How Many More Fish?

This unit focuses on comparative subtraction. The students use fish-shaped crackers to explore five meanings for the operations of subtraction (counting, sets, number line, balance, and inverse of addition). Comparative subtraction extends the students early understandings about counting, addition, and subtraction in the take-away mode. In this unit, the students investigate properties of subtraction, represent subtraction in objects and pictures, and record subtraction in both vertical notation and equations. They create and solve problems involving comparative subtraction. Students answer such questions as "How many more?" and "How many less?" Missing addend activities provide students with an experience in algebraic thinking. Data is an area that is a logical extension of this unit.

Standards & Objectives

Academic standards
CCSS.ELA-Literacy.L.2.1
Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
CCSS.ELA-Literacy.L.3.1
Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
CCSS.ELA-Literacy.L.4.1
Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
CCSS.ELA-Literacy.L.5.1
Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
CCSS.ELA-Literacy.L.5.2
Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
CCSS.ELA-Literacy.L.5.3
Use knowledge of language and its conventions when writing, speaking, reading, or listening.
CCSS.ELA-Literacy.SL.5.6
Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation. (See grade 5 Language standards 1...
CCSS.ELA-Literacy.W.5.3
Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.
CCSS.Math.Content.1.NBT.B.3
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
CCSS.Math.Content.1.NBT.C.4
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete...
CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative...
CCSS.Math.Content.1.OA.B.4
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
CCSS.Math.Content.1.OA.C.5
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
CCSS.Math.Content.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 (e.g., 8 +...
CCSS.Math.Content.1.OA.D.7
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of...
CCSS.Math.Content.1.OA.D.8
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number...
CCSS.Math.Content.2.MD.B.6
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and...
CCSS.Math.Content.2.MD.D.10
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together,...
CCSS.Math.Content.2.NBT.A.4
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of...
CCSS.Math.Content.2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the...
CCSS.Math.Content.2.OA.B.2
Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.
CCSS.Math.Content.3.MD.B.3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and...
CCSS.Math.Content.3.MD.B.4
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where...
CCSS.Math.Content.3.MD.C.5
Recognize area as an attribute of plane figures and understand concepts of area measurement.
CCSS.Math.Content.3.MD.C.6
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
CCSS.Math.Content.3.MD.C.7
Relate area to the operations of multiplication and addition.
CCSS.Math.Content.3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties...
CCSS.Math.Content.3.OA.A.1
Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a...
CCSS.Math.Content.3.OA.A.2
Interpret whole-number quotients of whole numbers, e.g., interpret 56 / 8 as the number of objects in each share when 56 objects are partitioned...
CCSS.Math.Content.3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g.,...
CCSS.Math.Content.3.OA.A.4
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number...
CCSS.Math.Content.3.OA.B.5
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative...
CCSS.Math.Content.3.OA.B.6
Understand division as an unknown-factor problem. For example, find 32 / 8 by finding the number that makes 32 when multiplied by 8.
CCSS.Math.Content.3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 =...
CCSS.Math.Content.3.OA.D.8
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity....
CCSS.Math.Content.3.OA.D.9
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations....
CCSS.Math.Content.4.MD.A.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room...
CCSS.Math.Content.4.MD.B.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of...
CCSS.Math.Content.4.NBT.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place...
CCSS.Math.Content.4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the...
CCSS.Math.Content.4.OA.A.2
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown...
CCSS.Math.Content.4.OA.A.3
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which...
CCSS.Math.Content.4.OA.C.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself....
CCSS.Math.Content.5.NBT.A.2
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the...
CCSS.Math.Content.5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
CCSS.Math.Content.5.OA.A.2
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express...
CCSS.Math.Content.5.OA.B.3
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting...
CCSS.Math.Content.K.CC.A.1
Count to 100 by ones and by tens.
CCSS.Math.Content.K.CC.A.3
Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
CCSS.Math.Content.K.CC.C.6
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using...
CCSS.Math.Content.K.CC.C.7
Compare two numbers between 1 and 10 presented as written numerals.
CCSS.Math.Content.K.MD.B.3
Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.1
CCSS.Math.Content.K.OA.A.1
Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal...
CCSS.Math.Content.K.OA.A.2
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
CCSS.Math.Content.K.OA.A.5
Fluently add and subtract within 5.
GLE 0201.1.1
Demonstrate control of basic English usage, mechanics, spelling, and sentence structure.
GLE 0206.2.1
Understand and use place value concepts to 1000.
GLE 0206.2.2
Understand and use the base-ten numeration system.
GLE 0301.1.1
Demonstrate knowledge of Standard English usage, mechanics, and spelling.
GLE 0306.1.3
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0306.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0306.2.2
Develop understanding of multiplication and related division facts through multiple strategies and representations.
GLE 0306.2.3
Relate multiplication and division as inverse operations.
GLE 0306.2.4
Solve multiplication and division problems using various representations.
GLE 0306.3.1
Develop meaning for and apply the commutative, associative, and distributive properties using various representations.
GLE 0306.3.2
Develop understanding that a letter or a symbol can represent an unknown quantity in a simple mathematical expression/equation.
GLE 0306.3.3
Describe and analyze patterns and relationships in contexts.
GLE 0306.5.1
Organize, display, and analyze data using various representations to solve problems.
GLE 0401.1.1
Demonstrate knowledge of Standard English usage, mechanics, and spelling.
GLE 0406.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0406.2.2
Develop fluency with multiplication and single-digit division.
GLE 0501.1.1
Demonstrate knowledge of Standard English usage, mechanics, and spelling.
GLE 0501.3.2
Write in various modes and genres, including narration, literary response, personal expression, description, and imaginative.
SPI 0306.1.5
Represent problems mathematically using diagrams, numbers, and symbolic expressions.
SPI 0306.1.8
Express answers clearly in verbal, numerical, or graphical (bar and picture) form, using units when appropriate.
SPI 0306.2.5
Identify various representations of multiplication and division.
SPI 0306.2.6
Recall basic multiplication facts through 10 times10 and the related division facts.
SPI 0306.2.7
Compute multiplication problems that involve multiples of ten using basic number facts.
SPI 0306.2.8
Solve problems that involve the inverse relationship between multiplication and division.
SPI 0306.3.4
Describe or extend (including finding missing terms) geometric and numeric patterns.
SPI 0306.4.6
Measure length to the nearest centimeter or half inch.
SPI 0306.5.1
Interpret a frequency table, bar graph, pictograph, or line plot.
SPI 0306.5.2
Solve problems in which data is represented in tables or graph.
SPI 0306.5.3
Make predictions based on various representations of data.
SPI 0406.3.2
Make generalizations about geometric and numeric patterns.
SPI 0406.3.3
Represent and analyze patterns using words, function tables, and graphs.
SPI 0501.1.2
Identify the correct use of verbs (i.e., action/linking, regular/irregular, agreement, tenses) within context.
SPI 0501.3.10
Select appropriate time-order or transitional words/phrases to enhance the flow of a writing sample.
TSS.ELA.5.FL.SC.6
Demonstrate command of the conventions of standard English grammar and usage when speaking and conventions of standard English grammar and usage, including...
TSS.ELA.5.FL.WC.4
Know and apply grade-level phonics and word analysis skills when encoding words; write legibly.
TSS.ELA.5.SL.PKI.6
Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation.
TSS.ELA.5.W.TTP.3
Write narratives to develop real or imagined experiences or events using an effective technique, such as descriptive details and clear event sequences.
TSS.Math.2.MD.B.6
Represent whole numbers as lengths from 0 on a number line and know that the points corresponding to the numbers on the number line are equally spaced. Use...
TSS.Math.2.MD.D.10
Draw a pictograph and a bar graph (with intervals of one) to represent a data set with up to four categories. Solve addition and subtraction problems...
TSS.Math.2.NBT.A.4
Compare two three-digit numbers based on the meanings of the digits in each place and use the symbols >, =, and
TSS.Math.2.NBT.B.7
Add and subtract within 1000 using concrete models, drawings, strategies based on place value, properties of operations, and/or the relationship between...
TSS.Math.2.OA.B.2
Fluently add and subtract within 30 using mental strategies. By the end of 2nd grade, know from memory all sums of two one-digit numbers and related...
TSS.Math.3.MD.B.3
Draw a scaled pictograph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less...
TSS.Math.3.MD.B.4
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the...
TSS.Math.3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of...
TSS.Math.3.OA.A.1
Interpret the factors and products in whole number multiplication equations.
TSS.Math.3.OA.A.2
Interpret the dividend, divisor, and quotient in whole number division equations.
TSS.Math.3.OA.A.3
Multiply and divide within 100 to solve contextual problems, with unknowns in all positions, in situations involving equal groups, arrays, and measurement...
TSS.Math.3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one...
TSS.Math.3.OA.D.9
Identify arithmetic patterns (including patterns in the addition and multiplication tables) and explain them using properties of operations.
TSS.Math.4.OA.C.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For ...
TSS.Math.5.OA.A.2
Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them.
TSS.Math.5.OA.B.3
Generate two numerical patterns using two given rules.
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Learning objectives: 

Learning Objectives

Students will:

  • Review the models for subtraction.
  • Practice subtraction in a variety of formats.

NCTM Standards and Expectations:

  • Count with understanding and recognize "how many" in sets of objects.
  • Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  • Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
  • Use multiple models to develop initial understandings of place value and the base-ten number system
  • Understand the effects of adding and subtracting whole numbers.
  • Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.
  • Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Lesson Variations

Blooms taxonomy level: 
Understanding

Helpful Hints

Materials:

  • Buttons  
  • Brightly colored paper  
  • Crayons  
  • Graphing tool (for Station 3)  
  • Button Bingo Grid Activity Sheet (for Station 5)

References

Contributors: