3rd Grade - Gateway 2

The instructional materials for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. Materials attend to the Grade 3 expected fluencies, single-digit products and quotients (products from memory by end of Grade 3) and add/subtract within 1000.

The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills.

The materials attend to the Grade 3 expected fluencies, fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations (3.OA.7). By the end of Grade 3, know from memory all products of two one-digit numbers. For example, In Module 3, Lesson 1, students build fluency through completing Maintaining Concepts and Skills. In Maintaining Concepts and Skills, students identify addition, subtraction and multiplication facts primarily of fives and tens.

In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency:

• Maintaining Concepts and Skills lessons incorporate practice of previously learned skills from the prior grade level. For example, Maintaining Concepts and Skills in Module 1, Lesson 2, provides practice for adding and subtracting within 20 (2.NBT.2).
• Each module contains a summative assessment called Interviews.  According to the program, “There are certain concepts and skills , such as the ability to route count fluently, that are best assessed by interviewing students.”  For example, Module 4’s Interview 1 has students demonstrate fluency of 2’s multiplication facts and Interview 2 has students demonstrate fluency of 4’s multiplication facts.
• Fundamentals Games contain a variety of computer/online games that students can play to develop grade level fluency skills. For example Double Bucket, students demonstrate fluency of 2’s multiplication facts and on Interview 2 students demonstrate fluency of 4’s multiplication facts (3.OA.7).
• Some lessons provides opportunities for students to practice the procedural fluency of the concept being taught in the Step Up section of the student journal.
• Activities provide practice for skills learned earlier in the grade such as, Module 9, Lesson 6 where students practice multiplication facts (3.OA.7).

The instructional materials for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that the materials are designed so teachers and students spend time working with engaging applications of the mathematics.

Engaging applications include single and multi-step word problems presented in contexts in which the mathematics is applied. There are routine problems, and students also have opportunities to engage with non-routine application problems. Thinking Tasks found at the end of Modules 3, 6, 9, and 12, provide students with problem-solving opportunities that are complex and non-routine with multiple entry points.

Examples of routine application problems include, but are not limited to:

• In Module 1, Lesson 7, addresses standard 3.OA.3, “Henry cut 5 lengths of rope. Each piece was 4 meters long. What was the total length of rope?".
• In Module 4, Lesson 6, addresses standard 3.OA.3, “32 chicken nuggets are shared equally among 8 friends. How many nuggets are in each share?”.
• Maintaining Concepts and Skills includes some application problems and addresses standard 3.OA.8, for example Module 3, Lesson 8, “Samuel’s mom bought 3 tickets for the roller coaster. Tickets are $4 each. What was the total cost?”.
• In Module 4, Lesson 4, addresses standard 3.OA.8, “Michelle’s grandmother gave her $40 to spend at the county fair. Michelle had 6 rides on the Mega Drop and 4 rides on the Rollercoaster. Rides on the Mega Drop cost $5 each and rides on the Rollercoaster cost $8 each. She also bought lunch for $12 at the end of the day, she has $2 left. How much of her own money did she take to the fair?”.
• In Module 1, Problem Solving Activity 3, addresses standard 3.OA.3, “Stella has been collecting baseball cards. Every week she doubles the number of baseball cards she has. Stella has 120 cards. How many cards did she have three weeks ago? How many cards will Stella have next week?”.
• In Module 8, Problem Solving Activity 4 has eight story problems and addresses standard 3.OA.3, “A farmer planted fruit trees in rows of 9. He planted 81 trees in total. How many rows did he plant?”.

Examples of non-routine application problems with connections to real-world contexts include, but are not limited to:

• In Module 2, Investigation 2, students brainstorm a list of real-life situations where it would be necessary to read and write time to the nearest minute. In the extension, students brainstorm situations where it would be necessary to write time to the nearest second (3.MD.1).
• In Module 3, Thinking Task, Question 2 states, “A class of Grade 3 students is raising money for a field trip. They decide to run a car wash as a fundraiser. Customers can decide between three different types of car washes (A chart with car wash prices is provided). At the end of the carwash, the Premium Wash option raised $90. The Quick Wash option raised the same amount. How many cars were washed with the Quick Wash option?”
• In Module 6, Thinking Task, Question 1 states, “This year, the PTA raised $300 to plant a school garden. The PTA president announces that this year they raised $124 more dollars than last year. How much money did they raise last year.”
• In Module 9, Thinking Task, Question 1 provides a diagram of where students and families will sit during a choir performance in the gym. Questions include, “How many students will fit in each full row of the risers? What is the greatest number of students who can stand on all the risers to perform all at once?”
• In Module 12, the Thinking Task states, “Mrs Chopra’s Grade 3 class has been asked to hang their drawings on a folding display board, the board has four rectangular panels, each panel is 3 feet x 6 feet, drawings can be posted on the front and the back of each panel, all the drawings were made on rectangular paper in three different sizes.” A table of drawing sizes is provided with the following information: 32 small 1 x 1, 16 medium 1 x 2, 8 large 2 x 2. Question 1: “What is the area of each panel?” Students must use the information from the table to answer the question. Question 2 states, “Write an expression that shows how to find the total area for the front and the back panels of the display board."

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

All eight MPs are clearly identified throughout the materials. For example:

• The Math Practices are initially identified in the Steps portion of each module course information.
• Videos for each module can be found under the Resources tab which explains the Math Practices and Habits of Mind.
• A table is provided to show which mathematical practices are in each lessons.
• Resources states that each practice standard is, “experienced, practiced, and enhances as a result of working on meaningful problems”.
• Module Lessons tabs have a Lesson Contents overview that lists each lesson and the standards and mathematical practices in the lesson.

The MPs are used to enhance the mathematical content and are not treated separately from  content in lessons. However, there is limited guidance for teachers on the connections between the MPs and the content standards.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of the lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments, and in other lessons, teachers are provided questions and sentence stems to facilitate students in analyzing the arguments of others, and to justify their answers.

Examples where teachers are provided guidance to engage students in constructing viable arguments and/or analyzing the think of others include, but are not limited to:

• In Module 3, Lesson 9, students reflect on the question, “When comparing 2 three-digit numbers, can one number be greater than the other even though there are fewer hundreds in the number? Students are invited to share their thinking with the class. Teachers encourage respectful critique using sentence stems such as: I agree/disagree with your answer because, So what you’re saying is, and Why do you think that?”.
• In Module 5, Lesson 6, students explain the pattern in their own words to a partner and the partner responds. Teachers prompt students to listen without interrupting and to use the sentence stems, “I noticed the same pattern and I also noticed, I don’t think that shows a pattern because, and I looked at the equations in a different way.”.
• In Module 8, Lesson 9, students place fractions on a number line and name other fractions located at the same point. Teachers encourage students to justify their thoughts and critique the reasoning of others by prompting the discussion with sentence stems, "I know these fractions are equivalent because, I think the fractions ___ and ___ are equivalent because, and I agree/disagree with your answer because...”.
• In Module 10, Lesson 6, students share their labeled sketches for Question 1. Teachers are prompted to remind students to listen carefully and critique the problems using the sentence stems, “I can identify the numbers from the equation in Problem, I don’t think that problem matches because, We could change the problem by, and The area is not correct because.”