Place Value Concepts, Multiplication/Division Strategies, Fractions / Projected Time Allotment:
11days
Global Concept Guides:Place Value Concepts, Multiplication/Division Strategies, Fractions
Prior Learning:These concepts have been taught earlier in the year; however, in the past district data has strongly suggested that students struggle in the above concepts.
Sample Show What you Know Task:Use Mock FCAT, Form 2, and all other formal and informal data you have collected on your students to determine their strengths and weaknesses.
NGSSS
Place Value Concepts:
MA.3.A.6.1 Represent, compute, estimate and solve problems using numbers through hundred-thousand.
MA.3.A.6.2 Solve non-routine problems by making a table, chart, or list and searching for patterns.
Multiplication/Division:
MA.3.A.1.1 Model multiplication and division including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement, partitioning.
MA.3.A.1.2 Solve multiplication and division fact problems by using strategies that result from applying number properties.
MA.3.A.1.3 Identify, describe and apply division and multiplication as inverse operations.
Fractions:
MA.3.A.2.1 Represent fractions, including fractions greater than one, using area, set, and linear model.
MA.3.A.2.2 Describe how the size of the fractional part is related to the number of equal sized pieces in the whole.
MA.3.A.2.3-Compare and order fractions, including fractions greater than one, using models and strategies.
MA.3.A.2.4- Use models to represent equivalent fractions, including fractions greater than 1, and identify representations of equivalence. / Comments:
Notes on Assessments:
There is no performance task associated with this unit of study.
FCAT sample problems for each critical area can be found by clicking the link for each standard on the left.
Unpacking the Standards for this Task:This unit of study involves students engaging in concepts that have already been introduced during the school year. Previous district data suggests that students struggle with the following concepts:
- Place Value Concepts
- Multiplication/Division Strategies
- Fractions
Common Performance Task for this unit: There is no performance task associated with this unit of study.
3rd / Global Concept 1 of 3for this Unit of Study: Place Value Concepts / Projected Time Allotment:
3days
Sample Essential Questions: Use your data to determine which of the following essential questions would be most beneficial to your students.
- How can making a list help you solve a problem?
- How can you flexibly represent 3 or 4-digit numbers in different ways?
- How are the different ways you read and write numbers related?
- What are strategies for solving estimation problems?
- How do you regroup when adding or subtracting?
- How can you use different strategies to add and subtract 4-digit numbers?
- How can you justify which operation to use when solving problems?
Related Go Math Chapter Test Questions: FCAT sample problems for each critical area can be found by clicking the link for each standard on the Unit of Study.
Instructional Resources
Manipulatives:
- Base Ten Blocks – to directly model the values of numbers and also to show addition and subtraction.
- Place Value Mat- to display the value of each digit in its location/value within a number.
- Number line- to display the location of numbers and solutions in problems.
- Grid paper- for students having difficulty with alignment of digits when adding and subtracting.
- Secret Code Cards- used to represent numbers in expanded form (Go Math Manipulative kit)
- Three Other Ways - Students will be given a number and then have to find at least three other ways of representing this number by composing and decomposing the number. They will also be given various models and numeric representations and will be asked to writethese in standard form.
- The Great Round Up! - Students will be using number cubes to compose the greatest three digit number, then round it to the nearest 100. Students will then compare their numbers with the members of their group.
- Field Day Fun -In this task, students will solve addition and subtraction word problems
- I have a Story, You have a Story - Students will solve two story problems and create their own story problems to match a given number sentence.
- How Many Ways? - In this task students find possible combinations of Base Ten Blocks that can be used to represent a given number.
- Clear the Mat - In this game, students roll a number cube, remove Base Ten Blocks from their place-value mats to model regrouping. They look for a strategy for being the first team to remove all the blocks from their mat.
- And the Winning Number Is… - In this task, students estimate the value of sets of base-ten blocksand discuss estimation strategies. The students use them to show numbers in different ways by regrouping ones, tens, and hundreds. They solve problems requiring them to compare numbers shown in different ways. Finally, students investigate the effect of changing place values with given quantities of models or digits.
- Value System - Students will write numbers in expanded form, standard form and use a place value chart. Omit all expanded powers of ten problems.
Sample HOT Questions: Use these to facilitate student discussion (SMP 1, 3)
- Explain how rounding and using compatible numbers can help you solve addition and subtraction problems?
- Explain which strategy is the most efficient when solving problems?
- When do you use regrouping when adding or subtracting? Justify your reasoning.
- Explain how you decided which operation to use when solving problems?
- Why do we estimate sums and differences?
Our students are able to…
- Represent and identify numbers through the hundred thousand’s place in real-world contexts. (SMP 4)
- Compare and order numbers through the hundred thousand’s place in real-world contexts. (SMP 4)
- Find estimates of sums and differences based on real world scenarios using both rounding and compatible numbers. (SMP 1)
- Justify why rounding will help when finding an estimate. (SMP 3)
- Justify how compatible numbers will help when finding estimates. (SMP 3)
- Accurately regroup and provide reasoning when it is necessary in addition and subtraction problems. (SMP 3, 7)
- Communicate precisely using terms such as: regrouping, and addend, sum, difference, estimate, round and, compatible, expanded form, standard form, word form, digit, number, cubes, flats, rods, and units. (SMP 6)
- Provide real world problems. (SMP 4)
- Provide students with number lines. (SMP 5)
- Provide opportunities for students to discuss their strategies and solutions with peers. (SMP 3)
- Provide opportunities for students to see multiple strategies when adding and subtracting larger numbers. (SMP 4)
- Provide students with real world situations when estimating would be appropriate. (SMP 1)
- Have students determine if the actual sum or difference would be greater than or less than their estimates. (SMP 2)
- Provide students with opportunities to use tables and charts to explore patterns. (SMP 7)
- Communicate precisely using terms such as: regrouping, and addend, sum, difference, estimate, round and, compatible, expanded form, standard form, word form, digit, number, cubes, flats, rods, and units. (SMP 6)
3rd / Global Concept 2 of 3for this Unit of Study: Multiplication/Division Strategies / Projected Time Allotment:
4days
Sample Essential Questions: Use your data to determine which of the following essential questions would be most beneficial to your students.
- How can you use equal groups to find how many in all?
- How can I use tools and pictures to help write equations to solve problems?
- How can we use arrays to write related facts?
- How can you use multiplication to solve division problems?
- How can you use the Distributive Property to find products?
- How do combination problems relate to multiplication and what strategies con you use to solve them?
Related Go Math Chapter Test Questions: FCAT sample problems for each critical area can be found by clicking the link for each standard on the Unit of Study.
Instructional Resources
Manipulatives:
- Unit Cubes – to directly model problems
- Two Color Counters – to directly model problems
- Snap Cubes – to directly model problems
- Color Tiles – to directly model problems
- Number Line- Students will use jumps to represent equal groups and the intervals to represent the number in each group. Click hereto see how to connect equal groups to the linear model.
- Big Idea 1 Review Project: Horses in the Movies – GoMath Florida Benchmark Practice Book SE p. 315-318 and TE p. 156-157 Watch the GoMath On Location Video Unit 2 Horses in the Movies and then students complete the activity from the Benchmark book.
- It’s in the Bag - In this task, students work in groups to determine whether or not a collection of Base-Ten Blocks can be shared equally with no remainders. Students have the opportunity to predict outcomes, make equal shares, look for patterns in division problems, and discover multiplication is the inverse of division.
- One Hundred Hungry Ants! - In this task, students will determine the factors of a product by creating equal groups of counters/colored tiles.
- Arrays on a Farm - In this task the students use arrays to make estimates and solve multiplication problems.
- Family Reunion - In this task students are given a multi-step problem scenario where they are to find multiple ways for grouping a number of items.
- The Doorbell Rang - In this task students are building the conceptual understanding of division through a literature connection. Other problem solving questions are given in addition to the literature connection.
- Seating Arrangements - In this task, students will solve a word problem requiring them to make arrays using the number 24 to provide seating for a school presentation.
- Stuck on Division - In this task, students will experiment with a set of 12 connecting cubes to determine the division patterns when the dividend is 12. Students will explore 3 strategies when solving division problems: separating into equal groups, repeated subtraction, and multiplication (inverse operation).
- Sharing Pumpkin Seeds - In this task students will decide how to share pumpkin seeds fairly with a group; this lesson also reviews multiplication and division as inverse operations.
- Field Day Blunder - In this task students are given a multi-step problem scenario where they are to find multiple ways to arrange relay race teams.
Sample HOT Questions: Use these to facilitate student discussion (SMP 1, 3)
- How can you use a number line to skip count to find the total?
- What information in the problem is represented by the intervals on your number line?
- What do the numbers in your expression/equationrepresent from the problem?
- Does your expression/equation match the problem? Explain.
- How did you know what operation to use to solve the equation?
- What happens to the product when you change the order of your factors?
- Why would grouping factors make it easier to multiply?
- How would making an array help you group the factors?
- How do you know when you have made all possible combinations?
- Could you have grouped your combinations in any other way? Explain?
Our students are able to…
- Use multiple tools to represent given situations. (SMP 1,5)
- Explain what their models represent and justify the models created. (SMP 3)
- Directly model given situations and write expressions to match them. e.g. 7+7+7 or 3X7 (SMP 2)
- Explain what the models represent. (SMP 1,4)
- Create models which show the actions in a problem. (SMP 1,2,4)
- Write equations that represent what is happening in the problem. (SMP 2)
- Determine whether a problem can be solved using multiplication or division (SMP 1, 3)
- Use strategies (tools, pictures, Distributive Property) to solve problems. (SMP 5)
- Evaluate efficiency of strategies used. (SMP 1,3)
- Communicate precisely using terms such as: addend, sum, multiplier, factor and product, Distributive Property, Associative Property, decompose, compose, dividend, divisor, quotient, and difference to explain the actions of the problem.(SMP 6)
- Provide opportunities for students to utilize manipulatives to model problems including equal groups. (SMP 1,5)
- Question student responses and require justification of strategies (SMP 3).
- Examine students’ models to ensure the model and/or expression matches the given situation. (SMP 3)
- Encourage students to decompose arrays to solve problems (SMP 1,5)
- Examine students’ models to ensure the model and/or expression matches the way they decomposed their array (SMP 3)
- Have students record thinking to ensure all combinations are created. (SMP 4,6)
- Ensure students are creating models and equations that match what is happening in the problem and communicate strategies, analyze each other’s solutions, and justify conclusions. (SMP 3)
- Ensure students communicate strategies, analyze each other’s solutions, and justify conclusions. (SMP 2,3)
- Communicate precisely using terms such as: addend, sum, multiplier, factor and product, Distributive Property, Associative Property, decompose, compose, dividend, divisor, quotient, and difference to explain the actions of the problem.(SMP 6)
3rd / Global Concept 3 of3 for this Unit of Study: Fractions / Projected Time Allotment:
4days
Sample Essential Questions: Use your data to determine which of the following essential questions would be most beneficial to your students.
- How can you show fair shares in different ways?
- How do you know when a fraction is greater than one? Explain.
- What is the relationship between the numerator and denominator?
- How do you represent sets that are greater than one whole?
- How can I plot and identify fractions on a number line, including fractions greater than one?
- How can I use models, including number lines to compare and order fractions?
- How can you use the benchmarks 0, , 1 to compare and order fractions?
- How can you compare fractions that have the same numerator?
- How can you use the strategy pieces missing to compare fractions?
- How can you compare fractions, including fractions greater than one using efficient strategies?
- How can you use models and number line to name equivalent fractions, including fractions greater than one?
Related Go Math Chapter Test Questions: FCAT sample problems for each critical area can be found by clicking the link for each standard on the Unit of Study.
Instructional Resources
Manipulatives:
- Number line- students plot points on a number line to compare and order
- Pattern Blocks/DeciBlocks- use blocks to determine fractional areas of each shape
- Fraction Circles- use fraction circles to determine fractional parts to compare
- Fraction Tiles- use fraction tiles to determine fractional parts (great connection to linear model and number line)
- Cuisenaire Rods- use Cuisenaire rods to determine fractional parts
- Two color counters- these can be used to create set models
- Centimeter cubes- these can be used to create set models
- Color Tiles- these can be used to create set models
- Fraction Strips- Connect area models to linear models
- Big Idea 2 Review Project: The Skateboard Designer – GoMath Florida Benchmark Practice Book SE p. 319-322 and TE p. 158-159 Watch the GoMath On Location Video Unit 3The Skateboard Designer and then students complete the activity from the Benchmark book.
- Pattern Block Fractions – In this activity students partition pattern blocks to represent various fractions. This activity does not only use a single hexagon to represent a whole so students will have to use some critical thinking.
- Comparing Fractions with Brownies - Students will demonstrate their understanding of comparing fractions with the same numerator through engaging problem solving using real-world application with brownies as a model. Students will be actively engaged in a fraction war game and "would you rather have" statements to solidify their understanding of comparing fractions with the same numerator.
- It’s All About the Whole - Students explore the concept of unit fractions. They make sense of the structure of a fraction and make generalizations about unit fractions, and then apply those generalizations when creating a whole from a unit fraction.
- Fun With Pattern Block Fractions – This activity includes five lessons on naming fractions, each one getting more complex. All these activities use pattern blocks to name and identify fractions.
- Fun With Fractions – This activity includes five lessons on naming and identifying fractions. These lessons use Cuisenaire Rods.
- The Fractions String - In this lesson students create a model of a number line using string and adding machine tape. Students discover how to partition the string into equal sections, and name the fractional pieces, including fractions greater than 1.
- Eggsactly With Fractions – This activity includes six lessons on looking at the set model for fractions.
- Fishin’ For Fractions – In this activity students can compare fractions to benchmark fractions. There are games and activities aligned with several tasks involving benchmark fractions. Teachers are even provided with anecdotal forms for documenting student progress.
- Wipe Out! -This is a game that has students pick pattern blocks and then compare and order the fractions created.
- Logic Riddles -Students create and solve logic riddles using color tiles and identifying what fraction of a set is given