smusd common core math scope and sequence first grade 1... · smusd common core math scope and...

1st Grade Revised July 2014 (pg. 1)

SMUSD Common Core Math Scope and Sequence First Grade

Year Long Standards of Focus

*1.OA.1 Use addition and subtraction within 20 to solve word problems *1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10

Trimester One Trimester Two Trimester Three

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 4 weeks 5 weeks 4 weeks 9 weeks 12 weeks

Data Geometry &

Time Measurement Place Value Addition & Subtraction

1.MD.4 1.OA.2

1.G.1 1.G.2 1.G.3

1.MD.3

1.MD.1 1.MD.2

1.NBT.1 1.NBT.2 1.NBT.3 1.NBT.5

1.NBT.4 1.NBT.6 1.OA.1** 1.OA.2** 1.OA.3** 1.OA.4** 1.OA.5** 1.OA.6** 1.OA.7**

1.OA.8

All units include the Standards of Mathematical Practice

*Standards will be taught throughout the year and have specific trimester goals ** Standards will be addressed through number talks and problem solving with year-long standards


Standards for Mathematic Practice

Explanations and Examples for Grade One

MP.1 Make sense of problems and persevere in solving them.

In first grade, students realize that doing mathematics involves solving problems and discussing how they solved them. Students explain to

themselves the meaning of a problem and look for ways to solve it. Younger students may use concrete objects or math drawings to help

them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They are willing to try

other approaches.

MP.2 Reason abstractly and quantitatively.

Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative

reasoning entails creating a representation of a problem while attending to the meanings of the quantities.

In first grade students make sense of quantities and relationships while solving tasks. They represent situations by decontextualizing tasks

into numbers and symbols. For example, “There are 14 children on the playground and some children go line up. If there are 8 children still

playing, how many children lined up?” Students translate the situation into the situation equation: 14 − ? = 8, and then into the related

equation 8 + ? = 14 and solve the task. Students also contextualize situations during the problem solving process. For example, students refer

to the context of the task to determine they need to subtract 8 from 14 because the total number of children on the playground is the total

number less the 8 that are still playing. Teachers might ask, “How do you know” or “What is the relationship of the quantities?” to reinforce

students’ reasoning and understanding.

Students might also reason about ways to partition two-dimensional geometric figures into halves and fourths. The Mathematics Framework

was adopted by the California State Board of Education on November 6,

MP.3 Construct viable arguments and critique the reasoning of others.

First graders construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They practice mathematical

communication skills as they participate in mathematical discussions involving questions like “How did you get that?” or “Explain your

thinking,” and “Why is that true?” They explain their own thinking and listen to the explanations of others. For example, “There are 9 books

on the shelf. If you put some more books on the shelf and there are now 15 books on the shelf, how many books did you put on the shelf?”

Students might use a variety of strategies to solve the task and then share and discuss their problem solving strategies with their classmates.


MP.4 Model with mathematics

In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical

language), drawing pictures, using objects, acting out, making a chart or list, and creating equations. Students need opportunities to connect

the different representations and explain the connections. They should be able to use any of these representations as needed.

First grade students model real-life mathematical situations with an equation and check to make sure equations accurately match the

problem context. Students use concrete models and pictorial representations while solving tasks and also write an equation to model

problem situations. For example to solve the problem, “There are 11 bananas on the counter. If you eat 4 bananas, how many are left?”

students could write the equation 11 – 4 = 7. Students should be encouraged to answer questions, such as “What math drawing or diagram

could you make and label to represent the problem?” or “What are some ways to represent the quantities?”

MP.5 Use appropriate tools strategically.

Students begin to consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools

might be helpful. For instance, first graders decide it might be best to use colored chips to model an addition problem.

Students use tools such as counters, place value (base ten) blocks, hundreds number boards, concrete geometric shapes (e.g., pattern blocks,

3-dimensional solids), and virtual representations to support conceptual understanding and mathematical thinking. Students determine

which tools are appropriate to use. For example, when solving 12 + 8 = __, students might explain why place value blocks are appropriate to

use to solve the problem. Students should be encouraged to answer questions such as, “Why was it helpful to use…?”

MP.6 Attend to precision.

As young children begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions

with others and when they explain their own reasoning.

In grade one, students use precise communication, calculation, and measurement skills. Students are able to describe their solutions

strategies to mathematical tasks using grade-level appropriate vocabulary, precise explanations, and mathematical reasoning. When

students measure objects iteratively (repetitively), they check to make sure there are no gaps or overlaps. Students regularly check their

work to ensure the accuracy and reasonableness of solutions.


MP.7 Look for and make use of structure.

First grade students look for patterns and structures in the number system and other areas of mathematics. While solving addition

problems, students begin to recognize the commutative property, for example 7 + 4 = 11, and 4 + 7 = 11. While decomposing two-digit

numbers, students realize that any two-digit number can be broken up into tens and ones, e.g. 35 = 30 + 5, 76 = 70 + 6. Grade one students

make use of structure when they work with subtraction as an unknown addend problem, such as 13 – 7 = __ can be written as 7+ __ = 13 and

can be thought of as how much more do I need to add to 7 to get to 13?

MP.8 Look for and express regularity in repeated reasoning.

In the early grades, students notice repetitive actions in counting and computation. When children have multiple opportunities to add and

subtract “ten” and multiples of “ten” they notice the pattern and gain a better understanding of place value. Students continually check their

work by asking themselves, “Does this make sense?”

Grade one students begin to look for regularity in problem structures when solving mathematical tasks. For example, students add three

one-digit numbers by using strategies such as “make a ten” or doubles. Students recognize when and how to use strategies to solve similar

problems. For example, when evaluating 8 + 7 + 2, a student may say, “I know that 8 and 2 equals 10, then I add 7 to get to 17. It helps if I can

make a 10 out of two numbers when I start.” Students use repeated reasoning while solving a task with multiple correct answers. For

example, solve the problem, “There are 12 crayons in the box. Some are red and some are blue. How many of each could there be?” Students

use repeated reasoning to find pairs of numbers that add up to 12 (e.g., the 12 crayons could include 6 of each color (6 + 6 = 12), 7 of one

color and 5 of another (7 + 5 = 12), etc.) Students should be encouraged to answer questions, such as “What is happening in this situation?”

or “What predictions or generalizations can this pattern support?”

(Adapted from Arizona Department of Education [Arizona] 2010 and North Carolina [N. 89 Carolina] Department of Public Instruction 2012)


Trimester One

Year Long Standards of Focus to be taught and practiced through number talks:

1.OA.6- Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on;

making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the

relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or

known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 +1 = 13).

All of the following information and problems have been adapted from Number Talks: Helping Children Build Mental Math and

Computation Strategies by Sherry Parrish. For more detailed information refer to your personal or grade level copy of the book.

The following number talks are designed to elicit and foster specific computation strategies. While each strategy possesses distinct

characteristics, often similarities overlap. For example many of the strategies build on changing numbers to landmark or friendly numbers;

this is a similarity. The difference lies in how the landmark or friendly number is created. This subtle difference is the essence of the strategy.

As you begin to implement number talks in your classroom, start with small numbers. Using small numbers serves two purposes:

1) Students can focus on the nuances of the strategy instead of the magnitude of the numbers

2) Students are able to build confidence in their mathematical abilities.

As students’ understanding of different strategies develops, you can gradually increase the size of the numbers. When the numbers become

too large, students will rely on less efficient strategies, such as counting all, or resort to paper and pencil, thereby losing the focus on

developing mental strategies.

Addition Number Talks:

Number talks at the first-grade level are designed to provide students with opportunities to continue to build fluency with numbers up to

ten and develop beginning addition strategies. Dot images, rekenreks, and five-and ten-frames may be used during number talks to provide

context for reasoning with numbers. When using these tools, recording number sentences to match student thinking is often helpful.

Instructions: The following image number talks are designed to be used in a single session, in any order. Image number talks consist of

three to five problems, each sequentially labeled A, B, C, and so on. The sequence within a given number talk allows students to apply

strategies from previous problems to subsequent problems. As each problem is shown, ask students, “How many dots do you see? How do you

see them?”


Strategy One: Counting All (Pages 59, 98-106)

Counting every number is an addition strategy used primarily by kindergarten and beginning first-grade students. Students who use this

strategy are not yet able to add on from either addend. They cannot visualize and hold a number in their mind; instead they must mentally

build every number quantity.

Example: 8 + 9

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, The student literally starts with 1 and counts up to 17 using every number. 11, 12, 13, 14, 15, 16, 17 Using models to help the student keep track of their location when counting is helpful. Strategy Two: Counting On (Pages 60, 98-106)

Counting On is a traditional strategy used primarily in first and early-second grade. The students starts with one of the numbers and counts

on from this point. When students are able to conceptualize a number, they will transition from Counting All to Counting On. It is tempting to

show students this strategy, however, if students don’t construct this strategy for themselves, it becomes a magical procedure with no

foundation.

Example: 8 + 9

8…9, 10 , 11, 12, 13, 14, 15, 16, 17 It is not unusual to hear students say, “I put the 8 in my head and counted up 9 more.”

Or

9… 10, 11, 12, 13, 14, 15, 16, ,17 From an efficiency standpoint, it is important to note whether the student counts up from

the smaller or larger number.

See next pages for examples

The following number talks consist of counting on/counting all using Dot Images (pages: 99-100)

As each number talk is shown, ask students, “How many dots do you see? How do you see them?”


The following number talks consist of counting on/counting all using Double Ten-Frames (Pages 104-105)

When the focus is on the numbers 3 to 9, ask students, “How many dots do you see? How do you see them?”

When the focus is on the number 10, the question shifts to, “How many more to make ten?”


The following number talks consist of counting on/counting all using Number Sentences (Page 106)

3 + 6 3 + 7 3 + 8

4 + 6 7 + 4 4 + 8 4 + 9

9 + 1 9 + 3 9 + 5 9 + 7

6 + 4 6 + 6 6 + 8 6 + 9

7 + 3 7 + 7 7 + 9 7 + 5

9 + 11 9 + 13 9 + 15

5 + 5 5 + 7 5 +9

8 + 2 8 + 5 8 + 7 8 + 9

11 + 5 12 + 4 13 + 3


Year Long Standards of Focus to be taught and practiced through problem solving:

1. OA.1- Use addition and subtraction within 20 solve word problems involving situations of adding to, taking from, putting together, taking

apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number

to represent the problem.

Teaching Mathematics through Problem Solving

(Adapted from Teaching Student-Centered Mathematics)

Teaching mathematics through problem solving is a method of teaching mathematics that helps children develop relational

understanding. With this approach, problem solving is completely interwoven with learning. As children do mathematics-make sense of

cognitively demanding tasks, provide evidence or justification for strategies and solutions, find examples and connections, and receive and

provide feedback about ideas-they are simultaneously engaged in the activities of problem solving and learning. Teaching mathematics

through problem solving requires you to think about the types of tasks you pose to children, how you facilitate discourse in your classroom,

and how you support children’s variety of representations as tools for problem solving, reasoning, and communication.

Teaching mathematics through problem solving promises to be an effective approach if our ultimate goal is deep (relational)

understanding because it accomplishes these goals:

1) Focuses children’s attention on ideas and sense making. When solving problems, children are reflecting on the concepts inherent in

the problems. Emerging concepts are more likely to be integrated with existing ones, thereby improving understanding.

2) Emphasizes mathematical processes and practices. Children who are solving problems will engage in all five of the processes of doing

mathematics-problem solving, reasoning, communication, connections, and representation, as well as the eight-mathematical practices

outlined in the Common Core State Standards, resulting in mathematics that is more accessible, more interesting, and more meaningful.

3) Develops children’s confidence and identities. Every time teachers pose a problem-based task and expect a solution, they implicitly

say to children, “I believe you can do this.” When children are engaged in problem solving and discourse in which the correctness of the

solution lies in justification of the processes, they begin to see themselves as capable of doing mathematics and that mathematics make

sense.


4) Provides a context to help children build meaning for the concept. Using a context facilitates mathematical understanding, especially

when the context is grounded in an experience familiar to children and when the context uses purposeful constraints that potentially

highlight the significant mathematical ideas

5) Allows entry and exit points for a wide range of children. Good problem-solving based tasks have multiple paths to the solution, so

each child can make sense of and solve the task by using his or her own ideas. Furthermore, children expand their ideas and grow in their

understanding as they hear, critique, and reflect on the solution strategies of others.

6) Allows for extensions and elaborations. Extensions and “what if” questions can motivate advanced learners or quick finishers,

resulting in increased learning and enthusiasm for doing mathematics.

7) Engages students so that there are fewer discipline problems. Many discipline issues in a classroom are the result of children

becoming bored, not understanding the teacher directions, or simply finding little relevance in the task. Most children like to be challenged

and enjoy being permitted to solve problems in ways that make sense to them, giving them less reason to act out or cause trouble.

8) Provides formative assessment data. As children discuss ideas, draw diagrams, or use manipulatives, defend their solutions and

evaluate those of others, and write reports or explanations, they provide the teacher with a steady stream of valuable information that can

be used to inform subsequent instruction.

9) It’s a lot of fun! Children enjoy the creative process of problem solving and sharing how they figured something out. After seeing the

surprising and inventive ways that children think and how engaged children become in mathematics, very few teachers stop using a

teaching-through-problem solving approaching.


A Three-Phase Lesson Format

Before: In the before phase of the lesson you are preparing children to work on the problem. As you plan for the before part of the lesson,

analyze the problem you will give to children in order to anticipate children’s approaches and possible misinterpretations or

misconceptions. This can inform questions you ask in the before phase of the lesson to clarify children’s understanding of the problem (i.e.,

knowing what it means rather than how they will solve it.)

During: In the during phase of the lesson children explore the problem (alone, with partners, or in small groups). This is one of two

opportunities you will get in the lesson to find out what the children know, how they think, and how they are approaching the task you have

given them (the other is in the discussion period of the after phase). You want to convey a genuine interest in what the children are thinking

and doing. This is not the time to evaluate or to tell children how to solve the problem.

When asking whether a result or method is correct, ask children, “How can you decide?” or “Why do you think that might be right?” or “How

can we tell if that makes sense?” Use this time in the during phase to identify different representations and strategies children used,

interesting solutions, and any misconceptions that arise that you will highlight and address during the after phase of the lesson.

After: In the after phase of the lesson your children will work as a community of learners, discussing, justifying, and challenging various

solutions to the problem that they have just worked on. It is critical to plan for and save ample time for this part of the lesson. Twenty

minutes is not at all unreasonable for a good class discussion and sharing of ideas. It is not necessary to wait for every child to finish. Here is

where much of the learning will occur as children reflect individually and collectively on ideas they have explored. This is the time to

reinforce precise terminology, definitions, or symbols. After children have shared their ideas, formalize the main ideas of the lesson,

highlighting connections between strategies or different mathematical ideas.


Trimester One Word Problem Focus Questions

(Adapted from the California State Board of Education Mathematics Framework)

In grade one, students add and subtract numbers within 20 to solve word problems. By first grade, students have had prior experiences

working with various problem situations (Add To with result unknown; and Take From with result unknown; and Put Together/Take Apart

with total unknown). First grade students represent word problems (e.g., using objects, drawing and equations) and relate strategies to a

written method to solve addition and subtraction word problems within 20. Students extend their prior work in three major and

interrelated ways:

Representing and solving a new type of problem situation (Compare problems- Tri. 2&3)

Representing and solving the subtypes for all unknowns in all three types (represented below)

Using Level 2 (Counting on) and Level 3 (Convert to an easier problem) methods to extend addition and subtraction problem solving

beyond 10, to problems within 20.

In Trimester One, the focus should be to increase the students’ use of Level 2 (Counting on) method to solve problems. Level 2 methods for

addition and subtraction represent a new challenge for students, since when “counting on,” an addend is already embedded in the total to be

found; it is the named starting number of the “counting on” sequence. For example when adding 5 + 4, a student would count on from 5

saying, “5, 6, 7, 8, 9.”

It is important to be aware of these common misconceptions for first graders:

Some students misunderstand the meaning of the equal sign. The equal sign means “is the same as,” but many students think the

equal sign means “the answer is coming up” to the right of the equal sign. Students should see equations written multiple ways, for

example 5 + 7 = 12 and 12 = 5 +7.

Many students assume key words or phrases in a problem suggest the same operation every time. To help avoid this misconception,

do not over emphasize key words and include problems in which key words represent different operations.

The various addition and subtraction problem types are listed in the following table.


Add To (with change unknown) “Bill had 5 toy robots. His mom gave him some more. Now he has 9 robots. How many toy robots did his mom give him?” In this problem the starting quantity is provided (5 robots), a second quantity is added to that amount (some robots) and the result quantity is given (9 robots). The question type is more algebraic and challenging than the “result unknown” problems and can be modeled by a situational equation 5+ ___ = 9, which can be solved by counting on from 5 to 9.

Take From (with change unknown) “Andrea had 8 stickers. She gave some stickers away. Now she has 2 stickers. How many stickers did she give away?” This question can be modeled by a situational equation 8 - ____ = 2 or a solution equation 8 – 2 = ___. Both the Take From and Add To questions involve actions.

Put Together/Take Apart (with addend unknown) “Roger puts 10 apples in a fruit basket. 4 are red and the rest are green. How many are green?” There is no direct or implied action. The problem involves a set and its subsets. It can be modeled by 10 – 4 = ___ or 4 + ___ = 10. This type of problem provides students with opportunities to understand addends hiding inside a total and also to relate subtraction and an unknown-addend problem.


Trimester 2









see them?”

Strategy Three: Doubles/Near Doubles (Page 60, 109-111)

Beginning as early as Kindergarten, children are able to recall sums for many doubles. This strategy capitalizes on this strength by adjusting

one or both numbers to make a double or near-doubles combination.

Example: 8 + 9

1) 8 + (8+1) (8 + 8) +1 (16) + 1 = 17 Students will decompose the 9 into an 8 and 1 in order to solve this problem. 2) 9 + 9 = 18 18 – 1 = 17 Students will add 1 to the 8 so that they use the doubles fact (9+9), after finding the sum, they subtract 1 from the total. 3) 10 + 10 20 – 3 = 17 Students will add 2 to the 8 and 1 to the 9 in order to add 10 + 10. Then they subtract 3 from the sum.



The following number talks consist of Doubles/Near-Doubles using Double Ten-Frames (pages: 110)



The following number talks consist of Doubles/Near-Doubles using Number Sentences (Page 111)

2 + 2 2 + 3 3 + 3 3 + 4

7 + 7 7 + 6 7 + 8 8 + 8

12 + 12 12 + 13 13 + 13 13 + 14

4 + 4 4 + 3 3 + 3 3 + 4

8 + 8 8 + 9 9 + 9

9 + 10

15 + 15 15 + 16 14 + 14 14 + 15

5 + 5 5 + 6 6 + 6 6 + 7

10 + 10 10 + 11 11+ 11 11 + 12 12 + 12

20 + 20 19 + 19 19 + 18 18 + 18 18 + 17


Year Long Standards of Focus to be taught and practiced through problem solving:

1.OA.1- Use addition and subtraction within 20 solve word problems involving situations of adding to, taking from, putting together, taking



Trimester Two Word Problem Focus Questions


The focus of Trimester 2 will be to introduce compare problems. In a compare situation, two quantities are compared to find “how many

more” or “how many less.” One reason compare problems are more advanced is that in compare problems, one of the quantities (the

difference) is not present in the situation physically, and must be conceptualized and constructed in a representation, by showing the “extra”

that when added to the smaller unknown makes the total equal to the bigger unknown, or by finding this quantity embedded within the

bigger unknown.

The language of these problems can also be difficult for students. For example, “Julie has 3 more apples than Lucy,” states that both (1) Julie

has more apples and (2) the difference is 3. Many students “hear” the part of the sentence about who has more, but do no initially the part

about how many more. Students need experience hearing and saying a separate sentence for each of the two parts to help them comprehend

and say the one sentence form.

See next page for visual examples from the framework:



Compare (with difference unknown) “Pat has 9 peaches. Lynda has 4 peaches. How many more peaches does Lynda have than Pat? Compare problems involve relationships between quantities. While most adults might use subtraction to solve this type of Compare problem (9 – 4 = ___), students will often solve this problem as an unknown addend problem (4 + ___ = 9) or by using a counting up or matching strategy. In all mathematical problem solving, what matters is the explanation a student gives to relate a representation to a context and not the representation separated from its context.

Compare (with bigger unknown – “more” version) “Theo has 7 action figures. Rosa has 2 more action figures than Theo. How many action figures does Rosa have?” This problem can be modeled by 7 + 2 = ___.

Compare (with smaller unknown – “fewer” version) “Bill has 8 stamps. Lisa has 2 fewer stamps than Bill. How many stamps does Lisa have?” This problem can be modeled as 8 – 2 = ___.


Trimester 3









see them?”

Strategy Four: Making Tens (Pages: 61, 114-117)

Developing fluency with number combinations that make ten is an important focus in the primary grades. The focus of this strategy is to be

able to utilize fluency with ten to expedite adding. Being able to take numbers apart with ease, or fluency, is the key to understanding this

strategy. Several examples can help us consider how this strategy can be efficient and effective.

Example: 8+9.

1) (7 + 1) + 9

7 + (1 + 9)

7 + 10 = 17 By changing the 8 to a 7 + 1 the student can restructure the problem to create a combination of 10 with 1 + 9

2) 8 + (2 + 7)

(8 + 2) + 7

10 + 7 = 17 The student could also choose to make a 10 by breaking apart the 9 into 7 + 2 and combining the 2 with the 8 to create 10.



The following number talks consist of Making Ten using Double Ten-Frames (pages: 115-116)



Strategy Five: Making Landmark or Friendly Numbers (62, 118) Landmark or friendly numbers are numbers that are easy to use in mental computation. Fives, multiples of ten, as well as monetary amounts such as twenty-five and fifty are examples of numbers that fall into this category. Students may adjust one or all addends by adding or subtracting amounts to make a friendly number. Example: 23 +48 23 + 48 + 2 23 + 50 = 73

- 2

71 In this example only the 48 is adjusted to make an easy landmark number (50.) Then the extra 2 that was added on must be subtracted.

The following number talks consist of Making Tens using Number Sentences (Page 117)

9 + 1 9 + 3 + 1 9 + 5 + 1

5 + 5 5 + 5 + 4 5 + 3 + 5

8 + 2 8 + 3 + 2 2 + 5 + 8

3 + 7 7 + 5 + 3 3 + 6 + 7

4 + 6 4 + 6 + 4 6 + 5 + 4

1 + 8 + 9 9 + 3 + 1 1 + 6 + 9

5 + 5 5 + 6 + 5 4 + 5 +5

2 + 8 2 + 5 + 8 8 + 6 + 2

5 + 5 + 8 3 + 4 + 6

4 + 5 + 6 + 5


The following number talks include numbers that encourage students to adjust one or all of the addends by adding or subtracting amounts

to make a landmark or friendly number. (Page 118)

9 + 1

9 + 1 + 4

9 + 5

9 + 6

6 + 4 6 + 4 + 3

6 + 7 6 + 10 6 + 9

8 + 2 8 + 2 + 11

8 + 13 8 + 15

8 + 2

8 + 2 + 4

8 + 6

8 + 5

10 + 12

9 + 12

9 + 15

20 + 5

19 + 1 + 4

19 + 5

19 + 8

7 + 3

7 + 3 + 3

7 + 6

7 + 9

10 + 10

9 + 9

9 + 8

20 + 20

19 + 20

19 + 19


Long Standards of Focus to be taught and practiced through problem solving:

1.OA.1- Use addition and subtraction within 20 solve word problems involving situations of adding to, taking from, putting together, taking



Trimester Three Word Problem Focus Questions


First grade students should be exposed to the following types of problems in Grade One, however, mastery is not expected until Grade Two.


Add to (with start unknown) “Some children were playing in the playground. 5 more children joined them. Then there were 12 children. How many children were playing before?” This problem can be represented by ___ + 5 = 12. The “start unknown” problems are difficult for students to solve because the initial quantity is unknown and therefore cannot be represented. Children need to see both addends as making the total and then some children can solve this by 5 + ___ 12.

Take From (with start unknown) “Some children were lining up for lunch. 4 children left and then there were 6 children still waiting in line. How many children were there before?” This problem can be modeled by ___ - 4 = 6. Similar to the previous Add To (start unknown) problem, the Take From problems with the start unknown require a high level of conceptual understanding. Children need to see both addends as making the total and then some children can solve this by 4 + 6 = ___.

Compare (with bigger unknown- “fewer,” misleading language version) “Lucy has 8 apples. She has fewer apples than Marcus. How many apples does Marcus have?” This problem can be modeled as 8 + 2 = ___. The misleading language “fewer” may lead students to choose the wrong operation.

Compare (with smaller unknown- “more” misleading language version “David has 7 more bunnies than Keisha. David has 8 bunnies. How many bunnies does Keisha have?” This problem can be modeled by 8 – 7 = ___. The misleading language “more” may lead students to choose the wrong operation.


Essential Learning for the Next Grade Adapted from: The Mathematics Framework was adopted by the California State Board of Education on November 6, 2013.

First Grade

To be prepared for grade two mathematics students should be able to demonstrate they have acquired certain mathematical concepts and

procedural skills by the end of grade one and have met the fluency expectations for the grade. For first graders, the expected fluencies

are to add and subtract within 10 (1.OA.6▲).

Of particular importance for students to attain in grade one are the concepts, skills and understandings necessary to represent and solve

problems involving addition and subtraction (1.OA.1-2▲); understand and apply properties of operations and the relationship between

addition and subtraction (1.OA.3-4▲); add and subtract within 20 (1.OA.5-6▲); work with addition and subtraction equations (1.OA.7-

8▲); extend the counting sequence (1.NBT.1▲); understand place value and use place value understanding and properties of operations to

add and subtract (1.NBT.2-6▲); and measure lengths indirectly and by iterating length units (1.MD.1-2▲).

Place Value

By the end of grade one, students are expected to count to 120 (starting from any number), compare whole numbers (at least to

100), and read and write numerals in the same range. Students need to think of whole numbers between 10 and 100 in terms of

tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones).

Addition and Subtraction

By the end of grade one, students are expected to add and subtract within 20 and demonstrate fluency with these operations within

10 (1.OA.6▲). Students can represent and solve word problems involving add-to, take-from, put-together, take-apart, and compare

situations including addend unknown situations. They know how to apply properties of addition (associative and commutative)

and strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems. Students use methods to

add (within 100), subtract multiples of 10 (using various strategies), and mentally find 10 more or 10 less without counting.

Students understand how to solve addition and subtraction equations.

Measure Lengths

By the end of grade one, students are expected to order three objects by length (using non-standard units). Students indirectly

measure objects by comparing the length of two objects by using a third object as a measuring tool.

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