Solve addition and subtraction problems by going through tens.
Solve addition and subtraction problems by going back through tens.
Number Framework Stages 5 and 6.
Or magnetised tens frames with counters
Two blank Tens Frames and counters
Bundles of sticks or BeaNZ in tens and ones
Equipment: A magnetic whiteboard with two tens frames drawn on it and magnetised counters (or use two blank tens frames [Material Master 4-6] and counters); bundled sticks (ones and tens) or beans in film canisters (ones and tens) or a 30-bead string; student sheets of number lines by tens with empty number lines printed on the back (Material Master 5-12).
Using materials
Problem: Rangi has fourteen mussels and eats six of them. How many mussels does Rangi have left?
Record 14 – 6 = ? on the board or in the modelling book.
Model ten and four counters on the tens frames.
Ask the students, without them touching the tens frames, to say what remains when six are removed.
Invite a student who says that eight is the answer to come and demonstrate how they got the answer.
Typically, a student will remove four from the four frame and then two from the ten frame to leave eight.
Sometimes they will remove six from the ten frame to leave four, and then add four and four to give eight.
While this second method is correct, it is not to be encouraged in this learning experience as it does not model going back through ten.
Record 14 – 6 = 8 on the board or in the modelling book.
As students become more confident repeat the learning experience with a number line.
Examples: Word problems and recording for: 15 – 6, 21 – 5, 16 – 9, 12 – 4, 23 – 8, 11 – 4, 13 – 6 …
Using imaging
When using the tens frame, present problems relevant to your students, such as: Chris has fifteen books and returns seven to the library. How many books does Chris have now?
Build the numbers on the tens frames behind a shield.
Say: “Tell your partner what the tens frames look like behind this shield.” “Now tell your partner what I am doing as I remove counters from one of the tens frames. What will I remove first? What do the tens frames look like now? How would we record this?”
Step one: 15 – 7 = (15 – 5) – 2
Step two: 10 – 2 = 8.
Using materials
Problem: Tara has $34 and spends $5. How much money does Tara have left?
Ask: “How would we record this problem?”
Have the students discuss the suggestions.
Record 34 – 5 = ? on the board or in the modelling book.
Let the students model thirty-four with bundled sticks or beans in film canisters.
Look for the students who break a ten to get the answer.
Discuss how the students get the answer twenty-nine.
Examples: Word problems and recording for: 45 – 6, 33 – 5, 46 – 7, 32 – 7, 36 – 8, 41 – 4, 33 – 6 …
Using imaging
Problem: Work out 43 – 5.
Record 43 – 5 = ? on the board or in the modelling book.
Model forty-three on sticks or beans out of sight of the students.
Ask the students to image removing five and describe what is happening.
Look for the students who partition the five into three and two, take the three away, and then break a ten to take the final two away, leaving thirty-eight.
Fold back, if necessary, to “Using materials”.
Record 43 – 5 = 38 on the board or in the modelling book.
43 – 5 = (43 – 3) – 2
↓
2 + 3
Examples: Word problems and recording for: 35 – 7, 41 – 9, 26 – 8, 31 – 5, 32 – 8, 31 – 3, 25 – 7 …
Using Number Properties
Examples: Word stories and recording for: 75 – 8, 83 – 8, 96 – 9, 61 – 5, 65 – 7, 51 – 6, 81 – 9 …