Addition+and+Subtraction

|| QT Elements ** Indicators: **Students learn about: using mental strategies for addition and subtraction involving two-, three- and four-digit numbers, including  · ** the jump strategy ** eg 23 + 35; 23 + 30 = 53, 53 + 5 = 58  · ** the split strategy ** eg 23 + 35; 20 + 30 + 3 + 5 is 58  · ** the compensation strategy **eg 63 + 29; 63 + 30 is 93, subtract 1, to obtain 92  · ** using patterns to extend number facts **eg 5 – 2 = 3, so 500 – 200 is 300 <span style="margin: 6pt 0cm 6pt 35.7pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-indent: -17.85pt;"> · ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">bridging the decades **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">eg 34 + 17; 34 + 10 is 44, 44 + 7 = 51 <span style="margin: 6pt 0cm 6pt 35.7pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-indent: -17.85pt;"> · ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">changing the order of addends to form multiples of 10 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> eg 16 + 8 + 4; add 16 and 4 first <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">- Solve a variety of problems using problem solving strategies such as: trial and error, drawing a diagram, working backwards, looking for patterns, using a table <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">- Solves 2 & 3 digit addition with trading problems || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students are asked to calculate 34 + 17 in their heads. (Depending on student ability levels it may be necessary to use different numerals). They are then asked to record the strategy they used. This process is repeated for other problems, such as: <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">73 – 25 162 – 69 <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">63 + 29 188 – 89 <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students discuss which methods are the most efficient. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Extension: Students are given increasingly more difficult problems to solve mentally. Students explain and discuss the strategies they use eg for ‘188 – 89 = ?’ A student may say, ‘I took away 88 and that was easy because it left 100 but I had to take away one more, because 88 + 1 = 89, so the answer is 99.’ Students record the mental strategies they use. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Possible questions include: <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. Is there a better strategy? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. What is the best method to find a solution to this problem? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Strategies to model and revise with students include: jump strategy, compensation strategy, bridging the decades, using patterns to extend number facts, change the order of addends to form multiples. Refer to activity sheet 1. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students complete ‘Addition Strategies’ (activity sheet 2). || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students are shown the number sentence 157 + 22 and an empty number line. The teacher marks the number 157 on the number line. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Possible questions include: <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. What is the next multiple of ten after 157? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. How many do you add on to get that number? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students record their answers on the number line. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Possible questions include: <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. Can you work it out with fewer steps? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. Can you visualise the number line in your head and do it? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">. Can you write the numbers on paper to help you keep track? <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">As an additional activity, in pairs, students draw an empty number line. Student A chooses two three-digit numbers and places them on the number line. Student B uses the number line to work out and record the difference between the two numbers. Students explain the mental strategies they used to find the answer. They reflect on their method, considering whether it can be improved. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students complete activity ‘Addition using a number line’ (Activity sheet 3). Ensure that students also use a number line to solve subtraction problems. || =      = ||
 * ** <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">Term 1, Week: **
 * <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">1  ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">2   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">3   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">4   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">5   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">6   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">7   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">8    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">9    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">10   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">11   ||
 * <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">DK  ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">DU   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">PK   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">HOT   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">M   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SC   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">EQC   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">E    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">HE    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SS   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SSR   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SD   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">BK   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">CK   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">KI   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">I   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">C   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">N   ||
 * ** <span style="font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Outcome: **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> NS2.2 Uses mental and written strategies for addition and subtraction involving two, three and four digit numbers.
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 1 **  || = __<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt; text-decoration: none; textunderline: none;">Register <span style="font-family: 'Century Gothic','sans-serif';"> __ = ||
 * <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">**Mental Strategies**
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 2 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || = __<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt; text-decoration: none; textunderline: none;">Register  __ = ||
 * <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">**Number Lines**

<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Begin lesson with a quick game of recall of related addition and subtraction facts. Ask one of the students to model 9-6=3 with base 10 material and have another student model the sum as a number sentence. Then choose another student to model 90-60=30 with base 10 material. Record this number sentence also. Repeat with another set of numbers. For example 8-2=6, 80-20=60. Discuss with students the pattern that they can see emerging. Work with students to extend these number facts to use hundreds and thousands. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">As an additional activity, students use 2, 3 or 4 dice to generate a 2, 3 or 4 number and then represent this number using Base 10 material. Students then generate a second, smaller number by rolling one less die. Students represent this number using Base 10 material, then add the two numbers and show the result using Base 10 material. Students repeat this process, subtracting the second number from the first. Students record their solutions. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students independently work on ‘Patterns in addition and Subtraction‘(activity sheet 4). Students can also work on Addition with Trading (activity sheet 5). || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Revise with students addition with trading. If have access to an IWB teachers can use Rainforest Maths on the school server to demonstrate to students how to trade. When on Rainforest Maths Select Year 3 or 4 (depending on your year), addition+, 2 or 3 digit with regrouping. Work through algorithms with students. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">If do not have access to IWB, show students ‘Teach This’ poster demonstrating addition with trading. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students complete ‘Addition with trading’. (Activity Sheet 6). Students can also work on 3 digit addition with trading by completing the problems from the worksheet ‘Adding with 3 digits’ (activity sheet 7). || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Revise with students subtraction with trading. If have access to an IWB teachers can use Rainforest Maths on the school server to demonstrate to students how to trade. When on Rainforest Maths Select Year 3 or 4 (depending on your year), subtraction +, 2 or 3 digit. Work through algorithms with students. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">If do not have access to IWB, show students ‘Teach This’ poster demonstrating subtraction with trading. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students complete ‘Subtraction with trading. (Activity Sheet 8). Students can also work on 3 digit subtracting with trading by completing the problems from the worksheet ‘Subtracting with 3 digits’ (activity sheet 9 ). || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Discuss addition word problems with students. For example ‘There were 122 oranges on one tree and 37 on another tree. How many oranges were there altogether?’. Ask students for their ideas of how to solve the problem. Complete this problem and others as a whole class activity. Model and revise with students various strategies they can use to solve such problems. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Students then work independently on problems from Activity sheet 10, “Addition Word Problems/Subtraction Word Problems”. Repeat lesson with subtraction word problems. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">As an additional activity, students are given an activity called ** “Word Problem Mix-up” **(activity sheet 11). This activity requires students to complete the missing addition and subtraction number and word problems, then cut them into cards. Students can use cards to play ‘Concentration’ or ‘Snap’. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Another alternate activity is ** “What Went Wrong?”. ** Students are shown a number of completed subtraction problems with a consistent error eg subtracting the smaller number in a column from the larger number. Students correct the calculations and describe the error that was made. Students plan how to teach a person who made this mistake a correct method for obtaining solutions. || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> ||
 * **Lesson 3** || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Base 10 Material **
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 4 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Addition With Trading **
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 5 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Subtraction With Trading **
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 6 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Addition and Subtraction With Trading Problems **