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Student Activity Book page 226: Subtraction Problems with Die

Students will begin class by completing as many problems on page 226 of the student workbook as possible. The teacher will observe students during this time to gauge prior knowledge.

Can the student…

Solve subtraction problems without tools? With tools? Do they use the number lines on the name tags?

Solve subtraction problems with starting numbers greater than 10? Lower than 10?

How many problems are they able to complete?

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CCSS.1.OA.A.1: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions

CCSS.1.OA.B.3: Apply properties of operations as strategies to add and subtract.

CCSS.1.OA.C.5: Relate counting to addition and subtraction.

CCSS.1.OA.C.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.

CCSS.1.OA.D.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

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Grade 1 " Operations & Algebraic Thinking | Common Core State Standards Initiative

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CCSS.Math.Content.1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

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MP2: Reason abstractly and quantitatively

In this lesson, students explore the relationship between addition and subtraction. They must use the different properties of both operations to solve the three dice subtraction problems.

MP3: Construct viable arguments and critique the reasoning of others

Students must compare two or more viable options on their game board and use reasoning to determine which space would be the most advantageous.

MP7: Look for and make use of structure

Students must look for and make use of structure when playing the five-in-a-row subtraction game in order to complete a five-in-a-row vertically, horizontally, or diagonally.

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Engage NY Lesson 27:  Solve addition and subtraction problems decomposing and composing teen numbers as 1 ten and some ones.

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The Math Learning Center number line manipulative is highly versatile and appropriate for several grade levels and math activities. The intervals, spacing, numbering, and labeling are all adjustable to meet the specific needs of the lesson. Also, the manipulative is incredibly user-friendly, making it accessible for all learners. For this lesson, this manipulative could be used to support students in solving subtraction problems with starting numbers up to 12.

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Number Line helps students visualize number sequences and demonstrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing.

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Five-in-a-row subtraction with three cubes:

Students will display their understanding of subtraction with starting numbers up to 12 by using the numbers on three die to create subtraction problems and to strategically cover spaces on their gameboard. This activity will reveal students’ mastery of subtraction with starting numbers up to twelve, their understanding of the relationship between addition and subtraction, and their ability to reason abstractly and quantitatively.

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Bilingual Math Word Wall
I took a training on teaching math to English language learners in December, and the biggest take-away from that training was the importance of word walls in every classroom. Because our school has such a high Hispanic population, I would have both Spanish and English math terms on my word wall. I chose this resource in particular because it was aligned with CCSS for first grade, and each card features the word, a visual, and an explanation.

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1st Grade Math Vocabulary in Spanish / Tarjetas de vocabulario para matemáticas

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Are you in need of high-quality math vocabulary cards IN SPANISH? This pack has exactly that. This pack contains 74 high-quality math vocabulary cards that are aligned with the Common Core Standards for 1st grade along with 5 focus category cards. Check out the preview!

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Personal Math Dictionaries:
Aside from having a word wall, ESL students can benefit from creating their own personal math dictionaries. One popular format for personal dictionaries is four-square notes. Students write the vocabulary term in the middle, and fill four squares around the word with various descriptions. For first grade students, you may have them write the definition in one box, an example in another box, draw a diagram or a picture in the third box, and list an applicable math tool in the fourth box.

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Make problems relevant to students

Sometimes the math problems included in a curriculum speak of contexts unfamiliar to students. One simple way to make your math classroom culturally inclusive is to modify problems so they are culturally relevant for the students. For instance, I may adjust a story problem so that it mentions a student by name and involves a hobby, interest, or tradition of his.

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Jack Hartmann Video: Subitize

Investigations Teacher Presentation: Telling Time to the Half-hour

Investigations Teacher Presentation: Five-in-a-Row Subtraction with Three Cubes

1-6 dot cubes (2 for each partner group)

7-12 number cubes (1 for each partner group)

Differentiated number cubes

5-10

13-18

Five-in-a-row subtraction game boards

Dry erase markers/erasers

Math tools (number lines, unifix cubes, counters, etc.)

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Subtraction Strategies Poster
This poster serves to remind students of the many ways they can solve subtraction problems. I like this poster in particular because it mentions fact families, and one of the big ideas from my lesson was the relationship between addition and subtraction.

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Ticket Out the Door:
This formative assessment mirrors the pre-assessment in that it asks students to solve subtraction problems using dice in the same format as the student workbook. The assessment is aligned with the learning target because the subtraction problem has a starting number greater than ten and up to 12. Thought was given to the subtrahends chosen for the equation. The starting number of 11 requires students to think beyond solving with their fingers while the equation 11 - 5 can be solved using several problem-solving strategies including make ten and compensate.

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Schubin MAT Lesson Plan 2018 Ticket Out.pdf

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My mentor teacher uses a color-coded rubric to assess student's mathematical ability. Students are very familiar with the rubric as the class is structured around it, and my mentor teacher frequently models how to solve math problems while meeting the criteria of the rubric. Since the rubric is color-coded, you could use a self-assessment similar to the stop light method but with the colors matching the proficiency levels of the rubric (novice, apprentice, practitioner, expert). Students would pick the color matching the proficiency level they felt they were at by noting their color on their paper. Using the criteria on the rubric, students could then set goals to improve their proficiency.

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Count Back on the Number Track (2) (p. 33) [modified version]

This assessment mirrors the problem-solving procedure for five-in-a-row subtraction because it asks students to solve subtraction problems using a number line. In this case, I would modify the worksheet so that all the subtraction problems had starting numbers up to ten. In addition, the original worksheet asks students to use numeral cards (0-3) to fill in the blanks. I would have students use 1-6 number cubes or fill in the blanks myself.

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Work Backward

For students who complete the game early or display mastery, provide them with a nearly completed game board and ask them to identify the equations needed to complete the game. Students should be encouraged to find as many equations using numbers 1-12 as possible. For instance, if an eight is needed on the game board, the student could say 9 - 1, 10 - 2, 11 - 3 or 12 - 4. The board should be ambiguous enough to encourage students to think strategically as well. Students must record their equations and defend their decisions in writing.

Strategic thinking

Game allows for gifted students to use their higher-level reasoning skills in order to play the game strategically.

Game could also be played with two different color counters and students must play against each other to reach five-in-a-row first.

Option for starting dice with higher numbers (13-18)

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Recording equations

Students who need additional practice setting up subtraction problems correctly should be required to record their subtraction equations.

Think-pair-share

During the game introduction, students share their ideas about problem-solving strategies with a partner.

Number lines and other math tools provided to aid all students

Option for starting dice with lower numbers (5-10)

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Number Family Discussion

Teacher will roll three die and display them to class alongside three equations (number family).

Ex. 6 + 3 =9
9 - 6 = 3
9 - 3 = 6

Teacher will pose the question, “What do you notice when you look at these three equations?” in think-pair-share format.

Students will think about the question in regard to the three equations displayed by the teacher. The students will then share their thoughts with partners/teammates near them.

Teacher will select three students to share either their thoughts or the thoughts of a table mate by choosing three popsicle sticks from the class' cup.

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Knowledge:

Which number is larger? Which number is smaller?

Comprehension:

How would you set up this problem?

Application:

How would you use addition to solve this problem? How would you use subtraction to solve this problem? How could you use math tools to solve this problem?

Analysis:

What is the relationship between addition and subtraction? How did you choose which number to cover on your game board?

Synthesis:

What would happen if we chose the other subtraction problem? What would happen if we started the problem with the smaller number?

Evaluation:

How would you prove you solved the problem correctly?

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Relationship between addition and subtraction.

Students may be unable to see how a subtraction problem can be written as an addition problem so that addition strategies can be used to solve.

Commutative property

Students may try to apply the commutative property to subtraction without understanding that the property is reserved for addition and multiplication only

Symbol confusion

Students may not recognize or be unfamiliar with the minus symbol

Counting on fingers

Many students still rely on their fingers to solve addition and subtraction problems. Being that some of the starting numbers in this activity are greater than ten, using the fingers may not be a reliable strategy. Students who rely on this strategy may be forced to adopt a new strategy or use different math tools to solve problems.

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Illuminations Fact Families Activity:  The relationship between addition and subtraction is explored with books and with connecting cubes. Students search for related addition and subtraction facts for a given number using a calculator.

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Superhero subtraction is an online game in which students practice their subtraction facts up to 20. Eight superhero masks are hidden beneath the numbers, and students try to uncover them with the least amount of moves. With multiple solutions available to click on, students must think strategically in order to play. In this way, this game is similar to five-in-a-row subtraction.

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Play Superhero Subtraction at MathPlayground.com! Use your math skills to uncover the superhero masks.

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A Bilingual Math Word Wall
I took a training on teaching math to English language learners in December, and the biggest take-away from that training was the importance of word walls in every classroom. Because our school has such a high Hispanic population, I would have both Spanish and English math terms on my word wall.  I chose this resource in particular because it was aligned with CCSS for first grade, and each card features the word, a visual, and an explanation.

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1st Grade Math Vocabulary in Spanish / Tarjetas de vocabulario para matemáticas

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Are you in need of high-quality math vocabulary cards IN SPANISH? This pack has exactly that. This pack contains 74 high-quality math vocabulary cards that are aligned with the Common Core Standards for 1st grade along with 5 focus category cards. Check out the preview!

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"How Do I Teach Mathematics in a Culturally Responsive Way?"

Here is a wonderful article explaining ways in which teachers can teach math in a culturally responsive way. Some of the key points are:

Dispel the myth that math is a culturally neutral subject by discussing how math is influenced by culture.

As I mentioned above, math teachers can make their classrooms culturally responsive by integrating culturally relevant content and social issues.

Set high expectations for all students, but at the same time, make it evident to all students that you believe in them.

Build a learning community in your classroom by setting clear expectations about social behavior in the classroom and by allowing more time for cooperative learning in the school day. Use heterogeneous grouping so that students are exposed to a wide range of cultures.

Be accepting of and open to students' unique solving problem methods and thinking patterns.

Last but not least, teachers should model culturally responsive practices by advocating for their students!

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How Do I Teach Mathematics in a Culturally Responsive Way.pdf

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Students who are not getting subtraction facts with starting numbers up to 12 may benefit from additional subtraction fact practice using concrete manipulatives such as unifix cubes or counters on ten frames. Using these manipulatives, students can build their starting numbers and physically take away the subtrahend from the starting number. Students should practice building representations of subtraction problems in this way until they gain an understanding of what it means to subtract one number from another. Once students display understanding of 'take away' intervention support should be scaffolded so that parts of the starting number are hidden, and students must use subtraction to determine the hidden amount. For example, you may show a student ten counters and ask them to count the number of counters. Then, you may cover a certain number of counters with a cup and ask students to tell you how many are hidden based on how many are still visible.

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In this activity, students play a modified game of war using a deck of cards. A deck of cards is dealt between two players, and the players each flip two cards over from the top of their piles. The students create a subtraction problem using the numbers on their two cards, and the student with the highest difference gets to collect the cards. If both students arrive at the same answer, they play a round of war in which they lay the top four cards from their pile face down and choose two to flip. Both students add the numbers on their cards, and the student with the highest sum collects the cards. Struggling learners should be encouraged to record equations and to use pictorial or concrete representations to help them solve the subtraction problems as they play.

This would be an effective intervention activity for struggling learners for several reasons:

The game can be scaffolded by removing cards from the deck. For instance, you could play with cards ace through five, cards ace through ten, or cards ace through king, assigning values to the face cards.

In this game, students practice setting up subtraction problems correctly by starting with the largest number.

This game aids students in becoming fluent in their subtraction facts.

This game is sprinkled with additional  math skills like addition and number comparison.

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Subtraction War
In this activity, students play a modified game of war using a deck of cards. A deck of cards is dealt between two players, and the players each flip two cards over from the top of their piles. The students create a subtraction problem using the numbers on their two cards, and the student with the highest difference gets to collect the cards. If both students arrive at the same answer, they play a round of war in which they lay the top four cards from their pile face down and choose two to flip. Both students add the numbers on their cards, and the student with the highest sum collects the cards. Struggling learners should be encouraged to use pictorial or concrete representations to help them solve the subtraction problems as they play.

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This number talk by Sherry Parrish is meant to encourage students to remove the subtrahend from the starting number in parts. The first number string, featuring subtraction problems with a starting number of 12, would be particularly suited for this lesson.

Parrish, S. (2014). Number talks: Whole number computation, grades K-5. Sausalito, CA: Math Solutions.

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Jigsaw Student Rubric

This is the rubric that will be used to evaluate students. It is also the rubric that the self-assessment is structured around.

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Subtraction Story Problem Exemplar

This exemplar is an example of how students should solve subtraction story problems based on the Jigsaw rubric. It includes notations that students use to help them understand the problem, a strategy for solving the problem, a key, an answer, and an equation. This exemplar, however, is missing a personal connection to the problem so I would add this when making my own.

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Classroom Number Line
Although individual number lines were provided to students for this lesson, it is always a good idea to have a number line visible in the classroom as well.

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Examples of Rubric Criteria
These posters are concise descriptions of the criteria outlined by the Jigsaw rubric. Each poster provides a brief description of the expectations and features examples that students to which students can refer during classroom activities.