1st Grade - Gateway 2

The instructional materials for ORIGO Stepping Stones 2.0 Grade 1 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 1.OA.A includes representing and solving problems involving addition and subtraction. Modules 4, 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 2, Lesson 2, Step 3, Teaching the lesson, students are shown how to count on starting at 5. “Invite one student to come to the front and use their fingers to show a number from five to ten, starting from the class’s left, Make sure they use both hands to show each number. For example, to show six, they show five fingers raised on their right hand and one finger raised on their left.”
• In Module 7, Lesson 2, Student Journal 7.2 “Writing three-digit numbers to 120 (without teens)” The worksheet has students using base ten blocks to determine the number, then writing the number on the number expanders with it expanded, and writing it on the expander without it expanded.
• In Module 8, Lesson 1, Step 3, Teaching the lesson, “Allow time for the students to explore the different possible combinations of ten. Then have them paste groups of animals onto their paper, and write the matching equation next to each group. When they have finished, have students leave their work at their desk and stand to look at the other pairs’ combinations of animals and legs. After students have had the chance to view the different works, lead a discussion about the different ways student made ten legs. Ask students to share observations about making ten.”
• In Module 11, Lesson 5, Step 2, Starting the lesson, “Organize students into pairs. Project the Flare Number Board online tool. Ask the students to work together to identify patterns they find on the chart. sufficient time, invite several pairs to come to the board and highlight numbers to show and explain their patterns. After the students have shared their patterns, clear the hundred chart and highlight multiples of five in one shade, then highlight multiples of ten in a different shade. Ask a student to then come to the front and highlight of two in a third shade. Then discuss the points below: What patterns or observations can you make from our chart? Why do you think the tens column has three colors on each number? When looking at these patterns, are these the only numbers that can be said when asked to count by twos, fives, or tens? Why or why not?” This lesson addresses conceptual understanding of addition by examining the patterns on a 100s chart.

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

• In Module 7, Lesson 7, Step 3, Teaching the lesson, “Project slide 3, as shown, and discuss the points below: What do you see in this picture? How is it the same as the previous picture? (It is a think-addition card.) How is it different? (It has different numbers, one flap is down.) What equations could we create from this card? (8+___=17, 17-8=___.) What strategy could we use if we wanted to think addition? (Double-plus-1.) Who can think aloud and tell us how you use the strategy and give us the answer?” This lesson addresses filling in the blanks instead of the conceptual understanding of using addition to solve subtraction problems.
• In Module 8, Lesson 5, Student Journal 8.5, “Write an addition fact to match each picture. Then write the turnaround fact.” This worksheet gives students a domino and students are to write two addition facts based on the dots on the dominoes. These problems address the commutative property but not a conceptual understanding of the commutative property and when to best use it.
• In Module 10, Lesson 1, Student Journal 10.1, “Write numbers to match each picture.” The worksheet has students count the pictures and fill in the blanks instead of building conceptual understanding of subtraction.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 1 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 1, More Math, Problem Solving Activities, Activity 4 addresses standard 1.OA.1 and has students solve word problems. “Allan has fifteen stickers in his collection. Charlotte has two fewer stickers in her collection. How many stickers does Charlotte have?”.
• In Module 2, More Math, Problem Solving Activities, Activity 4 addresses standard 1.OA.1 and has students solve word problems. “Hugo saves seven dollars to buy a new game. If his dad matches the amount, how much will Hugo have in total?”.
• In Module 3, More Math, Problem Solving Activities, Activity 4 addresses standard 1.OA.1 and has students solve word problems. “Four students are using their fingers to show a number. Three students are holding ten fingers up. One student is holding five fingers up. Write in words the number they are showing.".
• In Module 7, More Math, Problem Solving Activities, Activity 4 and addresses standard 1.OA.1, “Robert is putting away his toy car collection. He has 13 cars in his collection. He has already put away 7 cars. How many more cars does Robert have to put away?”.
• In Module 8, More Math, Problem Solving Activities, Activity 4 and addresses standard 1.OA.1, “Mathew and Patricia are counting their collection of toy boats. Mathew has 8 boats and Patricia has 4 fewer than Mathew. How many boats do they have in total?”.
• In Module 9, More Math, Problem Solving Activities, Activity 4 and addresses standard 1.OA.1, “Joel has 62 cents in his wallet. He finds another 2 cents and puts it in his wallet. Amy has 10 cents less than Joel’s total amount. How much money does Amy have?”.
• In Module 10, Lesson 9, Student Journal 10.9, and addresses standard 1.OA.1, “Solve each problem. Draw pictures or write equations to show your thinking. a. There are 16 blocks in a box. 3 blocks are taken out. How many blocks are left in the box?”.
• In Module 11, More Math, Problem Solving Activities, Activity 4 and addresses standard 1.OA.1, “Reece is cleaning out his fish tank. He has 12 fish in total. Nine of the fish are swimming around the tank, and the rest are hiding behind plants. How many fish are hiding?".
• In Module 12, More Math Problem Solving Activities, Activity 4 and addresses standard 1.OA.2, “Connor buys a packet of 35 seeds to plant. He plants 20 seeds in the back garden and 7 seeds in the front garden. How many seeds are left in the packet?”.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 1 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.

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 overemphasis on fluency, procedures, and algorithms.

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

• In Module 1, Lesson 4, Step 3, Teaching the Lesson, students draw number cards and represent the number with cubes, counters, coins, or drawing a picture.
• In Module 9, Lesson 7, Student Journal 9.7, students use conceptual understanding to solve addition problems. “1. Add the two groups. Then write the matching equation. Use blocks to help you. a. 50 + 20” Under 50 and 20 are base ten blocks representing the numbers.
• In Module 10, More Math, Problem Solving Activities, Activity 4, “Dad has baked 12 muffins for the soccer team. There are four muffins leftover. How many muffins has the soccer team eaten?” (1.OA.1)
• In Module 12, Lesson 1, Step 3, Teaching the Lesson, students use conceptual understanding to solve number puzzles and see patterns in a 100s chart. “I am thinking of a number that has a nine in the ones place and a four in the tens place. Which number is it?”

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

• In Module 1, Lesson 9, Step 3, Teaching the Lesson, application and conceptual understanding are treated together. Students read the book Paint a Rainbow, students put each other in order, using the “numeral one and ordinal symbol 1st.”
• In Module 10, Lesson 6, application and conceptual understanding are treated together. Students read the book Bear and Badger, “They use cubes to model the subtraction story show on the spread”. Pages four and five, “introduce the language associated with comparison subtraction.”

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 8, Step 3, Teaching the Lesson, “Organize the students into pairs and distribute the resources. Encourage students to use these tools to model and help solve the problem (SMP4)” Students are given the models and are not allowed to come up with their own model.
• In Module 4, Lesson 4, Step 3, Teaching the Lesson, “Invite the students to model the same thinking on their number tracks. Repeat the activity several times so students become familiar with the count-back strategy using a number track. Each time, emphasize how you are counting back to find the answer. (SMP4)”
• In Module 7, Lesson 6, Step 2, Starting the Lesson, “Organize students into small groups and distribute the base ten blocks, expanders, and marker. Say, Today I’m going to say a number. I would like you to work as a team to create the number using blocks and write the number on the appropriate expander. The team who creates it correctly (and fastest) wins the round. Say a variety of numbers from 1 to 120. Each time a group wins, invite them to explain their concrete representations and show the number on their expander. Rotate the resources so students can use each twice. (SMP4)”

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:

• Module 2, Lesson 7, Step 3, Teaching the Lesson, “Invite one student to come to the front and use the rabbit to model an addition situation by making one or two hops along the number track (SMP 5)”
• In Module 4, Lesson 1, Step 2, Starting the Lesson, students solve subtraction problems using counters. “Instruct students to select a tool from the resource center (for example, teddy bear counters or connecting cubes) and use it to represent the equation on the board. (SMP5)”
• In Module 8, Lesson 6, Step 3, Teaching the Lesson, “Allow time for students to discuss and model their thoughts on the number track. (SMP 5)”

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials, however, while vocabulary is identified throughout the materials, there is no explicit directions for 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 greater than, less than, and teen numbers.
• The vocabulary words do not have the definitions.
• Not all the vocabulary words are in the glossary, for example, object.
• Materials use the term “Turn around facts,” 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.