3rd Grade - Gateway 1

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that they assess grade-level content and, if applicable, content from earlier grades. 

Each Grade Level consists of 12 modules. Each module contains three types of summative assessments. Check-ups assess concepts taught in the module, and students select answers or provide a written response. Performance Tasks assess concepts taught in the module with deeper understanding. In Interviews, teachers ask questions in a one-on-one setting, and students demonstrate understanding of a module concept or fluency for the grade. In addition, Quarterly Tests are administered at the end of Modules 3, 6, 9, and 12.

Examples of assessment items aligned to Grade 3 standards include:

• Module 1, Check-Up 1, Problem 2, “Solve each problem. Write an equation to show your thinking. a. Luke has a sheet of stickers that has 10 rows of 5 stickers. How many stickers does he have in total? b. Mom cut 5 lengths of ribbon. Each piece was 4 inches long. What was the total length of the ribbon? c. Dad bought 8 balloons. They cost 10 cents each. How much did Dad pay for the balloons?” (3.OA.3)

• Module 6, Quarterly Test B, Problem 22, “A student figured the difference between 325 and 257 using the count-on strategy. Choose the equation that best matches. A. 325 - 257 = 57, B. 325 - 257 = 68, C. 325 - 257 = 65, D. 325 - 257 = 168.” (3.NBT.2)

• Module 9, Performance Task, Problem 1, “On the number line the distance from 0 to 1 is one whole. a. Label \frac{4}{6} and \frac{11}{8} on the number line. b. Write a fraction that is greater than \frac{4}{6} but has a denominator of 8. c. Write a fraction that is less than \frac{4}{6} but has a denominator of 6.” (3.NF.3).

There are some assessment items that align to standards above Grade 3; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include: 

• Module 3, Interview, students double numbers by finding the product of 2\times 30, 43\times 2, 2\times 35, 2\times 45, and 17\times 2. (4.NBT.5).

• Module 3, Check-Up 2, uses numbers over 1,000 for rounding to the nearest ten or hundred. In item 1.a., students round the following numbers to the nearest hundred: 391; 4,386; 7,019; 1,089. In item 1.b, students round the following number to the nearest ten: 674; 899; 3,562; 1,499.

• Module 3, Performance Task, students write the nearest ten, nearest hundred, and nearest thousand depending on where the arrow points on a number line with values between 7,500 to 7,600. Module 3 uses numbers over 1,000 for rounding to the nearest ten or hundred. 

• Module 3, Quarterly Test A, Problem 19, students round 5,346 to the nearest ten. Test B item 19 students round 1,452 to the nearest ten. Module 3 uses numbers over 1,000 for rounding to the nearest ten or hundred.

• Module 10, Interview, students find the area of a room that is 13\times 7. Students would need to be provided graph paper so they could draw out the room and count squares (4.NBT.5).

• Module 11, Check-Up 2, Problem 2, students figure change and identify coins and values of money. This does not relate to the standard of fluently adding and subtracting within 1,000 because decimals are required (5.NBT.7).

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials provide extensive work in 3rd grade by including different types of student problems in each lesson. There is a Student Journal with problems in three sections: Step In, Step Up, and Step Ahead. Maintaining Concepts are in even numbered lessons and include additional practice opportunities, including Computation Practice, Ongoing Practice, Preparing for Module _, Think and Solve, and Words at Work. Each Module includes three Investigations and, within grade 3, students engage with all CCSS standards. Examples of extensive work from the grade include:

• Module 1, Lesson 12 and Module 2, Lesson 4 engage students in extensive work with 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) as students use place value reasoning to solve problems. Lesson 12, Multiplication: Reinforcing the tens and five facts, Student Journal, Maintaining Concepts and Skills, Page 41, Question 1, “Cross out blocks to help you write the number of hundreds, tens, and ones that are left. Then write the difference. 465 - 130= ___. There are ___ hundreds. There are ___ tens. There are ___ ones.” Lesson 4, Addition: Developing written methods, Student Journal, Maintaining Concepts and Skills, Page 55, Question 2, “Write the number of hundreds, tens, and ones. Then write an equation to show the total. You can use blocks to help. 267 + 25. There are ___ hundreds. There are ___ tens. There are ___ ones. ___+___+___=___.”  Student Journals in Lessons 2, 4, 6, 8, 10, and 12 of each module, include two pages called Maintaining Concepts and Skills that provide all students additional practice in order to engage in extensive work with grade-level problems.

• Module 5 engage students in extensive work with 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations). In More Math, Problem Solving Activities, Activity 2, students reason about the relationship between quantities in a word problem. The teacher projects the question “At the zoo, one display has several spiders and a nearby display has legless lizards. Jayden counts 56 legs and 13 bodies in total in the displays. How many spiders and lizards are there?” Students work in partners to use eights and zeroes strategies to solve the word problem. Students discuss strategies with partners and then the class shares strategies as a whole.

• Module 9, Lesson 9, Common fractions: Comparing unit fractions (number line), engages students with extensive work with 3.NF.3d (Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model). In Student Journal, Step Up, page 344, Question 1, students use number lines to compare and order common fractions. “On each number line, the distance from 0 to 1 is one whole. a. Write the correct fraction above each mark on the number line. b. Split the distance from 0 to 1 into eighths and write the correct fraction below each mark. c. Write the correct fraction above each mark on the number line. d. Split the distance from 0 to 1 into sixths and write the correct fraction below each mark.”

The instructional materials provide opportunities for all students to engage with the full intent of 3rd grade standards through a consistent lesson structure, including sections called Step In, Step Up and Step Ahead. Step In includes a connection to prior knowledge, multiple entry points to new learning, and guided instruction support. Step Up engages all students in practice that connects to the objective of each lesson. Step Ahead can be used as an enrichment activity. Examples of meeting the full intent include:

• Module 4, Lesson 10, Common fractions: Representing unit fractions on a number line, engages students in the full intent of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram), 3.NF.2a (Represent a fraction \frac{1}{b} on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size \frac{1}{b} and that the endpoint of the part based at 0 locates the number \frac{1}{b} on the number line), and 3.NF.2b (Represent a fraction \frac{a}{b} on a number line diagram by marking off a lengths \frac{1}{b} from 0. Recognize that the resulting interval has size \frac{a}{b} and that its endpoint locates the number \frac{a}{b} on the number line.) In the Student Journal, Step Up, page 147, Question 2, students label three number lines with one-fourth, one-sixth, and one-eighth. “The distance between 0 and 1 is one whole. Split each number line into more equal parts. Then draw an arrow to show the fraction.”

• Module 6, Lessons 8 and 9, engage students in 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 Lesson 9, Data: Working with many-to-one picture graphs, Student Journal, Step Up, page 220, Question 1, “This table shows the pizza sales for 5 days. Complete the graph at the top of page 221 to show the results.”  Students draw circles in the bar graph to represent the data from the table. Each circle represents 10 pizzas. Question 2a “Look at the graph above. On what day were the most pizzas sold?” Question 2b “How many pizzas were sold before Thursday?” Question 2c “How many more pizzas were sold on Friday than Wednesday?” Question 2d “How many pizzas were sold in 5 days?” Question 2e “How many more pizzas were sold on Thursday and Friday than on Monday and Tuesday?“

• Module 11, Lesson 6, Number: Reinforcing rounding with five-digit numbers, engages students with the full intent of 3.NBT.1 (Use place value understanding and properties of operations to perform multi-digit arithmetic). In the Student Journal, Step Up, page 411, Question 3, students round multi-digit numbers to the nearest ten or hundred using place value understanding. “Round each number to the nearest ten and hundred. 14,312, 51,678, 29,087, 26,305.” Step Ahead, page 411, “Carmen rounds a number to the nearest ten. Her answer is 26,000. She then rounds the same number to the nearest hundred. Her answer is 26,000. She then rounds the same number to the nearest thousand. Her answer is 26,000. Write five possible numbers Carmen could have rounded.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days are included.

• The approximate number of modules devoted to major work of the grade (including supporting work connected to the major work) is 10 out of 12, which is approximately 83%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work, but not More Math) is 105 out of 156, which is approximately 67%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 94 out of 144, which is approximately 65%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in. As a result, approximately 65% of the instructional materials focus on major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. These connections are sometimes listed for teachers on a document titled, “Grade __ Module __ Lesson Contents and Learning Targets” for each module. Examples of connections include:

• Module 2, Lesson 9, Time: Measuring intervals in minutes, Student Journal, Step Up, page 69, connects supporting work of 3.MD.B (Represent and interpret data) to the major work 3.MD.A (Solve problems involving measurement and estimation). Students solve problems about time intervals using a number line. Question 2b, “Draw jumps on the number line to solve each problem. A frozen pizza is put in the oven at 1:35 p.m. The pizza is taken out of the oven 40 minutes later. At what time was the pizza taken out?”

• Module 4, Lesson 8, Common fractions: Reviewing unit fractions, Student Journal, Step Up, page 141, connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas) to the major work of 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts.) Students partition shapes into parts and determine the fraction. Question 3, “Each shape below is one whole. Color one part of each shape. Record the number of parts and then complete the fraction words. a. __ part of __ equal parts. ___ is shaded. b. __ part of __ equal parts. ___ is shaded c. __ part of __ equal parts. ___ is shaded.”

• Module 5, Lesson 12, Subtraction: Solving word problems, Student Journal, page 190, Step Up, connects supporting work 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) and major work 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic). Students solve multi-digit, multi-step word problems. Question 2b “Solve each problem. Show your thinking. A spool holds 192 feet of rope. 54 feet was first cut off, then another 75 feet. How much rope is left on the spool?”

• Module 6, Lesson 10, Data: Working with bar graphs, Student Journal, Step Up, pages 222-223, connects supporting work of 3.MD.B (Represent and interpret data) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic). Students read tables, create graphs, and then solve word problems. Question 1, “This table shows the mass of some American animals. Complete the bar graph at the top of page 223 to show the results. Raccoon, 32, Beaver, 55, Wolf, 89, Coyote, 50.” Question 2a “Which two animals are of similar mass?” Question 2b “Which three animals have a total mass of about 150 pounds?” Question 2c “What is the difference in mass between the wolf and raccoon?” Question 2d “What is the difference in mass between the beaver and wolf?” Question 2e “What is the total mass of the beaver, wolf, and coyote?”

• Module 6, Lesson 12, Data: Working with line plots (fractions), Student Journal, Step Up, pages 228-229, connects supporting work of 3.MD.B (Represent and interpret data) to the major work of 3.NF.A (Develop understanding of fractions as numbers). Students measure the length of pieces of spaghetti to the nearest \frac{1}{4} inch then plot the lengths on a line plot and answer questions about the data. Question 1, “Your teacher will give your group some pieces of dry spaghetti. Use your inch ruler to measure the length of 20 pieces. Round each length to the nearest fourth of an inch. Use tallies to record the lengths on this chart.” Question 2, “Look at the tally chart in Question 1 on page 228. Draw an x on the line plot below to show each length.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Materials are coherent and consistent with the Standards. Examples of connections include:

• In Module 1, Lesson 8, Multiplication: Using the turnaround idea with arrays, Teaching the lesson, lesson notes, students interpret products of whole numbers, 3.OA.1, and apply properties of operations as strategies to multiply and divide, 3.OA.B, by using arrays to show the properties of operations. 

• Module 6, Lesson 4, Multiplication: Solving word problems, Student Journal, p. 204, Step Up, Problem 1c, connects represent and solve problems involving multiplication and division 3.OA.A to solve problems involving the four operations 3.OA.D. Students are given a chart of County Fair Admission with prices: Child $4 each, Adult $9 each, Senior $5 each, and Weekend Pass $12 each. Solve each problem. Show your thinking. “If you buy two weekend passes, how much change will you receive from $30?”

• In Module 4, students represent and solve problems involving multiplication and division, 3.OA, and develop understanding of fractions as numbers, 3.NF.A. 

• In Module 6 student represent and solve problems involving multiplication and division,3.OA, and solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects, 3.MD.A, by using graphs to solve word problems involving multiplication and division.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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. 

Materials relate grade-level concepts from 3rd Grade explicitly to prior knowledge from earlier grades. These references are consistently included within the Topic Progression portion of Lesson Notes and within each Module Mathematics Focus. At times, they are also noted within the Coherence section of the Mathematics Overview in each Module. Examples include:

• Module 1, Lesson 7, Multiplication: Introducing the symbol, Lesson Notes connect 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) to work from grade 2 (2.OA.4). “In Lesson 2.11.5, students build arrays and describe them using rows of __. The lesson relates the set and area models of multiplication as students join the connecting cubes in each row to show groups. In this lesson (1.7), students use cubes to model multiplication problems and describe the representations using a variety of language.” 

• Module 5, Mathematics, Focus, Numbers and Operations in Base Ten, relates 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to 2.NBT.7 (Add and subtract within 1000, 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). “This module reviews and extends strategies to add two-digit numbers, and is interwoven with work involving Operations and Algebraic Thinking described above. Students review composing with two-digit and three-digit numbers to add.” 

• Module 11, Lesson 7, Money: Adding amounts in cents (bridging dollars), Lesson Notes connect 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to the work from grade 2 (2.MD.8). “In Lesson 2.11.12, students solve word problems involving money. In this lesson (11.7), students use coins to add prices involving cents that total more than one dollar.”

Content from future grades is identified within materials and related to grade-level work. These references are consistently included within the Topic progression portion of Lesson Notes and within the Coherence section of the Mathematics Overview in each Module. Examples include:

• Module 2, Lesson 12, 2D shapes: Exploring relationships between shapes, Lesson Notes connect 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) to work of grade 5 (5.G.3, 5.G.4). “In this lesson, students examine shapes whose properties allow them to belong to more than one shape family. Venn diagrams are used to sort shapes. In Lesson 5.5.10, students examine a defining feature of parallelograms.”

• Module 7, Mathematics Overview, Coherence, “This work extends the learning from previous study of addition (3.2.1–3.2.5) and prepares students to fully understand and use the standard algorithm for addition (4.2.1– 4.2.7).”

• Module 10, Lesson 6, Area: Solving word problems, Lesson Notes connect 3.OA.8 (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) to the work of grade 4 (4.NBT.5, 4.MD.3). “In this lesson, students build square units of area with materials and then solve word problems involving the same units of measure. In Lesson 4.3.9, students calculate area by covering rectangles with square-inch tiles and using the dimensions of the rectangles to determine the total number of square units of area. Students use this practice to develop a rule for calculating the area of rectangles.”