade - Gateway 1

The instructional materials for  HMH Into Math Grade 3 meet 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 assessments.

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

• Module 4, Form A, Question 9, students “write a multiplication expression to complete the equation   _____$$\times$$_____ = 18”. (3.OA.4) 
• Unit 5, Performance Task, students draw a picture graph to represent the drinks sold at a coffee shop. “Mario collects information about the drinks sold today. Use the data to make a picture graph. Include a key.” (3.MD.3) 
• Module 9, Form A, students solve, “Roman has 293 snap blocks. He uses 69 of the snap blocks to make an airplane and 32 to make a car. About how many snap blocks does Roman have left?” (3.NBT.1)
• Module 16, Form B, Question 4, students identify equivalent fractions by matching pairs of differently-partitioned and shaded rectangles. (3.NF.3a.)

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for spending a majority of instructional time on major work of the grade.

• The number of modules devoted to major work of the grade is 14 out of 20, which is approximately 70%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 72 out of 100, which is approximately 72%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 118 out of 170 days, which is approximately 69%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and is not dependent on pacing suggestions. As a result, approximately 72% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for HMH Into Math Grade 3 meet 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:

• Lesson 10.6, Check Understanding, Question 1, 3.NBT.2 supports the major work of 3.OA.8 when students solve two-step word problems using the four operations. “Kai has 65 stamps. He buys 7 more stamps. He uses all of the stamps to fill 9 equal pages. How many stamps are on each page? Write two equations to model the problem.”
• Lesson 13.2, On Your Own, Question 8, 3.G.2 supports the major work of 3.NF.1 when students partition shapes into parts with equal areas and represent those parts as fractional values. Question 8, “Write a fraction to name the part of the whole or the part of the group that is blue”. A square divided into two parts is given. 
• Lesson 14.1, Teacher’s Manual, Question 3, 3.G.2 supports 3.MD.5. Students are asked to examine a rectangle divided into 4 shaded parts and determine if the parts are the same shape. Then students determine if the shapes have the same area by counting unit squares. 
• Lesson 14.3, Check Understanding, Question 2, 3.G.2 supports the major work of 3.NF.A.1. Students partition shapes into parts with equal areas and represent those parts as fractional values. “Divide the shape into 3 equal areas. What unit fraction names each equal part of the shape?”
• Teacher’s Manual, Lessons 18.1-4, align to 3.MD.3 and 3.OA.3.Lesson 2, Question 1, students choose a scale amount for their picture graph. They then divide the quantities in the data table by their chosen scale amount to determine how many representative pictures to draw. Students use subtraction to solve the remaining questions. 

The instructional materials for HMH Into Math Grade 3 meet 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 170 days, 121 days for lessons and 49 days for assessments.

• The Planning and Pacing Guide and Planning pages at the beginning of each module in the Teacher Edition provide the same pacing information. 
• Grade 3 has 6 units with 20 modules that contain 100 lessons. 
• The Planning and Pacing Guide designates 15 lessons as 2-day lessons and 85 as 1-day lessons, leading to a total of 115 days. The materials do not define the number of minutes in a lesson or instructional day.
• Each unit includes a Unit Opener, there are 6 unit openers for Grade 3 (6 days).
• Each lesson includes a variety of supplemental instruction, such as reteaching lessons, flipbook lessons, etc. However, there is no guidance around building in days for differentiation; therefore, no additional days were added.
• There are a total of 121 lesson days.

Assessments included: 

• The Planning and Pacing Guide indicates a Beginning, Middle, and End-of-Year Interim Growth assessment that would require 1 day each (3 days). 
• Each unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are 6 performance tasks for Grade 3 (6 days). 
• Each module has both a review and an assessment. There are 20 modules (40 days). 
• Based on this, 49 assessment days can be added.

The instructional materials for HMH Into Math Grade 3 meet expectations for the materials being consistent with the progressions in the Standards. The materials identify content from prior and future grade-levels, relate grade-level concepts explicitly to prior knowledge from earlier grades, and 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, which identifies standards from Prior Learning, for Current Development, and makes Future Connections, as well as clarifying student learning statements in these categories. For example, before Lesson 3.1, Multiply with 2 and 4, Prior Learning is identified as “counted objects by 2’s, write equations to represent the sum of equal addends.” (2.OA.3 and 2.OA.4) Future Connections identify “will solve multi-step word problems” and “will write equations with one variable to represent multi-step word problems.” (4.OA.3) Additional features of the materials further support the progressions of the Standards. These include:

• The beginning of each module includes a diagnostic assessment, Are You Ready?, that explicitly identifies prior knowledge needed for the current module. For example, Module 4 links prior learning to Grade 2, Lesson 2.3, Count Equal Groups. (2.OA.4)
• In each lesson the standard of focus is explicitly connected to future work. For example, Lesson 6.1 states the lesson focuses on standard 3.OA.3. This work will continue in Grade 4 with a focus on standards 4.OA.2 and 4.NBT.6 during Lesson 6.1-6.6 and 7.1-7.4. 

The materials give all students extensive work with grade-level problems. The lesson structure includes Spark Your Learning, Build Understanding, and Step It Out where “students connect important processes and procedures to mathematical concepts, Independent Practice, and Math Center Activities. For example: 

• Lesson 2.3, Build Understanding, students relate area to addition and multiplication. (3.MD.7a) Students find the area of a card two ways using both multiplication and addition. During Step It Out and On Your Own, students complete problems to “Find the area of the figure. Show repeated addition. Show multiplication.”
• Lesson 7, Build Understanding, students relate multiplication and division. (3.OA.6.) Question 1 states: “Jackson plants pepper plants in 3 equal rows. He plants 18 plants. How many plants are in each row?” Students write both multiplication and division equations for the problem and explain how the equations are the same and different.  
• Lesson 15.3, Build Understanding, has students compare fractions with the same numerator  using drawings, number lines, and by reasoning about the number and size of the parts. (3.NF.3d)

The materials explicitly relate grade-level concepts to prior knowledge from earlier grades in the Mathematical Progressions Across the Grade which links explicitly to standards. In addition, the materials include options for the lesson warm-ups to Activate Prior Knowledge to “Use these activities to quickly assess and activate prior knowledge…”; however, no standards are identified for these activities. For example:

• Lesson 3.3, Multiply with 3 and 6, Activate Prior Knowledge, Problem of the Day: “April and 5 of her friends each made 5 friendship bracelets. Write an equation to show the total number of friendship bracelets April and her friends made.” Based on student responses, teachers can use an Interactive Reteach from Lesson 3.2 or complete a prerequisite skills activity such as “Brienne has 7 bags of shells. There are 5 shells in each bag. How many shells does Brienne have?”
• Lesson 6.2 Separate Objects into Equal Groups, Activate Prior Knowledge, Problem of the Day: “Draw Arrays: Use 12 tiles. Make as many different arrays as you can using all 12 tiles.” Based on student responses, teachers can use an Interactive Reteach from Grade 3, Lesson 1.3, or complete an additional Prerequisite Skills Activity. 
• Lesson 13.2 builds on this knowledge to introduce fractions as partitioned areas of a shape. For example, question 1 asks students to draw a model of a fence that is divided into fourths where one of the fourths is painted. It then asks students to identify how many equal parts in the whole fence, how many parts are being counted, and relates that to writing a fraction as $$\frac{1}{4}$$. (3.G.2)

The instructional materials reviewed for HMH Into Math Grade 3 meet 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. Examples include:

• Lesson 2.3, the learning objective “Relate finding area to using an array to find a product,”  is shaped by 3.MD.3, geometric measurement: understand concepts of area and relate area to multiplication and addition.
• Lesson 8.4, the learning objective states “Develop strategies and use reasoning to represent and solve two-step word problems” which is shaped by 3.OA.4: “Solve problems involving the four operations and identify and explain patterns in arithmetic.”
• Lesson 10.2, the learning objective states “Use place value strategies to add 2- and 3- digit numbers” which is shaped by 3.NBT.1: “Use place value understanding and properties of operations to perform multi-digit arithmetic.”
• Lesson 12.1, the learning objective states “Read, write, and tell time on analog and digital clocks to the nearest minute” which is shaped by 3.MD.1: “Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.”

The materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

• Lesson 2.3 identifies and connects the following Mathematical Standards in the Lesson Focus and Coherence: “Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
• Lesson 4.4 connects 3.OA.1 with 3.OA.3 as students multiply with 7’s. Students use multiplication to solve word problems and fluently multiply within 100.
• Lesson 18.1 connects 3.NBT.2 with 3.MD.3 as students use scaled graphs to answer questions about how many more and how many less and fluently adding and subtracting within 1000.