Course Guide - USAID Teacher Education Project

More documents

Recommendations

Info

or repeating (such as 1/3’s equivalent of 0.33333…), which can be indicated by a shortline over the repetend or repeating portion.3. How children think about these conceptsa. Most of children’s misconceptions about decimals are rooted in whole numberthinking. For example, being familiar with the magnitude of natural numbers,they assume that a number with many digits must be a large number. Extendingthis to decimals, the child mistakenly believes that .283 > 2.5 because the firstnumber has more digits, thinking that “longer” decimals have a greater valuethan “shorter” ones.b. Other children may become focused on the denominator and think that anynumber of tenths must be greater than any number of hundredths (orthousandths) because tenths are greater than hundredths (or thousandths). Thesechildren believe, for example, that 6.45 > 6.731 because thousandths are verysmall parts of a number.c. There is also confusion about how decimals relate to fractions. For example,some children believe that 1/8 and 0.8 are the same quantity—often becausethey learned that 1/10 and 0.1 are equivalent4. What is essential to know or do in classa. Decimals are a way to represent fractions whose denominators are multiples of 10 andis an extension of place value, and as such every fraction has a decimal equivalentb. Comparing and ordering decimals can be visualized with a number line and a decimalgrid in order to better understand the quantity a decimal fraction represents.c. Relate each of the above to children’s thinking5. Class Activitiesa. Begin by asking students in groups of no more than four to brainstorm for three minutesabout what they know or recall about decimals. Chart their responses.b. Ask students what a decimal point means and help them articulate extending numbersto the right of the decimal point as being a pattern consistent with what they alreadyknow about place value for whole numbers.c. Distribute the decimal grid and discuss how it is only one unit, but subdivided intohundredths. Ask them to show one-tenth, then one-hundredth, and then one-thousandth.(For thousandths they will have to divide one of the cells into ten parts.) Then havethem find 7 tenths and ask how they would write it in decimal format. What would 73hundredths look like? How would they write it?d. Have students begin to compare decimals by using the grids. Which is greater, 0.45 or0.54? 0.08 or 0.8? How do they know?e. Continue using the decimal grid, having students describe how they would find 7/50 or1/4. How do they approach the task? How do they know their answer is correct?f. Distribute the 0.0 to 1.0 number line page and have students label the tenths in decimalnotation on one of the number lines, making sure they put a 0 to the left of the decimalpoint. After doing this, have them find various hundredths and label those.g. Then have the students label one of the number lines with any fractional equivalentsthey know. Ask about 1/8 and 1/6. How would they know where to write thosenumbers?h. Give students a series of numbers (such as above) and ask them to put them in orderfrom least to greatest. Discuss the various types of erroneous thinking that are common
in children, and then ask how they think children might put this group of decimals inorder.6. Assignmentsa. Have students read this article on student misconceptions about decimals:http://tinyurl.com/Dec-Misconceptsb. Have students create a list of five decimal numbers that could highlightchildren’s confusion about decimals and write them on five slips of paper. Havethem ask a child to put the decimals in order while describing his or herrationale for the choices. This is a type of performance assessment called aclinical interview. Have the student take notes on what the child says and does.
Page 3 and 4: This product has been made possible
Page 5 and 6: Subject: General MathematicsCredit
Page 7 and 8: Semester OutlineUnit 1: Numbers and
Page 10 and 11: Suggested Resources:These resources
Page 12 and 13: Unit 1 Number and OperationsWeek 1,
Page 16 and 17: Recall the various models of additi
Page 18 and 19: prepare for the this class session.
Page 20 and 21: Faculty Preparation for Upcoming We
Page 22 and 23: h) The number line model, used earl
Page 24 and 25: they would have placed the remainin
Page 28 and 29: 2. How do children think about thes
Page 30 and 31: ) Introduce the array or set model.
Page 32 and 33: g) End the class by posing a challe
Page 34 and 35: • The same is true for the follow
Page 36 and 37: • Fact Families: Just as (5, 7, 1
Page 38 and 39: The answer to 9 ÷ 5 is 1.8 or 1 4/
Page 42 and 43: 5. AssignmentsDistribute this hando
Page 48 and 49: 10. Class Activitiesa. Have student
Page 52 and 53: these pre-service teachers will nee
Page 54 and 55: . Have students devise ratio proble
Page 56 and 57: e. Rate problems in the real world
Page 58 and 59: vii. Ask them if there is a consist
Page 60 and 61: Unitt 1 Number and OperationsWeek 5
Page 62 and 63: • It is also important that stude
Page 64 and 65: 5. Assignment:l. Have students revi
Page 66 and 67: 2. To model the equation (-4) + (+2
Page 68 and 69: d. Introduce the idea of directiona
Page 70 and 71: It is also important for students t
Page 72 and 73: considered negative if today were a
Page 74 and 75: Session 2: Algebra as generalized a
Page 76 and 77: Unit 2 AlgebraWeek 1, Session 1: Pa
Page 78 and 79: d) Introduce the idea of a pattern
Page 80 and 81: Later, when y is replaced by functi
Page 82 and 83: Unit 2 AlgebraWeek 1, Session 3: Th
Page 84 and 85: • The idea of a pattern rule• T
Page 86 and 87: Students may also need to refresh t
Page 88 and 89: d) Help students understand how to:
Page 90 and 91: Unit 2 AlgebraWeek 2, Session 2: Co
Page 92 and 93: 4. Class Activitiesa) Begin the ses
Page 94 and 95:
Unit 2 AlgebraWeek 2, Session 3: Eq
Page 96 and 97:
Ask if they saw "first differences"
Page 98 and 99:
Unit 2 AlgebraWeek 3: Linear Functi
Page 100 and 101:
Unit 2 AlgebraWeek 3, Session 1: Li
Page 102 and 103:
Unit 2 AlgebraWeek 3, Session 2: Li
Page 104 and 105:
students use crayons or coloured pe
Page 106 and 107:
Unit 2 AlgebraWeek 3, Session 3: Or
Page 108 and 109:
g) Extend the discussion about C =
Page 110 and 111:
Session 2 continues the idea of mul
Page 112 and 113:
c) Leave plenty of time to discuss
Page 114 and 115:
Unit 2 AlgebraWeek 4, Session 2: In
Page 116 and 117:
c) Have students work in pairs for
Page 118 and 119:
d) As in the cartoon below, youngst
Page 120 and 121:
Faculty Preparation for Upcoming We
Page 122 and 123:
3. Class ActivitiesHere are some sa
Page 124 and 125:
Unit 3 GeometryWeek 1, Session 2: C
Page 126 and 127:
Again, listen to the way students a
Page 128 and 129:
\• Quadrilateral Venn Diagram: ht
Page 130 and 131:
figure EFGH."d) Knowing that corres
Page 132 and 133:
g) Note that certain polygons inclu
Page 134 and 135:
"For example, suppose a triangle ha
Page 136 and 137:
Make sure students realize that a s
Page 138 and 139:
Session 2: Angle Sums in Polygons,
Page 140 and 141:
Unit 3 GeometryWeek 2, Session 1: A
Page 142:
c) Angles can be categorized by mea
Page 145 and 146:
2. How do children think about thes
Page 147 and 148:
This is where the activity, ripping
Page 149 and 150:
than 180°are called reflex angles,
Page 151 and 152:
Unit 3 Geometry,Week 2, Session 2:
Page 153 and 154:
e) There is an angle of 360° aroun
Page 155 and 156:
4) Using the angle sum formula:http
Page 157 and 158:
e) Still other tessellations can be
Page 159 and 160:
d) Children can design their own te
Page 161 and 162:
To finish this activity, distribute
Page 163 and 164:
life situations every day. Therefor
Page 165 and 166:
However, this formulaic model does
Page 167 and 168:
Unit 3 GeometryWeek 3, Session 2: G
Page 169 and 170:
4. Class ActivitiesThese will inclu
Page 171 and 172:
d) Have students chart the results
Page 173 and 174:
Once again students will derive for
Page 175 and 176:
) Have students measure around cyli
Page 177 and 178:
d) After students share their direc
Page 179 and 180:
c) Have students work with boxes an
Page 181 and 182:
Students will extend this understan
Page 183 and 184:
Unit 3 GeometryWeek 5 Session 1: Ge
Page 185 and 186:
Unit 3 GeometryWeek 5, Session 2: S
Page 187 and 188:
Unit 3 GeometryWeek 5, Session 3: I
Page 189 and 190:
Session 3: Displaying Data in the E
Page 191 and 192:
Unit 4 Information HandlingWeek 1,
Page 193 and 194:
time.) Mention that these types of
Page 195 and 196:
Unit 4 Information HandlingWeek 1 S
Page 197 and 198:
How many pets does each icon stand
Page 199 and 200:
line plot to display data accuratel
Page 201 and 202:
3. What is essential to know or do
Page 203 and 204:
Read through the plans for this wee
Page 205 and 206:
Usually, when looking at a line plo
Page 207 and 208:
e) Once youngsters know that there
Page 209 and 210:
Perhaps in students' name length da
Page 211 and 212:
Unit 4 Information HandlingWeek 2 S
Page 213 and 214:
e) A data set that includes negativ
Page 215 and 216:
In situations where the data is ske
Page 217:
End of Course ReflectionDuring this
show all

Course Guide - USAID Teacher Education Project

Create successful ePaper yourself

Delete template?

Save as template?