1st Grade - Gateway 2

The instructional materials reviewed for Ready Grade 1 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Students use pictures, manipulatives, and models to demonstrate conceptual understanding.

The Teacher Resource Book contains a section called Concept Extension that provides teachers with additional ways to support building students’ conceptual understanding. Examples of how the Concept Extension supports teachers in building conceptual understanding include:

• Unit 2 Lesson 10 guides teachers to help students make a false number sentence true in order to develop the concept of the equal sign (1.OA.7). Teachers are given questions to ask to prompt thinking.
• Unit 6 Lesson 26 shows teachers how to guide students to explore non-defining attributes (1.G.1).

Clusters 1.NBT.B and 1.NBT.C focus on understanding the place value system and using place value to add and subtract.

• In Unit 3 Lesson 12 Understand Teen Numbers (1.NBT.B) the teacher engages students in using visual and concrete representations to develop their understanding of a “ten” using their fingers, 10-frames with connecting cubes, and connecting cubes. In addition, the teacher questions the students to find out “How can 10 and 1 ten be equal?”
• In Unit 4 Lesson 19 Understand 10 More and 10 Less (1.NBT.C) the teacher uses connecting cubes, base-ten blocks, counters, and number cards to engage students in finding out how adding and subtracting 10 is similar to the number line. Furthermore, the teacher asks, “How is finding 10 more and 10 less on the 120 chart like adding and subtracting 10 cubes?”

The instructional materials reviewed for Ready Grade 1 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The materials provide opportunities to attend to procedural skill and fluency throughout the lessons, including adding and subtracting within 20, demonstrating fluency for addition and subtraction within 10 (1.OA.6).

All lessons provide an opportunity for students to use computation skills. Each lesson contains a Building Fluency section which is designed to be used twice during a lesson. The Student Practice and Problem-Solving Book contains fluency practice pages, and Math Center Activities are included in the Teacher Toolbox which include activities for both procedural skill and fluency.

• The Student Practice and Problem-Solving Book contains fluency practice pages for adding and subtracting within 10 (1.OA.6).
• In Unit 2 Lesson 11 students find the missing number and practice facts for sums of 6, 7, 8, 9, and 10 (1.OA.6).
• In Unit 1 Lesson 4 Activity 1.12 Missing Number Addend Bonds one student solves the addition equation and then their partner solves the related subtraction equation (1.OA.6).
• In Unit 2 Lesson 6 Day 2 Hands-on Activity students use counters to add doubles (1.OA.6).

iReady Door 24 Plus is a free iPad app for fact fluency practice and is only available in the Apple platform. The game does include the fluencies for Grade 1.

The instructional materials reviewed for Ready Grade 1 meet the expectation for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Each lesson includes guided practice Try It and independent practice Practice by Myself where students apply what they have learned to solve real-world problems. Most lessons also have an online interactive tutorial for students which features real-world applications. In addition, there are Problem Solving Connection problems where students are exposed to situations to apply addition and subtraction (1.OA.A). The following problems are examples of the application problems included in the instructional materials:

• Unit 1 Lesson 2 Try It: “8 children are playing ball. 5 children leave. How many children are still playing ball?”
• Unit 3 Lesson 15 Try It: “Ana has 6 red blocks, 4 blue blocks, and 2 green blocks. How many blocks does she have in all?”

• Lesson 5 Tutorial: students apply their knowledge of subtraction to help pack cakes and pies into boxes for a bakery.

The instructional materials reviewed for Ready Grade 1 meet the expectations for balancing the three aspects of rigor. Overall, the three aspects of rigor are not always treated together and are not always treated separately within the materials.

Each lesson contains opportunities for students to build conceptual understanding, procedural skills and fluency, and apply their learning in real-world problems. Lessons are designed so students engage with all three components of rigor at different points in the lesson. During Guided Instruction and Guided Practice, students explore alternative solution pathways to master procedural fluency. During Independent Practice, students apply the concept in real world applications where they need to use both the procedural skills and their understanding of the concept to solve problems with multiple solutions and explain/compare their solutions.

For example, in Unit 1 Lesson 3 Introduction and Use What You Know students are introduced to modeling a problem after hearing the word problem, “First draw 1 animal, now draw 4 animals.” Students practice procedural skill and fluency in modeled instruction. Students practice counting on to find a missing addend in a word problem. Students then apply what they have learned to solving word problems to find missing addends.

In Unit 2 Lesson 9 students use conceptual understanding of making 10 by writing out and modeling number partners to 10 in numbers, words, and in part part whole models. Students use procedural skill and fluency by using repeated reasoning to find the number pairs that make 10. Students continue with fluency in the Talk About It section as they decide if a problem could be correct based on the work shown.

The instructional materials reviewed for Ready Grade 1 meet the expectations for identifying the Mathematical Practices (MPs) and using them to enrich the mathematics content within and throughout the grade.

The MPs for each lesson are identified in the CCSS Focus section as part of the Lesson Overview. SMP TIPs are found in the Teacher Resource Book throughout the lessons, and these tips highlight the integration of particular MPs within the lessons. The MPs are also identified for each lesson in the Table of Contents for the Teacher Resource Book on pages A4-A7.

Some examples of where the MPs are identified and used to enrich the mathematics content include:

• Unit 1 Lesson 1: MPs 2, 3, 5, 6, and 7 are identified in the Lesson Overview. The first SMP TIP in the lesson for MP6 states, “Connect the physical activity to the model by having children first place counters on the smiley faces, representing the girls and eliciting that these show a group of 5. Have children count on as they add counters to represent boys. As they do so, children refine the concept of counting on as a strategy for finding the number of objects in a group without having to count every member of the group.” The SMP TIP in the lesson for MP7 states, “Mathematical Discourse 3 is a concrete example of the commutative property. Asking children to describe the sets using two different number sentences helps them to make a symbolic connection. Emphasize that the sum has not changed even though the order of the addends has.” The SMP TIP in the lesson for MP2 states, “As they practice counting on to add, children can use physical objects and drawings to help them reason quantitatively. Recording the process in a number sentence allows them to connect the concrete model to the symbolic model.”
• Unit 3 Lesson 15: MPs 1, 2, 3, 4, 7, and 8 are identified in the Lesson Overview. The SMP TIP for MP4 states, “Continuing to emphasize the relationship between a real-life mathematical situation, a model, and a number sentence helps children develop skills that involve abstract reasoning.” The SMP TIP for MP8 states, “Children have found partners of 10 and have learned to use the make a ten strategy to add 2 one-digit numbers. Emphasize the benefit in making a ten to add 3 one-digit numbers. This important calculation will be repeated as children learn to add two-digit numbers and as they learn later concepts.”
• Unit 6 Lesson 27: MPs 2, 3, 4, 5, 6, and 7 are identified in the Lesson Overview. The SMP TIP in the lesson for MP7 states, “As children compose shapes, they are building understanding of patterns and iterating units. Encourage children to see not just the composite shape, but the shapes that form the composite shape.” The SMP TIP in the lesson for MP5 states, “Allowing children to use shape pieces of different colors to compose rectangles enables them to view situations in which tools can help solve a problem. Encourage children to continue to use concrete models to solve other geometry problems.”

The instructional materials reviewed for Ready Grade 1 meet the expectation for carefully attending to the full meaning of each practice standard. Overall, the materials attend to aspects of the mathematical practices (MPs) during different lessons throughout the grade, so when taken as a whole, the instructional materials attend to the full meaning of each MP.

Examples of where the instructional materials attend to each of the MPs include:

• MP1: In Unit 3 Lesson 14 students complete several word problems by using different strategies and models to add two numbers whose sum is greater than 10. For some of the problems, students have to make sense of the problem to determine what information they have and which strategy or model they would like to use. Students also persevere in solving the problems as they have the opportunity to revisit their initial solutions if they are not correct.
• MP2: In Unit 1 Lesson 2 students are asked to find the difference between two numbers based on word problems. The SMP TIP for in the lesson for MP2 states, “Ask children to describe how the number sentence tells what is happening in the problem. In order to contextualize and decontextualize the information in this problem, children need to make a clear connection between the problem situation, the illustration, and the number sentence.”
• MP4: In Unit 5 Lesson 23 students use models to solve problems and then share their models so that students can find efficient models to use in problem solving.
• MP5: In Unit 7 Lesson 20 students solve word problems that involve adding and subtracting tens. Students are able to choose from tens blocks, number bonds, or a 120 chart to help them complete the problems.
• MP7: In Unit 2 Lesson 6 students are using the doubles and doubles plus one strategies. Students use structure as they notice some numbers make equal groups and some have one left over.
• MP8: In Unit 2 Lesson 7 students are using repeated reasoning to find all the equations with a sum of 6. In Unit 2 Lesson 9 students are using repeated reasoning to find all the equations for the sum of 10 using ten frames.

The instructional materials reviewed for Ready Grade 1 meet the expectation for prompting students to construct viable arguments and analyze the arguments of others. Overall, the materials offer students multiple opportunities to construct viable arguments and/or analyze the arguments of others throughout the materials.

Examples where students are prompted to construct viable arguments and analyze the arguments of others include:

• In Unit 2 Lesson 7 Talk About It students analyze the work of fictional students and answer questions: “Who is right? How do you know?”
• In Unit 2 Lesson 10 students construct an argument as they answer “Do they have the same number of cubes? How do you know?”
• In Unit 5 Lesson 21 students think about the work of Buzz, a fictional student. Buzz says, “5 tens 8 ones = 5 + 80.” Students explain why or why not they agree with Buzz.

The instructional materials reviewed for Ready Grade 1 meet the expectation for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others concerning key grade level mathematics detailed in the content standards. The materials provide teachers with SMP TIPs to help facilitate students to construct arguments and/or analyze the arguments of others.

Examples where teachers are supported to help students construct viable arguments and analyze the arguments of others include:

• In Unit 2 Lesson 11 the teacher shows an incorrect problem 3 + 4 = 8 and asks students to respond. The students along with teacher guidance discuss how in miscalculating this one problem, all the other number sentences in the chart are incorrect.
• Unit 4 Lesson 17 prompts teachers to have students model tens with connecting cubes then show a partner. The materials tell teachers to “Encourage students to justify their decision.”

The instructional materials reviewed for Ready Grade 1 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of Mathematics.

• The Student Practice and Problem Solving Book has notes at the bottom of the pages where mathematical vocabulary is defined.
• The Teacher Resource Book has Lesson Vocabulary for each lesson with mathematical terms and their definitions.
• Teachers are prompted in the Teacher Resource Book to have students use precise mathematical language. For example, Unit 2 Lesson 10 Try It states, “Encourage children to use the words ‘is the same as’ when describing totals.”
• Each lesson has an “English Language Learners” section in the Teacher Resource Book that contains some ways to support vocabulary development for all students.
• Lessons contain language objectives. For example, Unit 2 Lesson 8 states: “Use visual models and number bonds to find missing number partners for 8 and 9. Tell why 0 can be a number partner for any number.”