Grade 1 Geometry Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary Shapes, sides, open, closed, defining attributes, non-defining attributes (color, size, slide, flip, turn), figure, two-dimensional shapes, three-dimensional shapes, composite shape, rectangle, square, trapezoid, half-circle, quarter-circle, cube, rectangular prism, cone cylinder We want students to understand that geometry is all around us in two-dimensional or three-dimensional figures. Geometric figures have certain properties and can be transformed, compared, measured, and represented. 1.G.1 - Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes. 1. What defining attributes are. 2. What non-defining attributes are. 1. How to determine which attributes of shapes are defining compared to those that are non-defining. Defining attributes are attributes that must always be present. Non-defining attributes are attributes that do not always have to be present. 1. State the non-defining attributes of a shape. 2. State the defining attributes of a shape. 3. Build or draw shapes that show defining attributes. 1.G.2 - Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape 1. The names of two-dimensional and threedimensional shapes. 1. How to compose (build) a two-dimensional or three-dimensional shape from two shapes. This standard includes shape puzzles in which students use objects (e.g., pattern blocks) to fill a larger region. 1. Manipulate two-dimensional and threedimensional shapes to make a new shape.
1.G.3 - Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 1. Students will know that circles can be divided in equal parts (halves, fourths, quarters). 2. Students will know that rectangles can be divided in equal parts (halves, fourths, quarters). 3. Students will describe the whole as two of, or four of the shares. 1. How to divide circles and rectangles into two and four equal parts. 2. That dividing circles and squares into smaller equal shares creates smaller shares. 3. The smaller shares create a whole. 1. Describe circles and rectangles that have been divided into equal shares using the words halves, fourths and quarters. 2. Model by drawing or using manipulatives (i.e. rectangle or circle cut outs) to show halves, fourths and quarters. 3. Explain and model that two parts or four parts equal a whole
Grade 1 Measurement Essential Questions: 1. How does estimation help you find a reasonable measurement? 2. How do you determine the tool and unit to help you accurately measure? 3. When do you need to measure? Essential Vocabulary Non-standard unit of measurement, shortest, longest, measure, length, compare, object, hour, half hour, analog clock, digital clock We want students to understand when to measure, what tool and unit to use, and how to use estimation to find a reasonable measurement. 1.MD.1 - Order three objects from a variety of cultural contexts, including those of Montana American Indians, by length; compare the lengths of two objects indirectly by using a third object. 1. How to compare two objects by using a third nonstandard unit of measurement. 1. How to order three objects in length. 2. How to measure with a non-standard unit. 3. How to compare the two objects being measured. 1. Put three objects in order from shortest to longest according to their length. 2. Measure with a non-standard unit. 3. Compare the objects being measured. 1.MD.2 - Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 1. When they are measuring with multiple copies of an object, the objects need to lay end to end with no gaps or overlaps. 1. How to correctly measure an object with a non-standard unit and know how many units long it is. 1. Measure an object with a non-standard unit of measurement and know how many units long the object is. 1.MD.3 - Tell and write time in hours and half-hours using analog and digital clocks. 1. Tell and write time in hours and half-hours using 1. Time to hours and time to half hours on an analog and digital clock. an analog and digital clock. 2. How to write time to the hour and half hour. 1. Tell time to the hour and half hour on an analog and digital clock. 2. Write time to the hour and half hour.
1.MD.4: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Data Category More Less 1. Data can be represented in multiple ways 2. Questions can be answered by observation of the data. 3. Data can compared 4. Data represents something in context 1. Organize, represent and interpret data in multiple ways 2. Categorize the data 3. Compare the data
Grade 1 Number Sense Essential Questions: 1. Why do we use numbers, what are their properties, and how does our number system function? 2. Why do we use estimation and when is it appropriate? 3. What makes a strategy effective and efficient and the solution reasonable? 4. How do numbers relate and compare to one another? Essential Vocabulary Count, number, counting on, digits, standard form, ones place, tens place, hundreds place, patterns, digits, ones, tens, place value, comparing, less than (<), greater than (>), and equal to (=), addition, subtraction,multiple, tens place, ones place, forward, backward, addition, subtraction, mental math, multiples of 10, subtract We want students to understand that all numbers have parts, values, uses, types, and we use operations and reasonableness to work with them. 1.NBT.1 - Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1. how to read, write and count numbers to 120 2. ones place, tens place, hundreds place 1. 1.NBT.1 calls for students to rote count forward to 120 by Counting On from any number less than 120. Students should have ample experiences with the hundreds chart to see patterns between numbers, such as all of the numbers in a column on the hundreds chart have the same digit in the ones place, and all of the numbers in a row have the same digit in the tens place. 1. count, read, and write to 120 2. represent a number of objects with a numeral and standard form 3. identify patterns on a hundreds chart 4. count on from any number less than 120 5. identify ones and tens place 1.NBT.2 - Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones called a ten. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, nine tens (and 0 ones). Enduring Understandings 1. Place value for ones and tens. 1. 1.NBT.2 asks students to unitize a group of ten ones as a whole unit: a ten. This is the foundation of the place value system. So, rather than seeing a group of ten cubes as ten individual cubes, the student is now asked to see those ten cubes as a bundleone bundle of ten. 1. Identify the value of ones and tens in a two-digit number.
1.NBT.3 - Compare two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 1. Value of two- digit numbers. 2. Greater than, less than, and equal to symbols. 1.NBT.3 builds on the work of 1.NBT.1 and 1.NBT.2 by having students compare two numbers by examining the amount of tens and ones in each number. Students are introduced to the symbols greater than (>), less than (<) and equal to (=). Students should have ample experiences communicating their comparisons using words, models and in context before using only symbols in this standard. 1. Identify the value of ones and tens in a two-digit number. 2. Compare the value of two numbers (two-digit) to determine greater then, less than, or equal. 1.NBT.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 models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1. How to use manipulatives to make a concrete model of addition. 1. How to use concrete models, drawings and place value strategies to add and subtract within 100. Ex. I used place value blocks and made a pile of 37 and a pile of 23. I joined the tens and got 50. I then combined those piles and got to 60. So there are 60 people on the playground. 1. Add a two-digit with a one-digit number 2. Add a two-digit and a multiple of ten 3. Compose a ten when addition of the ones place creates a number larger than 9 when using manipulatives.
2. The problem can be solved through models, drawings, written methods and words. 3. When adding two-digit numbers, one adds tens and tens and ones and ones. 1.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. 1. When counting by tens forward or backward, only the number in the tens place changes. 1. How to mentally add ten more and ten less than any number less than 100. Ample experiences with ten frames and the hundreds chart help students use the patterns found in the tens place to solve such problems. Example: There are 74 birds in the park. 10 birds fly away. How many are left? 1. Count by tens forward or backwards from any number less than 100. 1.NBT.6: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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 to a written method and explain the reasoning used. 1. How to subtract multiples of ten using a concrete model and relating it to a written method. 1. How to use concrete models, drawings and place value strategies to subtract multiples of 10 from decade numbers (e.g., 30, 40, 50). 1. Subtract multiples of ten in the range from 10-90.
Grade 1 Algebraic Thinking Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related? 4. How do algebraic representations relate and compare to one another? 5. How can we communicate and generalize algebraic relationships? Essential Vocabulary Adding, taking from, putting together, taking apart, comparing, unknown position, Associative property, commutative property (begin using these terms as you talk about the process), related facts, count on, count back, decomposing, related facts, doubles, double plus 1 or 2, doubles minus 1 or 2, inverse, unknown, equation, equal sign, operations, true, false We want students to understand how we use patterns and relationships of algebraic representations to generalize, communicate, and model situations in mathematics. 1.OA.1 - Use addition and subtraction within 20 to solve word problems, within a cultural context, including those of Montana American Indians, 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. 1. There are three types of addition and subtraction story problems: Result Unknown, Change Unknown, and Start Unknown. 1. A process that represents the three types of addition and subtraction problems (ie. Model Drawing) 1. Solve addition and subtraction problems within twenty using a process. (i.e. Model Drawing) 2. Use objects, drawings and equations with a symbol for the unknown number to represent the problem. 1.OA.2 - Solve word problems, within a cultural context, including those of Montana American Indians, that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1. Add three numbers within a story problem whose sum is less than twenty with a symbol for the unknown number (Result unknown, Change unknown, Start unknown). 1. How to add (join) three numbers whose sum is less than or equal to 20 with a symbol for the unknown number, using a variety of mathematical representations. 1. Model and explain using a variety of ways to solve (i.e. tens frame, number line, objects, drawings, equations with a symbol) a story problem with three numbers whose sum is less than twenty.
1.OA.3 - Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 1. Commutative property 8+3 = 11 then 3+8 = 11 2. Associative property 6+2+4 = 10+2 =12 3. The student does not need to know the formal terms for these properties. 1. Connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). 1. Show and explain that order does not matter when adding two numbers. 2. Show and explain when adding a string of numbers you can add any two numbers first. 1.OA.4: Understand subtraction as an unknown-addend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. 7 4 = can be expressed as 4 + = 7 1. How to use subtraction in the context of unknown addend problems. 1. Use cubes and counters, and representations such as the number line and the100 chart, to model and solve problems involving related facts between addition and subtraction. 1.OA.5: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1. How to count on or count back from any given 1. The connection between counting on and number up to twenty. counting back, adding and subtraction. 2. You start at the largest number and count on or count back from that point. 1. Count on and count back from any given number up to 20. 2. Hold the start number in their head and count on or back from that number. 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).
1. Multiple strategies to use to add and subtract numbers to twenty. 1. The relationship between the numbers in the equation. 2. The different strategies involved in adding and subtracting (i.e. counting on, making a ten, decomposing a number, using related facts, and creating equivalent but easier or known sum. 1. Quickly and accurately add and subtract numbers to ten. 2. Add and subtract numbers to twenty using multiple strategies. 1.OA.7: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. 1. That the equal sign is showing that the right and the left side of the equation need to be the same 1. Students need to understand that the equal sign does not mean answer comes next, but rather that the equal sign signifies a relationship between the left and right side of the equation. 1. Solve various representations of equations such as: an operation on the left side of the equal sign and the answer on the right side (5 + 8 = 13) an operation on the right side of the equal sign and the answer on the left side (13 = 5 + 8) numbers on both sides of the equal sign (6 = 6) operations on both sides of the equal sign (5 + 2 = 4 + 3). 1.OA.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 = _ 3, 6 + 6 = _. 1. That when solving an addition problem with an unknown, they can use subtraction to find the unknown. When solving a subtraction problem with an unknown, they can use addition to find the unknown. 1. Addition is the inverse of subtraction and subtraction is the inverse of addition. 1. Solve an addition or subtraction problem with an unknown number by knowing the inverse of the given problem.