4 rods for 240 and 1 flat, 1 rod for 110). Demonstrate joining the two separate numbers. Point and count each base ten block and then say the addition equation (240 plus 110 equals 350). Student watches. “Good, watching me.” Lead Materials Teacher Says/Does Student Response Teacher Feedback Teacher: Base Ten Blocks “We can use base ten blocks to add whole numbers.” Lay down base ten blocks. Point to, count, and name each whole number separately. (e.g. For the addition expression 240+110, lay down 2 flats, 4 rods for 240 and 1 flat, 1 rod for 110). Now you show the same whole numbers. Student lays down base ten blocks to show the same whole numbers modeled by teacher. Student points to/says each whole number. “Good job.”
Demonstrate joining the two separate whole numbers. Point and count each base ten block and then say the addition equation (240 plus 110 equals 350). “Now you join the whole numbers to find the sum.” Student joins two whole numbers to show the addition equation. Say/select the correct sum (e.g., 350). “Good job joining the whole numbers to find the sum.” Test Materials Teacher Says/Does Student Response Teacher Feedback Teacher: Base Ten Blocks “You can use base ten blocks to add whole numbers.” Say, “Now, you join the whole numbers in the addition expression.” Student lays down base ten blocks to show the whole numbers requested by the teacher. Student points to/says each whole number. “Good job.” Student makes an incorrect response or no response. “Watch me” and model the correct response, then have the student complete it correctly. Say, “Add your whole numbers.” Student joins two whole numbers to show the addition expression. Say/ select the correct sum (e.g., 350). “Good job joining the whole numbers to find the sum.”
FLS: MAFS.4.NF.1.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Access Point Narrative MAFS.4.NF.1.AP.2b Compare two given fractions that have different denominators. Essential Understandings: Concrete Understandings Representation Given a fraction (with a denominator of 10 or less), model the fraction with manipulatives in a rectangle or circle. Use manipulatives to model another fraction (with a different denominator of 10 or less) in the same whole. Compare the two models to determine if they are greater than, less than, or to one another. Locate two given fractions on separate number lines that are divided into equal parts to match each of the denominators. Use the number lines to determine if the fractions are equal, greater than, or less than each other based on their location on the number line (e.g., 3/4 > 1/2). Apply understanding of the symbols of <, >, and = with fractions. Understand the following concepts of comparison, greater than, less than, equal, fraction. Suggested Instructional Strategies: Compare fractions represented with models (e.g., circle divided in halves and in fourths with 1/2 and 3/4 shaded in.) Use rectangles that are the same size for students to partition and represent fractions. Use sentence strips/paper to generate number lines. Supports and Scaffolds: Assistive technology Virtual bars or tiles Pictures that have been divided Geoboards Dot Paper Cuisenaire Rods Color Tiles Pattern blocks or sets of objects Pie diagrams Fraction bars that are ruled into certain fixed partitions and lined up for comparisons.
Teacher: Fraction Bars “I can use fraction bars to model a whole and then divide it into equal parts.” Demonstrate a whole bar. Directly underneath it lay down unit fractions to equal the whole (e.g., (4) 1/4 pieces). Student watches. “Good, watching me.” “I have divided my whole into equal parts.” Student watches. “Good, watching me.” “Now I can see that a whole can be shown as repeated pieces of the same size (e.g., 3/4 = 1/4+1/4+1/4). Student watches. “Good, watching me.” Lead Materials Teacher Says/Does Student Response Teacher Feedback Teacher: Fraction Bars “We can use fraction bars to a whole and then divide it into equal parts” Demonstrate a whole bar. Directly underneath it lay down unit fractions to equal the whole (i.e., (4) 1/4 pieces). “Now your turn.” Student demonstrates a whole bar. Directly underneath it lay down unit fractions to equal the whole (i.e., (4) 1/4 pieces). “Good job modeling a whole and dividing it into equal parts.” Demonstrate pointing to the Student points to the whole. “Good pointing to the whole.”
Teacher says “Point to the whole.” “Now I can see that a whole can be shown as repeated pieces of the same size (i.e., 3/4=1/4+1/4+1/4). Demonstrate pointing to each of the equal parts. Teacher says “Point to each of the equal parts.” Student points to each of the equal parts. “Good job pointing to each of the equal parts.” Test Materials Teacher Says/Does Student Response Teacher Feedback Teacher: Fraction Bars “You can use fraction bars to model a whole and then divide it into equal parts. Lay down your whole bar and your unit fractions.” Student demonstrates a whole bar. Directly underneath it lay down unit fractions to equal the whole (i.e., (4) 1/4 pieces). “Good job modeling a whole and dividing it into equal parts.” Student an incorrect response or no response. “Watch me” and model the correct response, then have the student complete it correctly. “Point the whole.” Student points to the whole. “Good job pointing to the whole.” Student makes an incorrect response or no response. me” and model the correct response, then have the student complete it correctly.
MAFS.4.NF.2.AP.3c Match the vocabulary in a word problem to an action. Use manipulatives to model the context of the word problem. Count to find the answer. To add, use fraction manipulatives (each piece may be labeled with the corresponding unit fraction) to model each fraction and join them to find the sum (e.g., 1/4 + 2/4 = 3/4). To subtract, use fraction manipulatives (each piece may be labeled with the corresponding unit fraction) to model the first fraction in the expression and remove manipulatives that represent the fraction being subtracted (e.g., ¾ - 2/4 = 1/4). Create a pictorial representation of the word problem. Use context clues to interpret the concepts, symbols, and vocabulary for addition and subtraction. To add, use a visual representation of a whole divided into equal pieces (each piece may be labeled with the corresponding unit fraction). Shade each unit to represent the fractions in the expression and count the shaded units to find the sum. To subtract, use a visual representation of the first fraction in the expression. Cross out the piece(s) that represent the fraction being subtracted. Count the remaining piece(s) to find the remainder. Suggested Instructional Strategies: Model Materials Teacher Says/Does Student Response Teacher Feedback Teacher: Fraction Bars “I can use fraction bars to add fractions.” Lay down fraction bars. Point to and name each fraction separately. (E.g., for the addition expression 1/4 plus 1/4, lay down (2) 1/4 pieces Student watches. “Good, watching me.”
separately and say “1/4 and 1/4.” Demonstrate joining the two separate fractions and say the addition equation (e.g., 1/4 plus 1/4 is 2/4). Student watches. “Good, watching me.” Lead Materials Teacher Says/Does Student Response Teacher Feedback Teacher and Student: Fraction Bars “We can use fraction bars to add fractions.” Lay down fraction bars. to and name each fraction separately. (E.g., for the addition expression 1/4 plus 1/4, lay down (2) 1/4 pieces separately and say “1/4 and 1/4.” Student lays down fraction bars to show the same fractions modeled by teacher. Student points to/says each separate fraction. “Good job.” Demonstrate joining the two separate fractions and say the addition equation (e.g. 1/4 plus 1/4 is 2/4). Student two separate fractions to show the addition expression. Say/ select the correct sum (e.g., 2/4). “Good job joining the fractions to find the sum.” Test Materials Teacher Says/Does Student Response Teacher Feedback
Teacher and Student: Fraction Bars “We can use fraction bars to multiply a fraction by a whole number.” Demonstrate making an array by placing fraction bars in rows as indicated by the whole number in a given multiplication expression (e.g. 2x1/3=2 rows of 1/3, so lay down a fraction bar labeled 1/3 and say, “This is one group of 1/3,” and then lay down another fraction bar labeled 1/3 directly underneath it and say, “This is another group of 1/3”. Then say, “We have two groups of 1/3.”). Student lays down fraction bars to show the same multiplication array modeled by the teacher. Student points to/counts each group of the fraction. “Good job modeling the multiplication expression and counting each group.” Demonstrate using counting or repeated addition to find the product of the multiplication expression. (E.g., for counting, point to each fraction bar one at a time and say, “one third, two thirds. So, 2x1/3 is two thirds.”) For repeated addition, point to each fraction bar one at a time and say, “One third plus one third is equal to two thirds. So, 2x1/3 is two thirds.”). Student uses counting or repeated addition to find the product of the multiplication expression. Say/select the correct product. “Good job using addition to find the product.” Test Materials Teacher Says/Does Student Response Teacher Feedback
Student: Fraction Bars “Use fraction bars to multiply a fraction by a whole number.” “Lay your fraction bars on the array (template).” Student lays down fraction bars to show the multiplication expression requested by teacher. Student points to/counts each group of the fraction. “Good job modeling the multiplication expression and counting each group.” Student makes an incorrect response or no response. “Watch me” and model the correct response, then have the student complete it correctly. “Count or use repeated addition to find the product.” Student uses counting or repeated addition to find the product of the multiplication expression. Say/ select the correct product. “Good job using counting/repeated addition to find the product.” Student makes an incorrect response or no response. “Watch me” and model the correct response, then have the student complete it correctly. Repeat the *Model/Lead/Test with fractions that are not unit fractions. (E.g., for 2x2/5, lay two 1/5 fraction bars side by side to show one group of 2/5, and then lay two 1/5 fraction bars side by side directly beneath the other 2 fraction bars to show another group of 2/5, then use counting or repeated addition to find the product.) Pizza Fractions: cut out pizza circles the same size then cut them into a variety of labeled unit fractions and use them to multiply a fraction by a whole number by making groups of the fraction and then using counting or repeated addition to find the product. (E.g., for 3x1/4, put three groups of 1/4 onto a circle the size of the original circle, and then count 1/4, 2/4, 3/4 or add 1/4+1/4+1/4 to get 3/4.) Supports and Scaffolds: Circular fraction pieces (including wholes). Fraction bars that are ruled into certain fixed partitions. template for fraction bars Assistive technology iPad applications
Teacher: Image of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Image on a transparent overlay of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of the small base ten cube). Three cards, labeled 1/10, 1/100, and =. “I can use base ten shapes to find equivalent fractions.” Lay down an image of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Say, “This whole has been divided into ten equal parts and one of the parts is shaded, so this shows the fraction 1/10.” Lay down a card labeled with the fraction 1/10. Student watches. “Good, watching me.” Say, “Now I am going to show the same whole being divided into one hundred equal parts.” the image of the same square with a transparent overlay that has an image of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of the small base ten cube). Say, “the shaded area is still the same, but now there are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (pointing while counting) parts shaded because these parts are smaller. So, this shows the fraction 10/100.” Lay down a card labeled with the fraction 10/100. Student watches. “Good, watching me.” Lay down a card labeled with an equal sign. Student watches. “Good, watching me.”
Lead Materials Teacher Says/Does Student Response Teacher Feedback Teacher and Student: of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Image on a transparent overlay of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of the small base ten cube) cards, labeled 1/10, 1/100, and =. “We can use base ten shapes to find equivalent fractions.” Lay down an image of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Say, “This whole has been divided into ten equal parts and one of the parts is shaded, so this shows the fraction 1/10.” Lay down a card labeled with the fraction 1/10. Say, “Now, show me 1/10.” Student lays down/selects an image of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Then, lays down/selects a card labeled with the fraction 1/10. “Good job showing the fraction 1/10.” Say, “Now we are going to show the same whole being divided into one hundred equal parts.” Cover the image of the same square with a transparent overlay that has an image of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of the small base ten cube). Say, “the shaded area is still the same, but now there are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (pointing while counting) parts shaded because these parts are Student covers his/her same square with a transparent overlay that has an of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of a small base ten cube). Then, points to/counts the shaded parts and lays down/selects a card labeled with the fraction 10/100. “Good job showing the fraction 10/100.”
smaller. So, this shows the fraction 10/100.” Lay down a card labeled with the fraction 10/100. Say, “Now, show me 10/100.” Lay down a card labeled with an equal sign. Say, “Since the shaded area is the same for both squares, then 1/10 (lay down the 1/10 card in front of the equal sign) and 10/100 (lay down the 10/100 card after the equal sign) are equal.” Now, show me that these two fractions are equal. Student lays down/selects a card labeled with an equal sign. Then, the student lays down/selects the 1/10 card in of the equal sign and lays down/selects the 10/100 card after the equal sign. “Good job showing that 1/10 and 10/100 are equal.” Test Materials Teacher Says/Does Student Response Teacher Feedback Student: Image of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Image on a transparent overlay of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of the small base ten cube) “You can use base ten shapes to find equivalent fractions.” Say, “Show me 1/10.” Student lays down/selects an of a square (the size of a base ten flat) that has been divided into ten equal parts (the size of a base ten rod), with one of the parts shaded. Then, lays down/ selects a card labeled with the fraction 1/10. “Good job showing the fraction 1/10.”
Student: Image of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of a small base ten cube), with twenty-five of the parts shaded. Base Ten Blocks Place value chart labeled, ones, decimal, tenths, hundredths Cards labeled 25/100, 0.25, 0, 2, 5, and =. “You can use base ten blocks to find fractions and decimals that are equivalent.” Say, “Count the equal parts that are shaded and then show the matching fraction.” When given an image of a square (the size of a base ten flat) that has been divided into one hundred equal parts (the size of the small base ten cube), with 25 of the parts shaded, the student points to/counts the 25 shaded parts. Then, lays down/selects a card labeled with the fraction 25/100. “Good job showing the fraction 25/100.” Student makes an incorrect response or no response. me” and model the correct response, then have the student complete it correctly. Say, “Use the place value chart to show how many ones (hold up the base ten flat) are completely shaded.” The student places/selects a 0 in the ones column of the value chart. “Good job showing that there are zero ones shaded.” Student makes an incorrect response or no response. “Watch me” and model the correct response, then have the student complete it correctly. Say, “Use your base ten rods (hold up a base ten rod) to cover some of the shaded portion and then use your place value chart to show how many tenths are covered.” Student covers/selects two of the shaded tenths with the base ten rods. Then, places/ selects a 2 in the tenths column of the place value chart. “Good job showing that are two tenths shaded.” Student an incorrect response or no response. me” and model the correct response, then have the
student complete it correctly. Say, “Use your small base ten cubes (hold up a small base ten cube) to cover the rest of the shaded portion and then use your place value chart to show how many extra hundredths are covered.” Student covers/selects five of the shaded hundredths with the small base ten cubes. Then, places/selects a 5 in the hundredths column of the place value chart. “Good job showing that there are five extra hundredths shaded.” Student an incorrect response or no response. me” and model the correct response, then have the student complete it correctly. Say, “The shaded part shows twenty-five hundredths as decimal.” Next to the place value chart, lay down a card labeled with 0.25. Gesture to the place value chart to show how it is similar to the card. Say, “Show the decimal that matches the and the place value chart.” The student lays down/selects a card labeled with 0.25 next to the place value chart. “Good job showing the decimal 0.25.” Student makes an incorrect response or no response. “Watch me” and model the correct response, then have the student complete it correctly. Materials Teacher Says/Does Student Response Teacher Feedback Say, “Show a decimal that is equal to the fraction 25/100.” When presented with a card that is labeled with the fraction 25/100, followed by a card that is labeled with an equal sign, the “Good job showing that the fraction 25/100 and the decimal 0.25 are
“What types of lines are these? Perpendicular.” “Perpendicular.” “Good, are perpendicular lines. They form a 90 degree angle.” “What type of line segments are these? Perpendicular.” “Perpendicular.” “Good, are perpendicular line segments in a figure.” “What types of lines are these? Parallel.” “Parallel.” “Good, these are parallel lines. They are always an equal distance apart and never touch. “What type of line segments are these? Parallel.” “Parallel.” “Good, these are parallel lines in a figure.” Repeat each step above with a 4-second delay. Teacher may choose to do a zero round delay immediately followed by a 4-second delay for each expressive symbol (e.g. angles, perpendicular lines, parallel lines.) Use Example/Non-example for all different angles and a variety of shapes (See Instructional Resource Guide p.22) Supports and Scaffolds: Interactive Whiteboard Laminated cards with images Assistive technology