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Author: Alissa.Ouderkirk

  • Grade 4 Social Studies Unit 3

    Colonial and Revolutionary Period in New York

    Unit description:  In this unit, students will study how European exploration led to the colonization of the region that became New York State and how important Colonial New York was during the Revolutionary Period. Students will study how Colonial New York became home to many different peoples, including European immigrants, and free and enslaved Africans and the relationships that existed between colonizing people and the Native Americans. In addition, students will examine the many conflicts between England and the 13 colonies over issues of political and economic rights.

    Download the complete Grade 4 Social Studies Unit 3 framework to customize for your own planning.

    Standards

    Standards: 1, 3, 4; Themes: MOV, TCC, GEO, SOC, GOV

    Essential Questions and Big Ideas

    Big idea of the unit: The Colonial and Revolutionary period was an extremely important time in New York’s history.

    • How did European exploration lead to the colonization of the region that eventually became New York State?
      • Europeans in search of a route to Asia explored New York’s waterways. Early settlements began as trading posts or missions.
    • Beginning in the early 1600s, how did New York become home to so many people from different countries? 
      • Colonial New York became home to many different peoples, including European immigrants, and free and enslaved Africans. Colonists developed different lifestyles.
    • What events led to the American Revolution and what role did New York State play? 
      • Growing conflicts between England and the 13 colonies over issues of political and economic rights led to the American Revolution. 
        New York played a significant role during the Revolution, in part due to its geographic location.
    • What was the role of Native American’s and African American’s during the time of the Revolution? 
      • African Americans and Native American’s volunteered to fight for both sides during the Revolutionary War.

  • Grade 5 Math Unit 3

    Fractions: Add and Subtract, Multiply and Divide, Line Plots with Fractions

    Unit description:  Students will extend their knowledge of adding and subtracting fractions with like denominators from fourth grade to fractions with unlike denominators.  Students will extend their knowledge of multiplying fractions by whole numbers to multiply fractions by other fractions and mixed numbers.  Students will consider the contexts for dividing unit fractions by whole numbers and dividing whole numbers by unit fractions and the relationship of the quotient to the dividend and divisor.  Students will also use their knowledge of fractions to create and interpret line plots with fractional measures on the scale.  

    Essential Outcomes of the Unit 

    Number and Operations—Fractions- Use equivalent fractions as a strategy to add and subtract fractions.

    • 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
    • 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers

    Number and Operations—Fractions- Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

    • 5.NF.3 Interpret a fraction as division of the numerator by the denominator (𝑎𝑎 𝑏𝑏 = a ÷ b).  Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
    • 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction.
    • 5.NF.4a Interpret the product 𝑎𝑎 𝑏𝑏 × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
    • 5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with rectangles of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
    • 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.

    Measurement and Data- Convert like measurement units within a given measurement system.

    • 5.MD.2 Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems.

    Other Standards Addressed in the Unit

    Operations and Algebraic Thinking- Operations and Algebraic Thinking

    • 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

    Number and Operations—Fractions- Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

    • 5.NF.5 Interpret multiplication as scaling (resizing).
    • 5.NF.5a Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
    • 5.NF.5b Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case). Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence 𝑎𝑎 𝑏𝑏 = 𝑎𝑎 𝑏𝑏 × 𝑛𝑛 𝑛𝑛 to the effect of multiplying 𝑎𝑎 𝑏𝑏 by 1.
    • 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement until grade 6 (NY-6.NS.1).
    • 5.NF.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
    • 5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients.
    • 5.NF.7c Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.

    Essential Questions and Big Ideas

    How do operations with fractions relate to operations with whole numbers?

    • Addition, subtraction, multiplication, and division can be completed with fractions.  
    • Addition and subtraction still represent putting together or taking apart and part and whole relationships.  
    • Multiplication can represent finding a total made from equal groups or scaling. 
    • Division represents splitting an amount into equal groups.  

    What do equivalent fractions represent and why are they useful when solving equations with fractions?

    • Equivalent fractions are fractions that are equal or take up the same amount of space.  
    • To add and subtract fractions, they must have the same denominator or unit size.  

    How can I find the area of a rectangle with fractional side lengths?

    • Length times width equals area.  
    • Side lengths can be broken up and multiplied using the distributive property.  

    What are the effects of multiplying by quantities greater than 1 compared to the effects of multiplying by quantities less than 1?

    • Multiplying by an amount greater than one creates a product that is greater than the other factor. 
    • Multiplying by an amount less than one creates a product that is less than the other factor.  

    What does it mean to divide by a fraction?  Or to divide a fraction by a whole number?

    • Dividing by a fraction represents splitting a fraction into equal parts.  
    • Dividing a whole number by a fraction represents splitting a whole into fractional parts.    

    Download the complete Fractions: Add and Subtract, Multiply and Divide framework to customize for your own planning.

  • Grade 1 Math Unit 3

    Place Value Comparison- Addition and Subtraction Beyond 20

    In this unit, students will learn to use their number sense to compare (using symbols  >, =, and <.) and order values of two two-digit numbers. They will model, write and solve addition and subtraction equations within 100 including composing new tens when necessary when adding. The students will apply mental math strategies when adding and subtracting multiples of ten.

    Essential Outcomes of the Unit

    Number and Operations in Base Ten- Understand place value

    NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

    Number and Operations in Base Ten- Use place value understanding and properties of operations to add and subtract

    NBT.4 Add within 100, including • a two-digit number and a one-digit number, • a two-digit number and a multiple of 10. Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. Relate the strategy to a written representation and explain the reasoning used.

    Other Standards Addressed in the Unit

    Number and Operations in Base Ten- Understand place value

    NBT.2c Understand the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

    Number and Operations in Base Ten- Use place value understanding and properties of operations to add and subtract

    NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

    NBT.6 . Subtract multiples of 10 from multiples of 10 in the range 10-90 using • concrete models or drawings, and • strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy used to a written representation and explain the reasoning

    Essential Questions and Big Ideas

    How can we compare values of numbers?

    • Numbers sense and understanding of place value are used to compare values of numbers.
    • The symbols symbols  > means more than, = means equal to, and < means less than when comparing two numbers.

    How do we add and subtract within 100?

    • Concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction can be used to add and subtract within 100.
    • Sometimes it is necessary to compose a new ten when adding within 100.

    How can we use number sense and understanding of place value to add and subtract using mental math?

    • Understanding number pairs that make ten help to add and subtract mentally.
    • Understanding place value and being able to count by tens and add ones can be used to add and subtract mentally.

    Download the complete Grade 1 Math Unit 3 framework to customize for your own planning.