2nd Grade - Gateway 2

The instructional materials for ORIGO Stepping Stones 2.0 Grade 2 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include some problems and questions that develop conceptual understanding throughout the grade-level. Students have few opportunities to independently demonstrate conceptual understanding throughout the grade.

Cluster 2.OA.A includes representing and solving problems involving addition and subtraction. Modules 5, 6, 7, 8, and 9, explore a variety of real-world applications using a few mathematical representations.

Some opportunities exist for students to work with addition and subtraction addressing conceptual understanding through the use of some visual representations and different strategies. For example:

• In Module 8, Lesson 1, Step 3, Teaching the Lesson, “Organize the students into groups and distribute the base 10 blocks. Project the word problem (slide 1). Explain that Mr. Lee is carrying some base-10 blacks in a bag and that the blocks total 75. The students can then work in their groups to figure out the blocks the teacher might have in his bag. Explain that there are many possible combinations of tens and ones blocks and that one point will be awarded for each combination each group lists.”
• In Module 9, Lesson 2, Step 2, Starting the Lesson, “Project the empty number line (slide 1). Ask, What are some different numbers that we can show on this number line? Guide the students to explain that any number can be shown, as there are no marked numbers to act as benchmarks. On the left-hand side of the number-line mark the number 218. Ask, How can you show the number that is 100 greater? What about 200 greater? Choose a volunteer to draw jumps above the number line to show 318 and then 418. Reinforces that the size of each jump is not really important on an empty number line. Rather, it is the thinking behind the jumps being made. Repeat the activity by writing new three-digit numbers and having the students find a number that is 100, 200, or 300 greater.”
• In Module 10, Lesson 2, Step 3, Teaching the Lesson, “Project the word problem (slide 11), reading the problem aloud before asking, How could you figure out the amount of money that Sandra has left? Encourage the students to select resources (base-10 blocks, a number line, or the number chart) to help describe a variety of strategies and find the answer. Highlight the place value strategies.”

However, the instructional materials do not regularly provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level.

• In Module 1, Lesson 10, Student Journal 1.10, “Reviewing the count-on strategy.” Students are given dominoes to count-on and write the number sentence. Students don’t necessarily have to use the count-on strategy in order to solve the problem.
• In Module 1, Lesson 11, Step 2, Starting the Lesson, “Point to the vertical strip of numbers that is shown down the left-hand side. Clarify that these numbers show the totals. The numbers on the right-hand side show the parts. One part in each question is missing. Work through the equations, one at a time…” Students are not given any help in figuring out the missing numbers.
• In Module 8, Lesson 3, Step 3, Teaching the Lesson, “Say, I am going to give each pair of you 5 tens blocks and 15 ones blocks for this activity. Distribute the blocks and have students check that they have the correct value of the blocks. Project slide 1 as shown and discuss the points below: What is this question asking? How many blocks will you need to solve the problem? (5 tens and 5 ones.) Have students line up their 5 ten blocks and 5 ones blocks, placing their spare 10 ones blocks to one side. What number are you subtracting from 55? (46) If you use 5 ten blocks and 5 ones blocks, will you be able to show how to subtract 46? (No.) Have a volunteer demonstrate why." Students do not build conceptual understanding of subtraction with regrouping since the students are told exactly how to set up their problem to solve it.
• In Module 11, Lesson 10, Student Journal 11.10, “Write the missing numbers.” Students are given a selection of coins and a table showing how many of each coin is present and then asked to fill in the blank. For example, 4 dimes, 2 nickels and 3 pennies are shown. 4 dimes is ______¢. Students do not build conceptual understanding of money and its connection to the place value system.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 2 partially meet expectations that the materials are designed so that teachers and students spend time working with engaging applications of the mathematics.

The instructional materials have few opportunities for students to engage in non-routine application throughout the grade-level. There is little variety in situational contexts/problem types. Engaging applications include single and multi-step word problems presented in a context in which the mathematics is applied, however, these problems are often routine, and students have few opportunities to engage with non-routine application problems.

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

• In Module 2, More Math, Problem Solving Activities, Activity 4 addresses standard 2.OA.1 and has students read and find a solution to word problems. “Manuel has planted six seedlings in the garden. Kosa has planted one more seedling than Manuel in the same garden. How many seedlings are planted in total?”.
• In Module 3, More Math, Problem Solving Activities, Activity 4 addresses standard 2.OA.1 and has students read and find a solution to word problems. “There are some people on a bus. Four more people get on the bus. There are now nine people on the bus. How many were on the bus before?”.
• In Module 6, More Math, Problem Solving Activities, Activity 4 addresses standard 2.OA.1 and has students read and find a solution to word problems. “Emilia and Tyler are each using blocks to represent a two-digit number. Together they have 6 tens blocks, and 9 ones blocks. What possible numbers could their blocks be representing?”.
• In Module 7, Lesson 8, Whole Class, Step 3, Teaching the Lesson addresses standard 2.OA.1, “Project slide 2, as shown and read the problem aloud. Then discuss the points below (SMP 2): Norton has $72 in savings. Yasmin has $45 in savings. How much more money does Norton have?”.
• In Module 7, More Math Problem Solving Activities, Activity 4 addresses standard 2.OA.1, “Cooper has $65 in savings. Sara has $10 less than Cooper. Sara spends $28 at the store and gives $5 to her brother. How much money does Sara have left?”.
• In Module 8, Lesson 5, Student Journal 8.5, addresses standard 2.OA.1, “Read each problem. Then color the label to show your estimate. a. The movie runs for 96 minutes. Evan pauses the movie after 54 minutes to make some popcorn. About how many more minutes will the movie run?”.
• In Module 9, More Math, Problem Solving Activities, Activity 4 addresses standard 2.OA.1, “Noah is on vacation. He pays $502 for the hotel, $86 for food, and $219 for a tour package. How much does Noah pay in total?”.
• In Module 10, More Math, Problem Solving Activities, Activity 4 addresses standard 2.OA.1, “Nancy buys a bicycle for $172. Cody buys a bicycle for $5 less. How much did Cody spend?”.
• In Module 11, More Math, Problem Solving Activities, Activity 4 addresses standard 2.OA.1, “ Teresa has 3 bags of apples. Each bag has three apples in it. How many apples does Teresa have in total?”

There are no instances where students engage in non-routine problems.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 2 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

There is some evidence that the curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials have an emphasis on fluency, procedures, and algorithms.

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

• In Module 4, Lesson 2, Student Journal 4.2, students solve subtraction problems with a number track. For example, “2. Write an equation to match what is shown on each number track.”
• In Module 8, Lesson 3, Student Journal 8.3, students use conceptual understanding to solve subtraction with regrouping problems. For example, “1. In the pictures below, a tens block has been regrouped as 10 ones blocks. Cross out blocks and complete the sentences to figure out the difference.”
• In Module 9, Lesson 6, Step 3, Teaching the Lesson, students use conceptual understanding to solve addition problems. “Use base-10 blocks to demonstrate using a place-value method to find the total. As you demonstrate with the blocks, discuss the points below “How many hundreds are there? How many tens? How many ones? What is the total of the hundreds, tens, and ones? How do you know? Discuss the different ways of calculating the total from this point.”
• In Module 8, More Math, Problem Solving Activities, Activity 4, “A Grade 2 class has 121 prizes in their prize box. Students pick a prize after they earn 10 stars. In the first week of school, 17 students win a prize, 28 students win a prize in the second week. How many prizes are left after the second week?” (2.OA.1)

Examples of students having opportunities to engage in problems that use two or more aspects of rigor, include:

• In Module 6, Lesson 9, Student Journal 6.9, students use conceptual understanding and application to solve two-digit numbers, “1. Add the tens blocks then add the ones blocks. Write an equation to match.”
• In Module 7, Lesson 6, Student Journal 7.6, students use conceptual understanding and application to solve subtraction problems with a number line. For example, “1. Alisa’s jump was 53 inches and Allan’s jump was 75 inches. Count on to figure out the difference. Draw jumps to show your thinking. Then complete the equation.”

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MPs 4 and 5.

For MP4, students are given models to use and have few opportunities to develop their own mathematical models. In addition, students have few opportunities to compare different models in problem contexts, for example:

• In Module 3, Lesson 7, Step 2, Starting the Lesson, the teacher is playing a game with the students where they say 10 and 100 more or less than a number. “...You may also wish to display or refer students to a hundred chart to support students who require it, modeling the way in which this resource can be used to identify numbers that are 10 more or less - SMP4.)”
• In Module 8, Lesson 2, Step 2, Starting the Lesson, “At the end of each round have the students sit in their groups while the class discusses and explores the possibilities. Ask them to draw a picture of the blocks used to make the groups. (SMP4)” Students do not choose how to model the groups..
• Module, 10, Lesson 1, Step 3, Teaching the Lesson, “Project slide 2 and distribute the support pages. Have pairs of students use the eight number lines on their page to show how to figure out the eight problems. (SMP4)” Students do not choose which model to use.

For MP5, students are given few opportunities to use tools strategically, as they are most often given the tools to use for a problem, for example:

• In Module 3, Lesson 1, Step 3, Teaching the Lesson, “Using the blocks shown here, what will we write in the hundreds place? Have a student write 5 in the hundreds place on the expander (SMP5).”
• In Module 8, Lesson 1, Step 3, Teaching the Lesson, “Organize students into groups and distribute the base 10 blocks. Project the word problem (slide 1). Explain that Mr. Lee is carrying some base ten blocks in a bag and that the blocks total 75. The students can then work in groups to figure out the blocks the teacher might have in his bag. (SMP5)”
• In Module 10, Lesson 4, Step 3, Teaching the Lesson, “Have each group confirm the difference using base ten blocks and number lines. (SMP5)”

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials, but there are no instructions on how to use the language of mathematics. While vocabulary is identified throughout the materials, there is no explicit directions for the instruction of the vocabulary for the teacher in the Steps portion of the lesson. Examples include but are not limited to:

• Vocabulary for each module is found under Mathematics, Vocabulary Development. Vocabulary identified in bold print is developed throughout the module. The targeted module vocabulary words can be printed onto cards under the Resources tab. For example, in Module 1, vocabulary includes words such as addition, even, and odd.
• The vocabulary words do not have the definitions.
• Not all the vocabulary words are in the glossary, for example, straight sides.
• Materials use the term “Turn around facts” and “friendly pairs,” which is not accurate terminology.
• Each module contains a parent newsletter. The newsletter highlights key vocabulary and provides the definition for parents in the Glossary section of the newsletter.